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Quasiferromagnetism

Permanent Link: http://ufdc.ufl.edu/UFE0021295/00001

Material Information

Title: Quasiferromagnetism
Physical Description: 1 online resource (165 p.)
Language: english
Creator: Dubroca, Thierry Alexandre
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Magnetism has been a topic of interest for centuries. Throughout the 20th century its fundamental understanding has grown tremendously thanks to quantum physics. This fundamental understanding has allowed the development of new memories for computers, cell phones, flash cards, high capacity hard drives and more. The demand for faster and better electronics is very strong. This demand pushes the research such that new microelectronic devices must be developed and produced. In order to fulfill this demand, a better understanding of fundamental magnetism is necessary. In particular, as the microelectronic devices are becoming smaller and smaller, new magnetic phenomena are observed and need to be understood. In order to push further the frontieres of our knowledge, we present here, a comprehensive model for a new magnetic phenomenon which we named quasiferromagnetism.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Thierry Alexandre Dubroca.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Hummel, R. E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021295:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021295/00001

Material Information

Title: Quasiferromagnetism
Physical Description: 1 online resource (165 p.)
Language: english
Creator: Dubroca, Thierry Alexandre
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Magnetism has been a topic of interest for centuries. Throughout the 20th century its fundamental understanding has grown tremendously thanks to quantum physics. This fundamental understanding has allowed the development of new memories for computers, cell phones, flash cards, high capacity hard drives and more. The demand for faster and better electronics is very strong. This demand pushes the research such that new microelectronic devices must be developed and produced. In order to fulfill this demand, a better understanding of fundamental magnetism is necessary. In particular, as the microelectronic devices are becoming smaller and smaller, new magnetic phenomena are observed and need to be understood. In order to push further the frontieres of our knowledge, we present here, a comprehensive model for a new magnetic phenomenon which we named quasiferromagnetism.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Thierry Alexandre Dubroca.
Thesis: Thesis (Ph.D.)--University of Florida, 2007.
Local: Adviser: Hummel, R. E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021295:00001


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QUASIFERROMAGNETISM


By

THIERRY DUBROCA

















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2007
































O 2007 Thierry Dubroca





































To Jonathan Hack









ACKNOWLEDGMENTS

I must confess that I was pretty naive when I chose the topic of my dissertation. My

decision to study the magnetic properties of semiconductor materials came very quickly after

attending a seminar on spintronics, a related field. I felt passionate about semiconductor

magnetic properties right away. Professor Rolf Hummel, who has been my advisor during the

full length of my graduate studies, has fully supported my decision for the topic. It was only after

a couple years of studying this subj ect that I deeply understood the real difficulties of choosing

one' s own topic. Then, during the most difficult times, when a critical equipment of my work

caught on fire and was destroyed, he reassured me by giving me his full support a second time.

Without him, I most probably would have not completed my doctorate work. This is why my

deepest appreciation goes to Professor Hummel. He has been the best advisor a student could

ever dream of.

In addition, I am very grateful to Dr. Alexander Angerhofer for his generosity. Dr.

Angerhofer has not only given me a lot of his time to teach me how to use the EPR system, he

also amply advised me throughout my doctoral work. The main experiments of this dissertation

could not have been conducted without his supervision.

Our laboratory was not equipped with the magnetometer required to develop my work. Dr.

Arthur Hebard has been very kind in letting me use his SQUID magnetometer for many years

and I am very thankful to him for it.

I would also like to thank Dr. William Vernetson for letting us use the nuclear reactor in

order to prepare the neutron irradiated silicon samples.

I feel very lucky to have studied here in the Materials Science department at the University

of Florida, where I found very supportive and caring professors. In particular, I would like to









thank my committee members from this department, Dr. Paul Holloway, Dr. David Norton and

Dr. Wolfgang Sigmund for their continuing support.

Jonathan Hack discovered the magnetic hysteresis of spark processed silicon at UF several

years before I became a graduate student. Jonathan was very helpful and spent countless hours

discussing my experimental results and ideas. Jonathan will always hold a special place in my

heart and will never be forgotten. His sudden death came to all of us as a shock.

I am also very grateful to my colleagues and friends, Kwanghoon Kim, Anna Fuller, Julien

Gratier and Max Lemaitre who had to put up with my incisiveness during our weekly group

meetings. Their pertinent remarks have grown in me a way of thinking which, I am sure, will

help me all through my life.

I would like to express my gratitude to my long time friends, Anne Charmeau and Fabien

Gerard for their unconditional support, express my sincere appreciation to my friend Courtney

Allen for her patience and thank Orlando Rios for his support and help in preparing a magnetic

standard.

I will conclude my acknowledgement by thanking my parents, Michel and Christiane

Dubroca who deserve my deepest love for the support they have given me all along my

schooling and in particular during my doctoral work.











TABLE OF CONTENTS


page

ACKNOWLEDGMENT S .............. ...............4.....

LI ST OF T ABLE S ............ ...... .__ ...............9....

LIST OF FIGURES .............. ...............10....

AB S TRAC T ........._. ............ ..............._ 16...

CHAPTER

1 WHY STUDY QUASIFERROMAGNETISM? ............ ...............18.....

1.1 Definition of Quasiferromagnetism ................. ...............18...............
1.2 Motivation for Studying Quasiferromagnetism............... ..........2
1.3 Could Quasiferromagnetics Be Used in Spintronics? ............... ...............21....
1.4 Understanding the Fundamental Physics of Quasiferromagnetism ................. ...............21

2 WHERE DOES QUASIFERROMAGNETISM STAND WITHIN CLAS SICAL
MAGNETISM? ............. ...............23.....

2. 1 Diamagnetism ............ ...... ...............23...
2.2 Paramagnetism............... .............2
2.3 Ferromagnetism ................. ...............27.
2.4 Unclassified Magnetic Materials .............. ...............32....
2.5 Sum m ary ................. ............... 8.............

3 MANUFACTURING, MACROSCOPIC CHARACTERIZATION AND
EXPERIMENTAL RESULTS OF QUASIFERROMAGNETIC MATERIALS ..................40

3.1 Room Temperature Study of Spark-Processed Silicon ................ ...................4
3.1.1 Production of Spark-Processed Silicon for Magnetic Studies............... ...............40
3.1.2 Magnetic Characterization Process Parameter Influence ................. ................. .42
3.2 Magnetic Characterization of Spark-Processed Silicon at High Temperature .................46
3.2.1 Magnetic Characterization Method at High Temperatures .................. ...............47
3.2.2 Verification of the Modified Magnetometer ........._._... .......__. ..................55
3.2.3 High Temperature Spark-Processed Silicon Magnetization............... ..............5
3.2.4 Annealing Effect on the Magnetization............... .............6
3.3 Low Temperature Magnetization .......................... .. .. ....................6
3.3.1 Magnetic Reference Material HgCo(SNC)4 for the 2-100K Temperature
R ange ................... ... ... .. ..... ........ ........6
3.3.2 Aluminum Reference for the 50-300 K Temperature Range .............. .................65
3.3.3 Oxygen Effect at Low Temperature .........._...... .. ...__._ ...............66.
3.3.4 Spark-Processed Silicon Low Temperature Magnetization ................. ...............67
3.4 Summary ................. ...............71......... .....











4 INTERPRETATION OF QUASIFERROMAGNETISM INT SPARK PROCESSED
SILICON................ ...............72


4. 1 Model Concerning the Distribution of Paramagnetic Centers ................. ............... ....72
4.2 Electron Paramagnetic Resonance (EPR) Concepts ................. ........... .... ............... 74
4.3 Characterization of Continuous Wave Electron Paramagnetic Resonance Spectra.........75
4.4 Electron Paramagnetic Resonance Parameter versus Temperature ................. ...............87
4.4.1 Low Temperature 5 to 300K .............. ...............88....
4.4.2. High Temperature 300 to 800K................ .... ...............9
4.5 Characterization of Pulsed Electron Paramagnetic Resonance ..........._. .........._._......99
4.6 Relaxation Rates ................ ....... ...............9
4.6.1 Spin-Lattice Relaxation Rate............... ...............99..
4.6.2 Spin-Spin Relaxation Rate .................. ........ ..............10
4.7 Separation of Rates to Identify Paramagnetic Centers .......................... ...............104
4.8 Spin Density ................. ...............106........... ...
4.9 Summary ................. ...............111......... ......

5 FURTHER CONSIDERATIONS ................. ...............112...............


5.1 Annealing of Spark Processed Silicon ................. ...............112.............
5.2 lon Implanted Silicon ................. .. .............. ..... ........... .......11
5.2. 1 Magnetic Response of lon Implanted Silicon ................. .........................115
5.2.2 Electron Paramagnetic Resonance of lon Implanted Silicon ............. ..............117
5.3 Neutron Irradiated Silicon ............ ........... ...............119..
5.4 Highly Oriented Pyrolitic Graphite .............. ...... ..... ..... .... ..........12
5.4.1 Magnetization Response of Highly Oriented Pyrolitic Graphite .........................121
5.4.2 Electron Paramagnetic Response of Highly Oriented Pyrolitic Graphite ............121
5.5 Summary ................. ...............123......... .....

6 CONCLU SION............... ...............12


6.1 Macroscopic Magnetic Behavior of Spark-Processed Silicon............... .................2
6.2 Electron Paramagnetic Resonance of Spark-Processed Silicon .................. ...............124
6.3 Quasiferromagnetic Model for Spark-Processed Silicon .............. .....................2
6.4 Other Quasiferromagnetic Materials .............. ...............126....
6.5 Future Work............... ...............126.


APPENDIX

A SPARK PROCESS POWER SUPPLY ................ ...._.._ ...............129 ....


A. 1 Power Supply Principles of Operation. ........._.. ......... ............ ...........2
A.2 Power Supply Inner Components ........._._. ...._... ...............131..


B HgCo(SCN)4 MAGNETIC REFERENCE .........._._ .. .... .__ ....___ ............3

B. 1 SQUID Magnetometer Verification ........._..._.. ....._.. ...............134....
B.2 M odel W fighting .............. ...............138....











B.3 Temperature Independent Susceptibility .............. ...............145....
B.4 Zero Field Splitting and Exchange Interaction .............. ...............148....
B.5 Conclusions .........__.. ..... ._ __ ...............150...

C ALUMINUM MAGNETIC REFERENCE FOR TEMPERATURE RANGE 50 300 K .151

D OXYGEN CONTAMINATION AT LOW TEMPERATURES ................. ............... ....154

E ELECTRON PARAMAGNETIC RESONANCE SYSTEM OVEN APPARATUS ..........158

LIST OF REFERENCES ................. ...............161._.__ ......

BIOGRAPHICAL SKETCH ........._.._ ..... ._._ ...............165....










LIST OF TABLES


Table page

4-1 Characteristic values of echo detected field sweep and amplitude of exponential
decay as a function of magnetic field. ................ ............... ........ ......... ...106

B-1 Constants from susceptibility model............... ...............137.

B-2 Magnetic susceptibility [10-6 g-1] as function of temperature of HgCo(SNC)4 Of OUT
data set and O'Connor's data set. ................ ...............139.......... ..

B-3 Data example. ............. ...............140....

B-4 Fitting parameters. ............. ...............140....

B-5 Comparison of the direct and classic method of O'Connor data set. For the classic
method the diamagnetic constant is set and equal to the value found through the
direct m ethod. ............. ...............144....

B-6 Comparison of the direct and classic method with O'Connor data set. For the classic
method the diamagnetic constant is set and equal to the value proposed by
O 'Connor. ............. ...............145....

B-7 Diamagnetic correction per mol ................. ...............146........_ ...

C-1 Comparison of model constants for aluminum. ....___.................. ............... .....15












LIST OF FIGURES


Figure page

2-1 Magnetization of silicon as a function of magnetic Hield (own measurements). ..............24

2-2 Magnetization as a function of magnetic Hield for a paramagnetic material. ................... ..25

2-3 Magnetic susceptibility versus temperature for a paramagnetic material..........................26

2-4 Electronic configuration of Aluminum. ................. ......_._......._ ............... ..26

2-5 Magnetization as function of magnetic field for ferromagnetic materials. ................... .....28

2-6 Magnetization as a function of temperature at 1000 Oe for a nickel thin film on a
silicon substrate............... ...............2

2-7 Magnetization process.. ............ ...............30.....

2-8 Magnetic phases as a function of particle diameter. ................ ................ ............3 1

3-1 Spark-processing of silicon ................. ...............40......._.._....

3-2 Scanning electron micrograph of spark-processed silicon. A) large top view. B)
zoom -in view. ............. ...............41.....

3-3 Magnetization as a function of magnetic Hield strength measured at room temperature
for spark-processed silicon (sparking time = 6 hours, frequency = 22.5 k
3-4 Secondary ion mass spectrum of spark-processed silicon. The largest peaks have
been labeled accordingly. See also 3-5. ............. ...............44.....

3-5 Secondary ion mass spectrum of spark-processed silicon zoomed in around the iron
atomic number. An arrow marks the position of where the iron isotope with an
atomic mass of 54 should be if it was present in the sample. ................ ............. .......45

3-6 Spark-processed silicon magnetization at 0 Oe (i.e. remanence) and 1000 Oe as a
function of the spark frequency (sparking time was set at 12 hours for all samples)........46

3-7 Spark-processed silicon magnetization at 0 Oe (i.e. remanence,) 1000 Oe and
hysteresis area as a function of the sparking time (spark frequency was set at 16 k for all samples)............... ...............47

3-8 Super quantum interference device magnetometer with oven insert and sample
holder. ............. ...............49.....

3-9 Simulated detector voltage (a.u.) as a function of the position ................. ................ ...5 1










3-10 Simulated detector voltage (a.u.) as a function of the position (blue diamonds)
zoomed in around the sample located 7 cm away from the end of the holder. The
computer model is plotted in solid orange. .............. ...............52....

3-11 Simulated detector voltage (a.u.) as a function of the position ................. ................ ...53

3-12 Simulated detector voltage (a.u.) as a function of the position (blue diamonds)
zoomed in around the sample located 3.5 cm away from the end of the holder. The
computer model is plotted in solid orange. .............. ...............54....

3-13 Magnetization of pure nickel as function of temperature at 1000 Oe. A Curie
temperature of 625 K is found as indicated by the arrow. ................ ..................5

3-14 Magnetization versus magnetic Hield for a silicon sample weighting 10.3 mg,
measured at 300K. ............. ...............56.....

3-15 Magnetization versus temperature (grey dots) for a 10.3 mg silicon wafer measured
at 10,000 Oe. The plotted magnetization is divided by 10, equivalent to
magnetization at 1000 Oe. The average (solid line) is -2.8x10-6 emu. ........._..... .............57

3-16 Magnetization as a function of temperature upon heating (blue diamonds) at 1000 Oe
for spark-processed silicon (sparking time = 6 hours, frequency = 22.5 k Hield cooled magnetization (red square) ........._..._.. ....._.._ ....... ...........5

3-17 Magnetization as a function of the magnetic field strength before (blue curve) and
after Hield cooling (red curve) measured at room temperature for spark-processed
silicon (sparking time = 6 hours and frequency = 22.5 k
3-18 Normalized magnetization as a function of temperature for spark-processed silicon
measured at 1000 Oe represented by red diamonds ................. ................ ......... .60

3-19 Normalized magnetization as a function of temperature for spark-processed silicon
measured at 500 Oe represented by red diamonds............... ...............61

3-20 Remanent magnetization of spark-processed silicon (sparking time = 6 hours,
frequency = 22.5 k dots) and cooling (red dots). ............. ...............62.....

3-21 Magnetization as function of magnetic field for a spark-processed silicon sample
(sparking time = 6 hours and frequency = 22.5 k heating cycle (heating up to 800 K and cooling down to 300 K in a 1000 Oe Hield). .......63

3 -22 Magnetization at 1000 Oe (blue diamonds) and 0 Oe (red squares) versus annealing
time for spark-processed silicon (sparking time = 6 hours and frequency = 22.5 k
3-23 Magnetization versus field at 70 K and 35 K of spark-processed silicon (square and
round points, respectively)............... .............6










3 -24 Magnetization versus temperature for spark-processed silicon at 1000 Oe (red
triangle) and 0 Oe bleuu square s) ................. ...............69..............

3-25 Magnetization adjusted for diamagnetism and remanence as a function of inverse
temperature .. ......... ..... ._ ...............70....

4-1 Proposed paramagnetic centers distribution. ............. ...............73.....

4-2 Energy levels of an electron at the resonance field............... ...............73.

4-3 Lorentzian distribution and 1st derivative of electron microwave absorbance as a
function of the magnetic field. A) one type of paramagnetic center. B) two different
types of paramagnetic centers (red curves) and their deconvolution (blue and green
curves) ................. ...............75.................

4-4 Electron paramagnetic resonance spectrum of spark-processed silicon (back line) at
room temperature with its double Lorentzian 1st derivative model (red) .. ................. .......77

4-5 Electron paramagnetic spectra of spark-processed silicon along with DPPH reference
standard (black line) ................. ...............78........... ....

4-6 Nature of spark-processed silicon paramagnetic centers. ................. .................7

4-7 Amplitude of D paramagnetic centers as a function of microwave power. ................... ....80

4-8 Amplitude of D paramagnetic centers as a function of the square root of the
microwave power (dots). A linear trend is fitted for the lowest power data points
(R2=0.995) ................. ...............8.. 1......... ...

4-9 Amplitude of E' paramagnetic centers as a function of microwave power. ......................82

4-10 Amplitude of E' paramagnetic center as function of the square root of the microwave
power (dots). A linear trend is fitted for the lowest power data points (R2=0.995) ...........83

4-11 Saturation effect observed for the two paramagnetic centers in spark-processed
silicon. .............. ...............84....

4-12 Line width as a function of Log (power) for spark-processed silicon. ............. ..... ........._.85

4-13 Amplitude of D paramagnetic centers as a function of microwave power (dots). Two
saturation models are fitted to the data (solid lines). ............. ...... ............... 8

4-14 Amplitude of E' paramagnetic centers as a function of microwave power for sp-Si
(dots). Two saturation models have been fitted to the data (solid lines). ..........................86

4-15 Electron paramagnetic resonance spectra of spark-processed silicon at 4.2K (black
line) and two possible models:. ...86.............










4-16 Amplitude of D centers versus temperature. The data points above 40K have been
divided by 10 to account for the change in gain setting. The gain is changed to keep
the signal in the linear regime. .............. ...............87....

4-17 Amplitude of D centers versus inverse temperature (dots). The data points below
0.025K-1 have been divided by 10 to account for the increased gain. A linear trend is
fitted to the data (solid line). .............. ...............88....

4-18 Amplitude of E' centers versus temperature. The data points above 40K have been
divided by 10 to account for the increased gain. ............. ...............89.....

4-19 Amplitude of E' centers versus inverse temperature (dots). The data points below
0.025 K-1 have been divided by 10 to account for the increased gain. A linear trend is
fitted to the data (solid line). .............. ...............90....

4-20 Line width of the two paramagnetic centers present in spark-processed silicon versus
temperature in the low temperature range. Line width 1 corresponds to the D centers
and line width 2 corresponds to the E' centers. ............. ...............91.....

4-21 Spark-processed silicon paramagnetic centers g-factor (uncalibrated) versus
temperature. The g-factor 1 corresponds to the D centers while the g-factor 2
corresponds to the E' centers. ............. ...............92.....

4-22 Spark-processed silicon paramagnetic centers g-factor versus temperature......................93

4-23 EPR line width of the two paramagnetic centers present in spark-processed silicon
versus temperature in the high temperature range. ............. ...............95.....

4-24 Amplitude of D (blue) and E' (red) centers versus temperature for spark-processed
silicon in the high temperature range ................. ...............96...............

4-25 Amplitude of D centers (blue dots) and Magnetization at 1000 Oe (green dots) versus
temperature for spark-processed silicon in the high temperature range. ...........................97

4-26 Intensity versus time for a spin-lattice relaxation rate experiment of spark-processed
silicon (black line), one-exponential decay model (green line) and bi-exponential
decays (red line). ................. ...............100._._.. .....

4-27 Spin-lattice relaxation rates versus temperature for spark-processed silicon. .................101

4-28 Intensity versus time for a spin-spin relaxation rate experiment on spark-processed
silicon (black line), one-exponential decay model (green line) and bi-exponential
decays (red line) ................. ...............102._._.. ......

4-29 Spin-spin relaxation rates versus temperature for spark-processed silicon. ....................103

4-30 Field sweep pulsed electron paramagnetic resonance of spark-processed silicon
(black curve). ............. ...............104....










4-31 Amplitude of exponential decays in spin-spin relaxation rate experiments versus
field for spark-processed silicon (dots) ................. ...............105........... ...

4-32 Phase memory time for each paramagnetic center measured as a function of the input
power of spark-processed silicon ................. ...............107...............

4-33 Inverse phase memory time (1/Tm') versus sin2(7t/2 x(power/powero)1/2) Of spark-
processed silicon (dots)............... ...............108

4-34 Density of paramagnetic centers as a function of the spark frequency for spark-
processed silicon. ................ ...............110......... ......

5-1 Magnetization at 0 and 1000 Oe of spark processed silicon as a function of
cumulative isochronal (30 min) annealing temperature. ........... ..... .___ ..............113

5-2 Electron paramagnetic resonance peak to peak spectra line of spark processed silicon
as a function of cumulative isochronal (30 min) annealing temperature................_.__.....1 14

5-3 Magnetization as a function of the magnetic field strength at 300 K for silicon
implanted with argon ions. ................. ...............116._._ .....

5-4 Magnetization as a function of magnetic field strength at 300 K for silicon implanted
with silicon ions. ........._.__...... .__ ...............116...

5-5 Electron paramagnetic resonance spectra of argon implanted into silicon at a dose of
2x1016 CA-12 (blue squares) and its Lorentzian model (solid red). ........._._... ................11 7

5-6 Electron paramagnetic resonance spectra of silicon implanted into silicon at a dose of
10' 16 CA2 (blue squares) and its two-Lorentzian model (solid red). ............. ..... ........._..118

5-7 Magnetization versus magnetic field strength of neutron irradiated silicon at a dose
of4x 1016 Cm -2.. .......... ...............120......

5-8 Magnetization as a function of magnetic field strength of HOPG graphite. ........._._......121

5-9 Electron paramagnetic resonance spectra of HOPG graphite (blue squares) and its
Dysonian line model (solid red). ............_. ...._.. ...._... ...........2

A-1 Power supply schematic. ............_. ...._... ...............130...

A-2 Typical waveform observed at the read out (E) on the screen of an oscilloscope. ..........131

A-3 Power supply without its top cover. ............_. .......... ...............132..

A-4 Front side of the spark machine. The labels A G designate the same control as in
the schematic (A-1)............... ...............133.

B-1 Magnetization versus field at room temperature for HgCo(SNC)4 (Square). A linear
curve has been fitted to the data points (solid line). ............. ..... ............... 13










B-2 Magnetization versus temperature at 10000e for HgCo(SNC)4............... ................1 36

B-3 Magnetization adjusted for diamagnetism as a function of the inverse temperature
(squares) ................. ...............137................

B-4 Example of the Curie law model. A) M-T plot and its model. B) M-1/T plot and its
m odel ................. ...............141_____.......

B-5 Magnetic susceptibility of HgCo(SNC)4 and its model using the direct method. ...........142

B-6 Inverse magnetic susceptibility of HgCo(SNC)4 adjusted for diamagnetism versus
temperature and its model using the classic method. ......_.__ ... .....__ ..............143

B-7 Three dimensional representation of HgCo(SNC)4. X,Y,Z are the fractional
coordinates. ............. ...............147....

B-8 Magnetic susceptibility of HgCo(SNC)4 aS function of magnetic field at 2 K (square)
and its model (solid line)............... ...............149.

C-1 Magnetization versus field at room temperature of 99.999% pure aluminum
(squares)............... ...............15

C-2 Magnetization versus temperature at 1000 Oe for 99.999% pure aluminum. .................1 52

C-3 Magnetization as function of temperature square at 10000e for 99.999% pure
aluminum (diamonds). A linear trend is fitted to the data (solid line). ........._.................153

D-1 Magnetization versus temperature for a piece of plastic straw at 5000e. ........._............154

D-2 Magnetization at 1000 Oe of a piece of straw as a function of temperature for several
different pur ges.. ............ ...............155.....

D-3 Oxygen magnetization peak height versus number of purges (diamonds). .................. ...156

E-1 Picture and schematic cross section of the oven apparatus for the electron
paramagnetic resonance system. .............. ...............159....









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

QUASIFERROMAGNETISM

By

Thierry Dubroca

December 2007

Chair: Rolf E. Hummel
Major: Materials Science and Engineering

During the 20th century, the understanding of magnetic phenomena had a big breakthrough

thanks to quantum physics. However, there are still many unanswered questions. The research

work presented here attempts to answer the following question: where does the magnetic

hysteresis come from in semiconductors not containing magnetic elements, such as iron, nickel,

cobalt or rare earth elements?

We have found that materials composed of light elements, such as silicon, oxygen, or

nitrogen possess a magnetic hysteresis in contradiction to classical theory. In order to avoid

confusion between ferromagnets and those materials, a new name was coined to describe them:

quasiferromagnets. In our investigation we used two techniques, namely electron paramagnetic

resonance, and magnetometric measurements. We found a Curie temperature of 765 K for spark-

processed silicon. Further, we identified two paramagnetic centers called D and E' in spark-

processed silicon. We measured a density of 1.4x1019 Cm-3 for the D centers and 0.5x1019 Cm-3

for the E' centers leading to an average inter-spin distance of 3.7 nm. In addition, we present the

magnetic properties including magnetic hysteresis of spark-processed silicon, argon implanted

silicon as well as neutron irradiated silicon and highly oriented pyrolitic graphite.










We propose a model to explain quasiferromagnetism based on the inhomogeneous

distribution of paramagnetic defects. Our distribution model is based on the inhomogeneous

structure of the materials. Spark-processed silicon is known to have silicon nanoclusters

embedded into a silicon dioxide matrix. The clustering of paramagnetic centers allows positive

exchange interactions between them. We suggest that this clustering explains the observed

macroscopic magnetic behavior in particular the magnetic hysteresis at room temperature.









CHAPTER 1
WHY STUDY QUASIFERROMAGNETISM?

Magnetism has been a topic of interest since the discovery of ferromagnetism by the

ancient Greeks from the city of Magnesia several thousands of years ago. Much later, the

compass was invented using the properties of a magnetized iron needle which orients itself

toward the north direction. The first theories of magnetism were developed in the 19th century, a

magnetic field created by a current in a wire by Oersted and Ampere. Since, Weiss, Curie and

Langevin, to name a few, developed theories to explain other magnetic phenomena such as

antiferromagnetism, diamagnetism or paramagnetism. This was the beginning of what we know

today as the "theory of magnetism." Our study expands this theory with a new branch, which

should be tentatively called quasiferromagnetism.

1.1 Definition of Quasiferromagnetism

A "crystal" defines a material that can be sorted according to its crystallographic signature.

Bravais, in 1845, mathematically defined the maximum number of possible crystallographic

arrangements (lattices) to be 14. Therefore, for half a century, crystals were mathematically

defined and there was no room for other type of periodic arrangements of atoms which did not

correspond to the Bravais networks. Later, between 1970 and 1980, a researcher (D. Shechtman)

measured what seemed to be periodic lattices that were outside the Bravais networks. Because

the word crystal was so closely attached to the concept of the Bravais networks, newly

discovered pseudo-periodic lattices could not be named crystals, even though from a logical

point of view, they were like crystals. The very close similarities with the classical Bravais

networks, these periodic lattices were then named quasi-crystals! A few years later, the scientists

(among them D. Shechtman) who discovered the quasi-crystals received numerous awards for

their intensive work in this field.









A few years ago, I was telling this story to a dear friend, the late Jonathan Hack, after

brainstorming magnetic properties of semiconductors. He told me about his first time presenting

a magnetic hysteresis loop obtained on spark-processed silicon at a conference: the participants

did not agree to let him call what he was presenting ferromagnetismm." At that time, in the mid-

nineties, almost no one believed that one could observe ferromagnetic behavior in materials not

containing d or f shell electrons. Right after this conversation, there was no doubt that what we

were studying should not continue to be called ferromagnetism, in order to avoid further

semantic opposition and confusion. Thus, we decided to name our research topic

"quasiferromagneti sm" which occurred naturally to us after discussing the origin of the word

"quasi-crystals."

Moreover, it should be noted, that a group of scientists working on ferromagnetic

semiconductors (Si containing ferromagnetic trace elements) ran into a similar problem. They

could not use the word ferromagnetismm" by itself to describe their work because it was not

within the exact framework of classical ferromagnetism. Therefore to avoid their new results

being rej ected from the strict ferromagnetism label they came up with the word "dilute magnetic

semiconductors" (DMS). We discuss (Chapter 2) the differences between DMS and

quasiferromagnetics.

Quasiferromagnetics define materials displaying a behavior similar to classical

ferromagnetic materials, but without containing d or f shell electrons. The difference in the type

of electrons involved leads to large differences in observed magnetic behavior. For example,

quasiferromagnetics exhibit a magnetic hysteresis at room temperature, despite the fact that they

essentially do not contain domain walls in the commonly used sense.









This work is the continuation of what Jonathan Hack started 10 years ago when he

discovered the magnetic hysteresis of spark-processed silicon. This was discovered in our lab,

and back then, Dr. Hummel, suggested studying the magnetic properties of this material. He was

expecting to find that the magnetic susceptibility would go to minus one, characteristic of

superconductors. It turned out that sp-Si was not a superconductor but rather exhibited a new

effect which we call today: quasiferromagnetism. My doctoral work focuses mostly on

explaining the origin of this effect.

1.2 Motivation for Studying Quasiferromagnetism

At first, we thought we would be able to use these materials, so that we could assemble

them into a spintronic transistor. Spintronics are devices that use the spin of electrons rather than

their charge to store and transfer information. These devices are thought to be much faster than

the classical electronic devices and therefore would further the improvement of the computer

industry. However, as we advanced our studies for explaining quasiferromagnetism, we

understood that implementing quasiferromagnetic materials into Spintronics devices would very

likely be a difficult task, at least before we fully understand how they behave. Therefore, we

decided to limit the scope of this work to make experiments which would allow us to explain

where quasiferromagnetism originates from.

Consequently, our motivation shifted. Our passion pushed us toward understanding the

fundamental physics behind this newly discovered magnetic property. In addition, by broadening

of our research scope, we hope to promote the understanding of physics by changing the way we

saw magnetism as a whole. This is our goal and challenge.

In short, quasiferromagnets arise from unpaired bonds produced during processing of

materials. For example, silicon or (carbon,) which are ion implanted, neutron irradiated, plasma










sprayed or spark processed yield a high density of unpaired bonds leading to

quasiferromagneti sm.

1.3 Could Quasiferromagnetics Be Used in Spintronics?

Spintronics as a new branch of physics and engineering has a handful of applications. The

most commonly known application is the read head of hard drives in personal computers. But

spintronics is mostly a research discipline in which engineers and physicists try to understand

how they can control and transport the spin of electrons in semiconductors.

Early on, we thought that the materials we studied were part of the "spintronic world," in

particular the diluted magnetic semiconductors, but as we will show throughout this dissertation,

this is not the case. They share a common semiconductor host, as well as similar magnetic

hysteresis. Spintronics use classical ferromagnetic elements, such as Fe, Ni, Co, Gd, etc., all

containing d and/or f shell electrons which are at the origin of the observed magnetic behavior.

On the other hand, quasiferromagnetics are only composed of p and s shell electrons; therefore,

they have a very different origin for explaining their magnetic behavior. It is to be noted, as we

will see in detail through Chapter 2, that quasiferromagnetism is not a subpart of

ferromagnetism, paramagnetism, diamagnetism or other classical subfields of magnetism.

As a consequence, the significant differences between spintronics and

quasiferromagnetism lead us to the introduction of a new category of magnetic materials: the

quasiferromagnets. A new Hield of study in physics of magnetism is born.

1.4 Understanding the Fundamental Physics of Quasiferromagnetism

As a Hield of physics, quasiferromagnetism aims at describing the fundamental behavior of

electrons to explain macroscopic physical observation. Our goal is to develop a comprehensive

model of electron spin behavior which explains the magnetic behavior of quasiferromagnetics.









For example, we could try to describe the macroscopic hysteresis loop observed at room

temperature by using our understanding on how electron spins interact at the atomic scale.









CHAPTER 2
WHERE DOES QUASIFERROMAGNETISM STAND WITHIN CLASSICAL MAGNETISM?

Magnetism can be classified either through its response to a magnetic Hield or through its

electronic interactions. In the first case, we can distinguish several classes: diamagnetism,

paramagnetism, ferromagnetism, anti-ferromagnetism, ferrimagnetism. On the other hand, the

classification using electron behavior also separates the different classes of magnetic materials

according to their exchange interactions which can be direct or indirect, such as double

exchange, super exchange, anisotropic exchange or itinerant exchange. In this chapter we

develop most of the concepts which lead to the classification of quasiferromagnetism within

classical magnetism.

2.1 Diamagnetism

Diamagnetic materials have a negative response to an applied external magnetic Hield. The

magnetic moment (M) induced from an external applied magnetic Hield is opposed to the applied

Hield. Furthermore, the magnetic moment of diamagnetic materials is linearly proportional to the

applied magnetic field, where the coefficient of linearity, called the susceptibility, is negative.

For example, silicon (Si) shows a diamagnetic behavior (Figure 2-1). Its susceptibility (X) is

-0.32x 10-6 (unitless in the cgs system). In addition, the susceptibility as a function of temperature

is another way to characterize the magnetic behavior and classify materials accordingly. In the

case of diamagnetism, the susceptibility does not change as a function of temperature.

Diamagnetism is commonly explained by postulating the motion of electrons orbiting

around the nucleus within an atom. According to Ampere, the motion of an electron around its

nucleus creates a current within a loop (the orbit). This current, in a loop, creates an orbital

magnetic moment. In addition, each electron possesses a spin. The spin is a concept originating

from the relativistic quantum theory. Hence, each electron has a magnetic moment stemming














































I E-0I


from its spin and its orbital motion. Each atom (except hydrogen) is composed of several


electrons. To compute the magnetic moment per atom, one sums the contribution of each


electron spin. When the net sum of the spin magnetic moment is zero and only orbital magnetic


moment is left we have a diamagnetic materiall,2


4 E-06

II ~M =-3.18*10-9* H
3 E-06 -~R2 = 0.99
Sample mass: 10 mg

2 E-06




E 1 EII
o


CI
E
a

(II
I


-4 E-06
-1000 -800 -600 -400 -200 0 200 400 600 800 1000
Field (Oe)



Figure 2-1. Magnetization of silicon as a function of magnetic field (own measurements).

2.2 Paramagnetism

In the case of paramagnetism, the magnetization is proportional to the applied external


magnetic field, but the response is positive as shown in Figure 2-2 For example, Aluminum is a


paramagnet and its susceptibility is +1.65x10-6 (unitless in the cgs system) at room temperature.


In addition, the susceptibility is a function of temperature and can be used to classify materials


into the paramagnetic behavior: the phenomenon can be seen in Figure 2-3. The susceptibility (X)



*emu: electro-magnetic unit, measure of the magnetization in the centimeter-gram-second (CGS)
system.
24









follows the Curie law; it is inversely proportional to the temperature: X = C / T, where C is a

constant depending on each materials and T is the temperature in Kelvin.

Magnet zation








Magnetic Field Strength









Figure 2-2. Magnetization as a function of magnetic field for a paramagnetic material.

Langevin explains the origin of paramagnetism. We present the essence of his theory,

without going into the details of the quantum mechanical equations. We will continue with the

example of Aluminum (Al). Figure 2-4 displays the electronic structure of Al. The electrons

which compose the Al atom have different energy levels and spins. The possible energy levels

are: 1s, 2s, 2p, 3s and 3p whereby the possible spins are up or down. Electron energies and spins

can only take specific values, as displayed in Figure 2-4. For example, there are two electrons in

the 2s energy levels with opposite spins. Their magnetic moments cancel one another. This is

true for all paired electrons. Al has one unpaired electron in the 3p energy level, which

contributes to a positive atomic moment. It is oriented in the direction of the external magnetic

field and therefore explains the positive susceptibility.

It is to be noted that the magnetic moments of unpaired electrons do not interact with one

another in the case of Al.








Susceptibility (unitless)


Temperature (K)

Figure 2-3. Magnetic susceptibility versus temperature for a paramagnetic material.

Al: 1s2 2s2 2pG 3s2 1p





a s
Energy 3
Levels


2

Mss


Illmrr~r~iml


1


Figure 2-4. Electronic configuration of Aluminum.










Why is the susceptibility temperature dependant? For example, at room temperature and at

zero field, Al atomic moments are randomly distributed due to thermal energy and therefore the

net magnetic moment is zero. When one applies an external magnetic field, the Al atomic

moments tend to orient in the direction of the field. Thermal fluctuations are strong and tend to

randomize the atomic moments. As the temperature is lowered, the thermal fluctuation decreases

leading to a larger magnetic moment, which increases the susceptibility. Similarly, when the

temperature is increased the thermal fluctuation increases and the susceptibility decreases. For a

full description through equations of the relationship between the paramagnetic susceptibility

and the temperature see Cullityl or Hummel2

2.3 Ferromagnetism

In the previous section we introduced the Curie-Weiss law. This law stems from the Weiss

molecular field theory. In order to explain ferromagnetism, we will start with this theory which

explains the macroscopic magnetic behavior. Then, we will discuss how this theory is deepened

by quantum mechanics and gives an explanation for the magnetic behavior at the electronic

level .

Weiss introduced a new field in his theory. This field (Hm) is a local field "seen" by

electrons which is added to the external applied field (He). This local field is postulated to be

proportional to the magnetization of the material (Hm = yxM), where y is a proportionality factor.

Hence, the material under magnetic characterization is excited by the total field (Ht) equal to Hm

plus He. When there is no external magnetic field (He = 0) the material still experiences the

internal field which aligns the electron spins. This alignment of spins without external field

creates a remanent magnetization; therefore, when an external field is applied the magnetization

changes. A typical magnetization response is shown in Figure 2-5.










Magnetization


Magnetic Field Strength


Figure 2-5. Magnetization as function of magnetic field for ferromagnetic materials. The
saturation magnetization (Ms) as well as the remanent magnetization (Mr) are shown.

Using the molecular field theory, we can better explain the Curie-Weiss law starting with

the Curie law (X = C / T) and the definition of the susceptibility (X = M / H), C / T = M / H.

When replacing H by Ht (Hm + He) we obtain: C / T = M / (Hm + He). Since Hm = yxM, the

previous equation becomes: C / T = M / (He + yxM). This expression can be derived and

expressed as such: M / He = C / (T y xC). Using the definition of the susceptibility, we finally

get the Curie-Weiss law: X = C / (T 6), where 6 = yxC. In the case of ferromagnets, the

temperature term 6 is positive and is essentially identical with the Curie temperature, T,. Below

this temperature the material is ferromagnetic while above the Curie temperature it is

paramagnetic. For example, Figure 2-6 displays the magnetization measured as a function of

temperature for a thin film of nickel on a silicon wafer. The measured Curie temperature is 625K

for nickel, which is within 1% lower than previously published data2. Below 625K, Ni is


























I

Tc=65

I
I
I
I
I


ferromagnetic, that is, the electron spins are interacting together such that they align in the same

direction within a domain. While above 625K, Ni is paramagnetic, the temperature is such that

the thermal agitation randomizes the electron spin orientations more than the exchange

interaction aligns them.


Paramagnetic Phase


Ferromagnetic Phase


1.E-03


8.E-04


6.E-04



e 4.E-04


2.E-04


0.E+00


-2.E-04


300 350 400 450 500 550 600 650

T (K)


700 750


Figure 2-6. Magnetization as a function of temperature at 1000 Oe for a nickel thin film on a
silicon substrate. The measured Curie temperature is 625K. Below the Curie
temperature nickel is ferromagnetic and above it, nickel is paramagnetic (own
measurements) .

It should be noted in passing that the silicon wafer's magnetization is 2 orders of


magnitude smaller than the Ni fi1m and therefore is not taken into account into our analysis.

The magnetization can be zero at zero external field in the following cases: if the material

has never been exposed to a magnetic Hield (then it is called a virgin material) or if the material is


de-gaussed (use of an alternating Hield to randomize the spins) or by heating the sample above its

Curie temperature for example.


































I


In order to explain how the magnetization can be zero in a ferromagnet Weiss introduced

the concept of domains. Each domain contains only electrons having magnetic moments oriented

in the same direction. Figure 2-7 schematically represents the different magnetic orientations

which can be taken while exposed to an external magnetic field.


H =100Oe











M>0


H=0Oe











M=0


H = 100 Oe


H = 1000 Oe


M = Ms cos 6


M = Ms


Figure 2-7. Magnetization process. A) the magnetic field is zero and the magnetizations from
each domain cancel each other. B) under a small magnetic field the domain wall
moves and increases the magnetic moment of a domain while decreasing the other
one, the net magnetization is not zero. C) at a higher field there is only one domain
left and the total magnetization depends on the angle between the magnetic field and
the domain magnetic moment. D) at the saturation field the magnetization is
maximum.

In the example of Figure 2-7, at zero field the two domains have opposite magnetic

moment leading to a total magnetic moment of zero. Once we apply an external field, the

magnetic domain which is oriented the closest to the direction of the field increases in size. Once










the magnetic field is high enough there is only one domain left. Then as we continue to increase

the external magnetic field the domain magnetic moment orients itself toward the field until it is

completely aligned. At this point the total magnetization is equal to the saturation magnetization.

The notion of magnetic domains is essential in order to understand a limiting phenomenon

in ferromagnetic materials. This phenomenon is called superparamagnetism. It appears when the

theoretical domain size is larger than the particle of a given material. To explain this important

phenomenon, we will use the simple case where a material is formed of spherical, identical and

independent particles (no magnetic coupling). At a critical size, the thermal agitation randomly

orients the magnetic moment of the entire particle. Within the particle, the electron magnetic

moments stay coupled such that they all align in the same direction. Figure 2-8 shows the

different magnetic states as a function of the size.



n Single-domain Multi-domain



Superparamagnetism I ferromagnetism


ed I I
vl I
O
.1 I
I
U I





Critical diameter' Particle diameter


Figure 2-8. Magnetic phases as a function of particle diameter.

For example, the critical particle diameter for Cobalt is 2 nml (measured at 76K) which

equates to 380 atoms of cobalt. Above 2 nm cobalt particles behaves as ferromagnets while for










particles smaller than 2 nm it behaves like a paramagnet. From this definition, we now

understand why superparamagnetism is different from quasiferromagnetism.

In conclusion, ferromagnetism is originating from the positive exchange interaction from

the electron' s spins. It requires a minimum amount of unpaired spins grouped together in order to

prevent going into the superparamagnetic state.

What we have described so far is classical magnetism. Now, we are going to present recent

results on magnetic phenomena which have not been forecasted by the classical theory of

magnetism and in particular the theory of ferromagnetism.

2.4 Unclassified Magnetic Materials

Our group has been active in magnetic material research since the mid-nineties. In 1995

Hack3 discovered that spark-processed silicon had a magnetic hysteresis loop at room

temperature and demonstrated that the magnetic behavior was not due to ferromagnetic

impurities. He suggested that the magnetic behavior was due to defects present in the processed

material. Later, our group investigated silicon irradiated by Si, Ar and neutrons4. We found that

these Silicon-based materials have a high number of defects as well as similar magnetic behavior

as spark-processed Si. More details about the process and the characterization of these materials

will be given in the following chapters.

We can distinguish three main groups of materials which could not be classified according

to the pervious definitions of diamagnets, paramagnets, ferromagnets, or other classical magnetic

materials. These materials are not predicted by the classical theory of magnetism.

The first group of materials is based on carbon. Carbon in the form of graphite or diamond

is diamagnetic, but carbon can be made paramagnetic or ferromagnetic-like using specific

processes. For example, Esquinazis showed in 2002 that highly oriented pyrolytic graphite

(HOPG) has a magnetic hysteresis at room temperature stemming from defects in carbon rather









than from magnetic impurities such as Iron (Fe) or Nickel (Ni). They postulated that it is not a

ferromagnet because the observed hysteresis does not originate from partially filled d or f shells

like in Fe, Ni, Co or rare earth elements. In addition, HOPG graphite has topological defects such

as grain boundaries and edge states. It is understood that these defects are of the "dangling

bonds" type which provide unpaired spins. It is believed that these unpaired spins, when

correlated, give rise to the hysteresis behavior. The magnetization under a magnetic field only

changes by 10% with temperature ranging from 300 to 500K. This is characteristic of a high

Curie temperature. Also, it is to be noted that the HOPG graphite has a paramagnetic behavior at

low temperatures. HOPG graphite has two magnetic components, one which is strongly

temperature dependant at low temperatures, characteristic of dangling bond defects and one

which is weakly temperature dependant at high temperatures (well below the Curie

Temperature). It is associated with the hysteresis loop at room temperature which is

characteristic of ferromagnetism. HOPG graphite cannot be classified as a ferrromagnet since no

domains could be shown. Furthermore, Esquinazi6 and Spemann7 use proton irradiation (i.e.

ionized hydrogen) to increase the magnetization of the HOPG graphite leading to magnetic

domains. They present magnetic force microscopic images (MFM) and scans where magnetic

domains can be seen in or around the irradiated spot. Final judgment on their interpretations

needs to await further experimental results. Specifically, it is noted that they do not show

magnetic domains in non irradiated HOPG even though it has a magnetic remanence. Also,

proton irradiation of carbon changes the surface morphology and therefore affects the quality of

the MFM images. It is possible that the magnetic domains presented could be artifacts due to the

radiation damages. In addition, Spemann7 hypothesizes that magnetic ordering in HOPG is due

to defects (i.e. "dangling bonds") and the implanted hydrogen. Finally, no mechanism is










proposed to explain the exchange interaction between the unpaired spins (i.e. "dangling bonds").

Esquinazi's group has published many papers on this topic8-12

Carbon nanofoam also has unusual magnetic properties. This material is produced using

laser ablation/evaporation of carbon from an ultra high purity target onto a glass substrate.

Rodel3-15 in 2004-2006 presents evidence of ferromagnetism in carbon nanofoam below 90K.

Above this temperature the nanofoam behaves as a paramagnet. It is well demonstrated that

ferromagnetism is not due to impurities such as Ni or Fe and that the paramagnetic behavior is

not due to Oxygen. They observe a decrease in the magnetization over time. We call this

behavior room temperature annealing. It is another evidence of lack of impurities in the

nanofoam since impurities do not disappear or self anneal at room temperature. In particular it is

shown that carbon nanofoam has a coercive field of 420 Gauss at 1.8K. This is evidence of

ferromagnetism-like behavior. The authors explain that the nanofoam has a large number of

unpaired spins attributed to defects and they believe that it is at the origin of the observed

magnetic behavior. Furthermore, they speculate that the nanofoam is formed of metallic carbon

clusters separated by non conduction carbon walls, which would explain its overall magnetic and

electrical response. The nanofoam is a semiconductor (explained by the behavior of non

conducting walls) and has ferromagnetic-like clusters due to itinerant electrons which are

responsible for the positive exchange interaction between the unpaired spins.

The Carbon nanofoam as well as the HOPG graphite are not true ferromagnetic materials.

In addition, since the origin of the magnetic hysteresis and high Curie temperature is attributed to

defects we classify these materials as quasiferromagnets.

Several research groups modeled the magnetic properties of carbon structures. Orellanal6

demonstrated, through ab-inito calculations, that carbon nanotubes with a monovacancies









exhibits ferromagnetic ordering, while the same carbon nanotube with divacancies does not

exhibit ferromagnetic character. Orellana used defects in carbon nanotubes to introduce

undercoordinated carbon atoms. Furthermore, no mechanism is proposed to explain the positive

exchange interaction between unpaired spins and the unusually high Curie temperature of such

carbon structures. Similarly, Parkl calculated the stability of T-shaped carbon nanotube

structures which demonstrates the possibility of unpaired spins on carbon atoms specifically

located at the junction of carbon nanotubes. Park showed that curved graphite sheets modify the

electronic structure of certain carbon atoms leading to unpaired spins. We believe that these

unpaired spins have a similar role as dangling bonds. They are most probably at the origin of the

magnetic hysteresis behavior. No mechanism was proposed by these authors to explain the

exchange interaction between the unpaired spins.

All authors experimentalistt or theorist) who have studied the carbon based ferromagnetic-

like materials agree that it stems from defects allowing for unpaired spins. They disagree as to

where these unpaired spins come from. For some, it is due to dangling bonds while for others it

is due to a modified electronic structure of carbon atoms (curved sheets). None of these authors

propose a mechanism to explain the exchange interaction between the unpaired spins. Similar

work has been done on silicon-based materials. We review here the work of the main-stream

authors in this area.

In 1993, Laiho prepared porous silicon using anodic etching. The porous Si which he

manufactured presented a magnetic hysteresis response as well as a Curie temperature of 570K.

Porous Si is only composed of Si with a surface oxide (SiO2). Laiho investigated the Si dangling

bonds present in the material using Electron Paramagnetic Resonance (EPR). The EPR technique









showed direct evidence of dangling bonds. The dangling bonds create unpaired spins which are

believed to be at the origin of the magnetic hysteresis loop observed.

Another technique is used by KhokhloV19 in 1967 to prepare silicon samples with a high

number of paramagnetic defects (i.e. dangling bonds). Ion implantation using Neon and Argon is

used at high doses (up to 3 x1017 cm-2) to create large amount of defects. EPR is also used to

investigate the paramagnetic centers. It is shown that the intensity of the absorption of

microwaves, which is directly related to the susceptibility, does not follow a Curie law as it is

always the case for paramagnetic materials. This is why Khokhlov suggests that such a material

has a ferromagnetic phase. He measures a magnetic transition temperature of 150K using EPR. It

is to be noted that no hysteresis curve is shown in his work. Our research furthers this work. It

will be presented in Chapter 5 chapter.

Spintronics is the study and use of electron spins in electronic devices. Since it is a very

recent field of study, the boundaries of this field are not well defined. Spintronics regroup giant

magnetic resistance materials (metal alloys), semiconductors doped with magnetic ions, such as

Mn, Co, Gd.... Authors utilizing magnetic carbon also claim to be part of this field. In order to

be precise and clear, we will define the spintronics materials as containing magnetic elements, d-

shell or f-shell magnetic ions, like Gd, Mn, Co, Ni, with a ferromagnetic behavior and a potential

to be used as magnetically driven devices. Therefore, our definition excludes carbon-based

materials and other materials not containing magnetic ions.

More recently (2006) Bolduc20 inVCStigated the structural properties of ferromagnetic Mn

implanted Si. It is classified as a spintronics material. Mn is implanted at doses ranging from 1015

cm-2 to 1016 Cm-2 COrresponding to peak concentration of 0. 1 to 0.8 at. %. Hysteresis loops at

room temperature are presented before and after annealing. A 5 min annealing at 8000C









increases the area of the hysteresis. Bolduc suggests that the Mn implanted Si magnetic behavior

is due to carrier mediated interactions. In other words, the Mn electron spins interacts together

through the mediation of itinerant electrons.

Even if we do not agree with the conclusions of Bolduc and the origin of ferromagnetism

we do not dispute the facts presented in his paper. More arguments will be given in the

discussion part of this dissertation as to why we disagree with Bolduc on the origin of the

magnetic hysteresis.

Another interesting material for its magnetic properties is CaB6. Lofland21 meaSured, in

2003, the magnetic response of CaB6 aS a function of temperature and demonstrated that the

magnetic response varies with the environmental condition (gas employed during the annealing).

He explained these differences by an increased number of defects due to gas-sample's surface

interaction and subsequently that the ferromagnetic-like behavior in CaB6 WAS due to dangling

bonds.

Finally in 2005, Coey22-24 prOposed several mechanisms to explain the magnetic behavior

of the different carbon polymorphs, CaB6 aS well as the diluted magnetic semiconductors

(DMS). DMS are semiconductors such as Si, GaN, GaAs or ZnO doped with magnetic ions such

as Mn, Cr, Co, Ni or Gd. DMS are spintronic materials. First, Coey showed that the DMS

behavior cannot be explained by the magnetic responses of the diluted ions within the material.

For example, magnetization of ferromagnetic doped ZnO films decay with time24. When

magnetization is measured several times over a period of weeks, a clear decrease is observed due

to self annealing (it i s to be noted that thi s phenomenon i s unrelated with superparamagneti sm).

These observations are not compatible with the classical explanation given for DMS, i.e. that the

magnetic behavior is due to the interaction between itinerant electrons and electrons in the d or f-










shell of the magnetic ions. In addition Coey explained that DMS have a high number of crystal

defects. Therefore, similarly to ferromagnetic-like carbon, he suggested that the origin of the

magnetic hysteresis as well as the high Curie temperature is defects related. Even though Coey

conceptualized the Hield of ferromagnetic-like materials and spintronics, he did not demonstrate

which model or mechanism explains the observed phenomena.

In this dissertation we explore the origin of the magnetic hysteresis as well as the high

Curie temperature associated with it in the case of materials for which explanations are

incomplete or none existing.

Quasiferromagnetism is characterized by a magnetic hysteresis stemming from defects

rather than from magnetic ions. Usually, quasiferromagnets have high Curie temperatures. In

conclusion, all the unclassified materials which are believe to have their magnetic behavior

defects related are quasiferromagnetic. This includes HOPG and nanofoam carbon, spark

processed silicon, ion implanted silicon and to some extend ZnO doped with Mn where it is

demonstrated that defects rather than Mn ions are responsible for the magnetic behavior.

2.5 Summary

There are several classes of magnetism:

* Diamagnetism stems from the electrons orbital moment. It is opposite to the field which
created it.

* Paramagnetism originates from the spin of independent unpaired electrons. The
magnetization is in the same direction as the Hield which created it. It is proportional to the
inverse of the temperature.

* Ferromagnetism is characterized by its remanence and its Curie temperature. The
remanence is due to the interaction of electron unpaired spins. The Curie temperature is a
critical parameter as it is related to the strengths of that interaction.










* Superparamagnetism is a limiting case of ferromagnetism. It is observed when the thermal
agitation randomizes the domain magnetization in small particles.

* A new class of magnetic material is proposed as a way of labeling materials in order to
better explain their non classical magnetic behavior. Quasiferromagnetism appears in
materials, such as s-Si, with a high density of defects, i.e. dangling bonds. It is postulated
that the observed remanence is stemming from the interaction between the unpaired spins.
A Curie temperature similarly to ferromagnetism is observed.









CHAPTER 3
MANUFACTURING, MACROSCOPIC CHARACTERIZATION AND EXPERIMENTAL
RESULTS OF QUASIFERROMAGNETIC MATERIALS

3.1 Room Temperature Study of Spark-Processed Silicon

3.1.1 Production of Spark-Processed Silicon for Magnetic Studies

The manufacturing of spark-processed silicon (sp-Si) was first developed by Hummel25

with the intent of using the optical properties specificallyy luminescence) of this newly created

material. This method consists of applying a high voltage (several thousand volts) at a high

frequency (several tens of kilo-hertz) between a substrate and a counter electrode, typically made

of tungsten. I made several modifications to the original process in order to manufacture

quasiferromagnetic sp-Si. These modifications include a change in the position of the substrate

with respect to the stage and the use of a laboratory made power supply with slightly different

voltage and frequency ranges. A complete description of the power supply which I designed and

assembled is available in Appendix A. Figure 3-1 illustrates how sp-Si is produced: a silicon

substrate is glued on an aluminum stage with silver paint.


IPulsed DC
Power supply
: Tungsten tip

Cut
; ~\\ ~Spark Plasma





Stage Silver paint silicon wafer

Figure 3-1. Spark-processing of silicon. A power supply provides several kilo-volts between the
electrode and the substrate. The substrate is "hanging" from the stage and glued with
silver paint. The end of the substrate (i.e. the sparked area) is subsequently cut at the
mark to avoid any possible contamination of the sample.



































































Figure 3-2. Scanning electron micrograph of spark-processed silicon. A) large top view. B)
zoom-in view.









The silver paint provides the necessary conductivity for the current to flow from the

substrate to the stage. The substrate hangs from the stage in order to prevent contamination

through diffusion (or sparking) between the stage and the substrate. Once the silicon is spark-

processed the substrate is cut as shown in Figure 3-1, to separate the potentially contaminated

part (in contact with the stage) from the sample. The sample can be made to sizes ranging from

2mm x 5mm to 5mm x 10mm. The size of the sample is an important parameter in the

characterization process since each equipment has a different size requirement.

To manufacture the samples, the voltage, current, duty cycle and tip to substrate distance

are set while the frequency and the sparking time are varied with the laboratory made power

supply.

Scanning electron microscope (SEM) micrographs of sp-Si were taken to show how our

material looks like after being manufactured. Figure 3-2A is a large scale top view while Figure

3-2B is a zoomed-in picture of a small area of sp-Si. A large round sparked area is visible. It is

composed of silicon, oxygen and up to 5% nitrogen, as previously shown elsewhere26. The close

look at the surface reveals large porous, and sphere-like particles.

Note: I published a study on sp-Si27 in which I found a volume porosity of 43%.

Now that we have described the spark process technique, we can look how the process

parameters influence the magnetic response.

3.1.2 Magnetic Characterization Process Parameter Influence

Several samples of sp-Si were prepared under various processing conditions and their

magnetizations were observed as a function of an external magnetic field at room temperature,

i.e. 300 K. In this section, we will present the results of these experiments.

Figure 3-3 is a typical magnetization curve as a function of the magnetic field for sp-Si.

We used a commercial super quantum interference device magnetometer (SQUID) to conduct



















































200 400 600 800 1000


Figure 3-3. Magnetization as a function of magnetic field strength measured at room temperature
for spark-processed silicon (sparking time = 6 hours, frequency = 22.5 k

It could be argued that the hysteresis loop is due to ferromagnetic impurities such as iron,


nickel or cobalt. In order to investigate this Secondary lon Mass Spectroscopy technique (SIMS)


has been applied down to the resolution limit of the instrument. For example, SIMS maximum


resolution for iron in silicon is 5x1013 at.cm-3. Figure 3-4 displays the mass spectrum of sp-Si.


For clarity a zoom in around the area where the iron isotope with a mass of 54 amu should be, is


displayed Figure 3-5. As observed it iron is not detected. It should be concluded that


ferromagnetic impurities cannot explained the observed magnetic hysteresis of sp-Si.


It should be noted in passing that surface passivation with hydrogen did not change the size


or shape of the observed hysteresis.


IOt-05


~OE-05


,OE-05


OE-05


OE+OO


OE-05


,OE-05


)nFnE~


the experiment. A hysteresis loop is observed at room temperature. The sample was spark-


processed for 6 hours.


^_


d


~C) yL~


I:


-4 0E-05
-1000


-800 -600 -400 -200 0

Field (Oe)























































120


Figure 3-4. Secondary ion mass spectrum of spark-processed silicon. The largest peaks have
been labeled accordingly. See also Figure 3-5.


7I


We use two parameters to characterize the magnetic response: the remanence and the

magnetization at 1000 Oe. The remanence is define as the magnetization at zero field after the

sample has been exposed to an external field equal to or greater than the saturation

magnetization, taken to be 1000 Oe for sp-Si. Figure 3-6 displays the remanence (Mr) and the

magnetization at 1000 Oe (Ms) as a function of the processing frequency. Both, Mr and Ms

increase as a function of frequency up to 22.5 k
observe a similar behavior with the photoluminescence of sp-Si. The photoluminescence

intensity increases as a function of the frequency up to 10 k
for the green band and then decrease for high frequencies.

It is to be noted that below 8 k
spark through the air between the tip and the substrate.


o ~ ~ ~ si 3 S4









20 40 60
At


S5 W6

















80
omic Number


100

















Fe, isotope 54









Resolution limit








50 51 52 53 54 55 56 57 58 59 60
Atomic Number


3.5


3


2.5





1.5


1


0.5


Figure 3-5. Secondary ion mass spectrum of spark-processed silicon zoomed in around the iron
atomic number. An arrow marks the position of where the iron isotope with an atomic
mass of 54 should be if it was present in the sample.

Figure 3-7 displays the remanence and magnetization at 1000 Oe as function of sparking

time. The longer the substrate is processed the larger the magnetization. Stora28 published a

similar conclusion when studying the intensity of the photoluminescence of sp-Si as a function of

the sparking time.

Even though knowing the influence of the process parameters are important information,

more crucial information can be obtained by studying the magnetization as a function of

temperature. Since we know that the samples prepared at a frequency of 22.5 k
strongest remanence (Figure 3-6), the next section will focus on studying sp-Si magnetization at

high temperature (300 800 K) with samples prepared at this frequency.















Sample Name:
MSPO3-12


Cut-off

Frequency










Sparking commences here


5
E
a
b
r4

O
'E

ct
Q

(II
12



1



O


Frequency (kHz)

+ Mr (M at 00e) a Ms (M at 10000e)




Figure 3-6. Spark-processed silicon magnetization at 0 Oe (i.e. remanence) and 1000 Oe as a
function of the spark frequency (sparking time was set at 12 hours for all samples).


3.2 Magnetic Characterization of Spark-Processed Silicon at High Temperature


In this section, we describe the temperature dependence of the magnetic properties of sp-


Si. Measuring the high temperature dependence in a SQUID magnetometer is by no means a


trivial task for small signals as it is the case for spark-processed silicon. Therefore, we first


describe a new measurement procedure to overcome the limitation of the SQUID magnetometer


for temperature ranging from 300 to 800 K.












Sample Name:
SMSPO3-12















0 5 10 15 20 25 30
Sparking time (hrs)

Mr (M at 00e) a Ms (M at 10000e) A hysteresis area (a.u.)


Figure 3-7. Spark-processed silicon magnetization at 0 Oe (i.e. remanence,) 1000 Oe and
hysteresis area as a function of the sparking time (spark frequency was set at 16 k for all samples).

3.2.1 Magnetic Characterization Method at High Temperatures

All of our high temperature magnetization experiments were conducted in a commercial

SQUID with an oven option. This oven insert allows us to measure magnetization as a function

of temperature in the range 300 800 K. The commercial software sold with the SQUID is

designed to measure the magnetization with a maximum resolution of 10-7 emu without the oven

insert and 10-' emu with the oven insert while controlling the temperature with great accuracy

(0.01 K). But the resolution limit of 10-' emu was not acceptable for our purpose since our

samples have typical magnetization in the 10-6 emu range. Therefore, I modified the

measurement procedure in order to restore the magnetization resolution back to its 10-' emu

value. The drop in maximum resolution is due to the heating system within the oven. Figure 3-8









shows a schematic representation of the oven apparatus installed in the SQUID magnetometer. It

is important to notice that the oven is inserted in the detector loop. When the computer software

controls the temperature of the oven, it continuously adjusts the current in the heating element

which causes the detector to acquire an additional unwanted signal. This unwanted signal

decreases the resolution from 10-7 emu to 10-' emu. In order to avoid this unwanted signal the

temperature controller is turned off during the measurement. The measurement takes about 4 min

and during this time the temperature drifts. The maximum drift is about 1 K at the highest

temperature (800 K). This is down from the 0.01 K accuracy when the temperature controller is

on but it is acceptable for our purpose. To summarize, the new measurement procedure is:

* the temperature is set while the temperature controller is on,
* the temperature controller is turned off when the temperature is stable,
* the magnetization is measured,
* the temperature controller is turned back on.


This improvement allows us to measure the magnetization as a function of the temperature

of the samples with an acceptable loss of temperature accuracy.

Other procedures were suggested by the manufacturer of the SQUID magnetometer but

implementing them revealed to be extremely difficult. To our knowledge, no one else has ever

used this new procedure to measure small magnetization with the oven insert. It should be noted

in passing that this procedure has been validated by the manufacturer before it was implemented

to prevent any damages to our equipment. In addition to improvements in the computer software,

a new sample holder was constructed. Indeed, the two types of sample holders proposed by the

SQUID manufacturer were not intended to work at such high resolution with the oven insert. The

first type of holder is made of copper wires and has a limited resolution of about 10-4 OmU

(measurement not shown) due to magnetic impurities in the copper.








Moving stage


I


I


Oven apparatus


Moving axis


Copper hook


Detector
Signal

Sample


Sample position = 7cm
from end of glass tube

Quartz holder

SQUID magnetometer


Figure 3-8. Super quantum interference device magnetometer with oven insert and sample
holder.


Rod holder


SI


i~









The second type made of quartz had to be modified to reduce the diamagnetic response

added to the sample signal. We re-designed the quartz holder proposed by Lewis29. Lewis

proposed a quartz sample holder composed of an outer quartz tube with two inner quartz rods

fitted inside. In this case, the sample is being positioned between the two quartz rods. These two

rods have a diamagnetic response which is superimposed to the signal coming from the sample.

Such a holder reduces the accuracy of the magnetization measurement.

Our new design includes a thinner outer tube with a wall of 0.4 mm (instead of 0.6 mm for

Lewis design) leading to a 30% decrease in mass, allowing accommodation of larger samples

(2.2 mm up from 1.8 mm). In addition, the rods were removed while a notch in the quartz tube

was added to hold the sample in place as shown Figure 3-8. These two modifications improved

the magnetization signal coming from the sample while decreasing the influence of the signal

generated by the holder.

In addition to the general design of the sample holder, the position of the sample with

respect to the end of the holder is a critical parameter. It has been found30 that the end of the

quartz holder creates an artifact in the measurement. Also, it has been shown how to position the

sample with respect to the end of the holder to prevent this artifact from interfering with the

sample signal. Similarly, with our new designed holder we came to the same conclusion. In order

to understand how to remove the artifact stemming from the end of the sample holder we now

describe how the SQUID magnetometer calculates the magnetization from the detector voltage

output signal.

In a SQUID magnetometer the sample is moved up and down along the vertical axis

(Figure 3-8). When the sample moves, the detector measures the change in the magnetic flux as a

function of z (the sample position). Then, the detector outputs a voltage, proportional to the



































Sample at 7cm from
end of quartz holder


magnetic flux, which is plotted against z. Then, this curve is modeled by the computer to

calculate the magnetization in emu units. The model, f(z), used by the software is define as


followed: f (z) = 2[R2 + : ]3/ [R2 + (z + L)2 ]3/ [R2 + (z L)2 ] /, where R and L are


instrument constants. The computer only uses data spanning over a 4 cm range to calculate the

magnetization.





End effect of c uartz holder


o

*0 '
1
O
> 05


-10 -8 -6 -4 -2 0 2 4 6 8 10
Position (z) in cm



Figure 3-9. Simulated detector voltage (a.u.) as a function of the position. The simulated function
is define as: f (z)-0.1x f (z +7) .

In order to understand the artifact due to the end effect, we show on Figure 3-9 the

simulated output voltage from the detector including both signals from the sample and the end of

the holder. The simulated function is: f (z) +0.1 x f (z + 7) where f(z) is the signal coming from


the end of the quartz holder while the second term 0. 1 x f (z + 7) simulates the sample signal.


Usually, the sample signal is one order of magnitude smaller than the artifact signal and










positioned 7 cm away from the end of the holder. Figure3-10 shows the simulated function

centered at 7 cm (the sample position) with a range of 4 cm along with the modeled curve from

the software.




02
Sample at 7 cm from
0 1 end of quartz holder





o o


Position (z) in cm


Figure 3-10. Simulated detector voltage (a.u.) as a function of the position (blue diamonds)
zoomed in around the sample located 7 cm away from the end of the holder. The
computer model is plotted in solid orange.

When the sample is placed at 7 cm from the end of the holder the modeled curve is very

close to the simulated one (the correlation coefficient is greater than 0.9) and therefore the

calculated magnetization is the correct value. On the other hand, when we position the sample at

only 3.5 cm from the end of the holder the modeled curve does not fit with the detector voltage

(the correlation coefficient is only 0.4). Therefore the calculated magnetization is an incorrect

value. To illustrate this effect, Figure 3-11 shows the simulated curve when the sample is 3.5 cm










from the end of the holder. We observe that the signal from the sample and the one from the end

of the holder overlap.


25
End effect of quartz holder








1 Sample at 3.5cm from
end of quartz holder













-8 -6 -4 -2 0 2 4 6 8
Position (z) in cm


Figure 3-11. Simulated detector voltage (a.u.) as a function of the position. The simulated
function is defined as: f (z) 0.1 x f (z + 3.5) .

Upon zooming on the 4 cm range around the sample, as shown in Figure 3-12 we clearly

notice the large discrepancy between the model curve used to calculate the magnetization and the

simulated detector voltage curve which causes an incorrect measurement.

Now, it becomes clear that the further the sample is located from the end of the quartz

holder the more accurate the measurement. Unfortunately, the oven itself limits the length of the

holder and therefore the maximum practical distance is 7 cm. With this design and proper sample

position, the measurement accuracy is more than sufficient for our purpose.












Sample at 3.5cm from
end of quartz holder


-5 -4 5 -4 -3 5 -3 -2 5
Position (z) in cm


Figure 3-12. Simulated detector voltage (a.u.) as a function of the position (blue diamonds)
zoomed in around the sample located 3.5 cm away from the end of the holder. The
computer model is plotted in solid orange.

To summarize, here are the modifications done to the SQUID in order to measure the

magnetization in the temperature range 300 to 800 K:

* Add the oven insert,
* Use an ultra thin tube for the holder,
* Use a notch in the holder rather than inner rods for sample support,
* Position the sample with respect to the end of the tube as far as possible,
* Turn off the temperature controller during each measurement,
* Turn back on the temperature controller and go to the next data point.































































Figure 3-13. Magnetization of pure nickel as function of temperature at 1000 Oe. A Curie
temperature of 625 K is found as indicated by the arrow.

Secondly, we measured the magnetization at room temperature of a piece of silicon wafer

as function of the field. We used the newly designed sample holder without the oven. The result


is plotted Figure 3-14. The very well known diamagnetic response of silicon is observed. In


Curie temperature = 625K


3.2.2 Verification of the Modified Magnetometer

In order to validate the SQUID modifications and before measuring the magnetization of


sp-Si, three experiments were made.

First, the magnetization as function of temperature at 1000 Oe of a pure nickel sample was

measured; the data is presented in Figure 3-13. We observe a Curie temperature of 625 K to be


compared with published value of 631 K. This is a very good agreement and corresponds to a

discrepancy of less than 1%.


0


1.E O3

0. EO4

8. E 04

7. E 04

6. E 04

5. E 04

4. E 04

3. E 04

2. E 04

1.E 04

0. E+00
301


350 400 450 500 550 60

Temperature (K)











addition, the susceptibility (0.318x10-6) meaSured is less than 3% different from the published


value. This is acceptable and further validates the modification of the sample holder. In other


words, our sample holder does not interfere with the magnetization measurements.


4 E-06


3 E-06


2 E-06


E 1 E-06


~ OE+00






-2 E-06


-3 E-06


-4 E-06
-1000


-800 -600 -400 -200 0 200 400 600 800 1000
Field (Oe)


Figure 3-14. Magnetization versus magnetic field for a silicon sample weighting 10.3 mg,
measured at 300K.


Finally, we measured the magnetization of the same piece of silicon wafer as a function of


the temperature at 10,000 Oe. The resulting data is plotted on Figure 3-15. It is to be noted that


we measured the magnetization of the silicon sample at 10,000 Oe and then divided the


measured value by ten. This was done in order to compare directly with the magnetization as


function of temperature curves for sp-Si which we will present in the next section. The


magnetization is independent of the temperature over the entire range (300-800 K) as expected

for silicon. From the average magnetization we derive the susceptibility; it is about 15% smaller

































































Figure 3-15. Magnetization versus temperature (grey dots) for a 10.3 mg silicon wafer measured
at 10,000 Oe. The plotted magnetization is divided by 10, equivalent to magnetization
at 1000 Oe. The average (solid line) is -2.8 x10-6 OmU.


The magnetization versus temperature of nickel and silicon are satisfactory and provide us


with validation standards for our method of measurement.


than the susceptibility we obtained at room temperature without the oven insert. Since we use the


same holder in both measurements we attribute the discrepancy to the oven itself. The design of


the SQUID requires the oven to be inserted between the detector and the sample; therefore it


induces a perturbation during measurements. It seems that 15% is a large discrepancy, but this is


still better than what we initially observed before the modifications.


000E+00


Sample name:
SpSiHO


07



06



06



06


06*
* **
egg~ *, z


-5 00E-

1 O-


-100

-150
10-
O


Q)-2 00E-

20-


300 350 400 450 500 550 600

Temperature (K)


650 700 750 800











3.2.3 High Temperature Spark-Processed Silicon Magnetization


Using the improved high temperature SQUID oven, we measure the magnetization as


function of temperature for sp-Si spark-processed for 6 hrs at a frequency of 22 k

displays the resulting curve upon heating and cooling in an external magnetic field of 1000 Oe.


We observe that the magnetization decreases as the temperature increases and increases as the


temperature decreases. In addition, the magnetization at room temperature is larger (by 35%)


after cooling in the field than before going through the heating cycle. Cooling of a ferromagnetic


material in a magnetic field (field cooling) is known to cause additional alignment of spins. This


causes an increase in the remanence.


3 5E-05



3 OE-05



2 5E-05



2 OE-05
O


(1 1 5E-05



1 OE-05



5 OE-06


0 OE+00
300


350 400 450 500 550 600
Temperature (K)


650 700 750 800


Figure 3-16. Magnetization as a function of temperature upon heating (blue diamonds) at 1000
Oe for spark-processed silicon (sparking time = 6 hours, frequency = 22.5 k the field cooled magnetization (red square).











The effect of field cooling is better seen in Figure 3-17 where we plot the magnetization as

a function of the field at room temperature before and after field cooling. After field cooling, the


hysteresis loop is much larger than before.

4 OC-05

3 OE-05 --Sample name:
MSP104 35% increase

2 OC-05


S1 OE-05
300% mecrease







-1 0E 00 0 -0 -60 -0 -20 0 20 00 60 80 1 0
Fil ( e

-* bfr -*-after

Figue31.Mgeiaina ucino h antcfedsrnt eoe(lecre n
afe fil olng(e uv) esrda ro eprauefrsar-rcse











Fgivntmeaure, Mo1 isth agnetization a fnto t zer Kagelvin and sTo isth eCurie tblempraurve, we








find a very good agreement between the Weiss molecular field theory and our sp-Si data. Figure

3-18 and 3-19 display two measured samples along with their Weiss models. For the first sample


(spark time = 12 hours, frequency = 22.5 k
770 K while for the second sample (spark time = 6 hours, frequency = 22.5 k























Weiss Model
Mo = 3.25 10-5 emu
M/Mo = Tanh[ (M/Mo) / (T/Tc) ]

Mo = 3.8 10-5 emu
Tc =770K

o 12 = 0.983


to a Curie temperature of 760 K. The correlation coefficient between the model and the measured


data are very good, that is 0.983 for sample 1 and 0.988 for sample 2.The temperature


dependence of the magnetization shows a strong similarity between sp-Si and ferromagnetic

behavior.


12



1







O


The Curle Temperature
Is about 770K





)0 650 700


Sample name
-MSP104


Si wafer average magnetization


400 450 50(


0550 6
Temperature (K)


Figure 3-18. Normalized magnetization as a function of temperature for spark-processed silicon
measured at 1000 Oe represented by red diamonds. The sample was processed for 12
hours at a frequency of 22.5 k Curie temperature of 770 K. The average magnetization of a piece of silicon wafer
comparable in size to the measured sp-Si sample is plotted for comparison (green
dash line).

The sample was processed for 6 hours at a frequency of 22.5 k

the Weiss model with a Curie temperature of 760 K. The average magnetization of a piece of


silicon wafer comparable in size to the measured sp-Si sample is plotted for comparison (green


dash line).


~u7 -1











The two most important parameters for describing the macroscopic magnetic behavior of a

material are the remanence and the saturation magnetization. In our study, we use the

magnetization at 1000 Oe as saturation point. In the previous section we presented the

temperature dependence of the saturation magnetization.


Mo = 0.91 10-5 emu


Weiss Model

M/Mo = Tanh[ (M/Mo) / (T/Tc) ]

Tc =760K
Mo = 0.92 10-5 emu

r2 =0.988


300 350 400 450 500 550 600 650 700 750 800
Temperature (K)


Figure 3-19. Normalized magnetization as a function of temperature for spark-processed silicon
measured at 500 Oe represented by red diamonds.

In the next section we briefly describe the effect of temperature on the remanence. Figure

3-20 displays the remanence of sp-Si (sparking time = 6 hrs and frequency = 22.5 k
function of temperature. We observe a decrease in the remanence as the temperature increases

and an increase as the temperature decreases, but the heating and cooling curve are not


superimposed on one another (the cooling magnetization is smaller than the magnetization upon











heating). Heating up at the Curie temperature randomizes the spins. Upon cooling a small but

discernable spontaneous magnetization is observed.


8 E-06



6 E-06



4 E-06


2 -0





- 2E-06


-4 E-06 +-
300


350 400 450 500 550 600 650 700 750 800
Temperature (K)


Figure 3-20. Remanent magnetization of spark-processed silicon (sparking time = 6 hours,
frequency = 22.5 k dots) and cooling (red dots). The large error bars at high temperatures are caused by a
lower sensitivity of the instrument in such temperatures. Note that these
measurements were made at 0 Oe where as in Figure 3-16 they were made at 1000
Oe.

In this section, we presented the magnetization as a function of the temperature and

concluded that the magnetic behavior of sp-Si is very similar to ferromagnetic materials. Now

we investigate the effect of annealing on the magnetization.


3.2.4 Annealing Effect on the Magnetization

The magnetization as a function of the field was measured after a number of heating and

cooling cycle. A cycle included heating the sample at 800 K and cooling it down to room


























-L ~71


2 E-05



E 1 E-05
Q

O
~ij OE+OO
N
Q
~ 1 E-05
(II
I

2 E-05


3 E-05


c nE.


temperature at a Hield of 1000 Oe. A cycle takes 7 hours. The resulting curves are plotted in


Eigure 3-21. The area within the hysteresis loops, measured at room temperature, is observed to


become smaller as the number of cycle increases.


4 E-05


-Sample name:
MSP104


3 E-05 -


-1000 -800 -600 -400 -200 0 200 400

Field (Oe)

-1st -2nd -2nd -3rd -4th -5th


600 800 1000


Figure 3-21. Magnetization as function of magnetic field for a spark-processed silicon sample
(sparking time = 6 hours and frequency = 22.5 k heating cycle (heating up to 800 K and cooling down to 300 K in a 1000 Oe Hield).
The first two (grey and purple) were measured on the same day, while the others were
measured at a later time.


The relevant data, remanence and magnetization at 1000 Oe as a function of annealing


time, can be better seen in the next graph, Eigure 3-22. The remanence as well as the


magnetization at 1000 Oe decrease slowly in a linear manner with annealing time. The


magnetization at 1000 Oe decreases by about 15% over an annealing time range of 35 hrs. This


is only a 3% decrease per heating cycle. The previously presented data of magnetization as a


















Ms =-107* Time +3.5*1 05
R2 =0.997


function of temperature is only marginally affected. Therefore, our conclusions on the magnetic

behavior of sp-Si at high temperatures are unchanged.


3.5E-05





3 .0E-05



O

3 1.5E-05


1.0E-05


Sample name:
-MSP104


I ,


5.0E-06


0.0E+00


Mr=-4*108* Time+105
R2 =0.52

30 35


10 15 20 25
Annealing Time (Hours)

4 Ms (10000e) a Mr (00e)


Figure 3-22. Magnetization at 1000 Oe (blue diamonds) and 0 Oe (red squares) versus annealing
time for spark-processed silicon (sparking time = 6 hours and frequency = 22.5 k Linear models are plotted as solid lines. The annealing was performed during heating
at 800 K and cooling back to 300 K in a 1000 Oe field over a 7 hours heating-cooling
cycle.

3.3 Low Temperature Magnetization

In this section we present and analyze the magnetization as function of temperature of


spark-processed silicon at low temperatures. But, similarly to high temperatures, proper control

measurements need to be performed before doing experiments on unknown material such as sp-

Si. Therefore, we will use HgCo(SNC)4 and aluminum as low temperature references. Also, we

will discuss observed artifact caused by oxygen in the sample chamber.









3.3.1 Magnetic Reference Material HgCo(SNC)4 for the 2-100K Temperature Range

This reference material is used to make sure that the SQUID magnetometer measurements

are reliable. Several references can be used to validate magnetization measurements with the

SQUID magnetometer at very low temperature (2-100K). The cobalt mercury cyanide is a

widely used reference for this range and was readily available to us. This material comes in a

powder form and special handling is required due to its toxicity and potential to contaminate the

magnetometer. A special sample holder was designed to prevent loss or scattering of the material

during the measurement process. A description of the holder design can be found in the

Appendix B.

To evaluate the reliability of the SQUID magnetic measurements, we look at the

correlation between the magnetic susceptibility of HgCo(SNC)4 aS a function of temperature of

our own data and the one published by O'Connor32. We find an excellent match with a

correlation coefficient of 0.9999. Our results are also consistent with the values published by

Bunzli33

We concluded that HgCo(SNC)4 is a good choice of standard for very low temperature

magnetic measurements and that our SQUID magnetometer gives reliable magnetic

measurements in the 2 to 100K range since we had a very good correlation between our data and

previously published ones. This work is fully detailed in the Appendix B.

3.3.2 Aluminum Reference for the 50-300 K Temperature Range

Aluminum has been well studied in the 50-300K temperature range and is a better suited

magnetic standard than HgCo(SNC)4 in this range due to its large temperature coefficient.

First, we measured a magnetic susceptibility at room temperature of 3.3 77x 10s emu for

the aluminum sample. Using the measured weight of the sample (53.4 +0. 1 mg) we calculated a









sample volume of 0.0198 f0.00004 cm-3 leading to a volume susceptibility of 1.70f0.03 x 10-6

cm-3. This value is very close to the published value Of 1.65 x10-6 CA-13

Next, we measured the susceptibility as function of temperature. The aluminum

susceptibility is linearly dependant on the square of temperature according to Hedgcock34. This

dependence can be expressed by the following equation: X = Xda o + X,,+B x T where Xdia is

diamagnetic susceptibility, XZ ra is the temperature independent paramagnetic susceptibility and

where B is a constant characteristic of aluminum. We found a correlation coefficient of 0.997

between our data and this proposed model.

The results from HgCo(SNC)4 and Aluminum reference lead us to conclude that our the

magnetization measurements at low temperatures with our SQUID magnetometer are reliable. In

addition, to proper calibration, oxygen contamination could be an issue with high resolution

magnetization at low temperature. In the next section, we will discuss the oxygen contamination.

3.3.3 Oxygen Effect at Low Temperature

Oxygen contamination is a known problem with low temperature measurements with a

SQUID magnetometer but not very publicized. I have published on this topic35 and found out

that it was known to Quantum Design Inc., the manufacturer of our SQUID magnetometer but an

application note has never been written to help users properly interpret their measurements.

Therefore some clarifications are needed.

Oxygen is paramagnetic in its gas and liquid phases, becomes antiferromagnetic when

solid below 54.3 K, and changes its crystal structure36,37 (P to y at 43.8 K). The magnetic

transitions of oxygen at 54.3 K and 43.8 K generate a noticeable change in the measured

magnetic susceptibility of a sample while some gaseous oxygen is left in the sample chamber.










Typically a large peak around 50 K is observed in addition to the magnetization of the

characterized sample.

In our SQUID magnetometer, a sample is normally measured in a Helium gas. Following

the sample loading, the load lock (or the entire chamber) is purged with Helium gas. But due to

pumping and Helium quality there is still oxygen left in the chamber. When no purge is

performed a large peak is observed as expected since we leave a large amount of oxygen gas

from air in the chamber. But, even when we purged 3 times the oxygen peak is still visible. This

small trace of oxygen could be explained by the limiting pumping capability of the mechanical

pump and the presence of trace oxygen within the helium gas use to cool down the sample. See

Appendix D for more details.

Finally, this "oxygen" effect is only visible in samples with magnetization in the 10-5 or 10~

6 emu range. Therefore we recommend, in addition to multi-purging, using samples as large as

possible to decrease the relative effect due to oxygen magnetic transition.

Now that we have shown that our SQUID magnetometer works properly over the entire

temperature working range and that we have discussed the problem associated with the oxygen,

we can focus on spark-processed silicon.

3.3.4 Spark-Processed Silicon Low Temperature Magnetization

We have previously shown that spark-processed silicon had a magnetic hysteresis at room

temperature. Upon cooling, this magnetic hysteresis loop remains present as seen in Figure 3-23.

The magnetization versus field was measured at 35 and 70 K. The remanence is the same for

both temperature but the magnetization at non zero field increases as the temperature is cooled

down. The magnetization increases by 30% at 1000 Oe. Further, the hysteresis loop rotates

counterclockwise as the temperature is lowered. This can be explained using a complete model

of the magnetization for spark-processed silicon.














































Figure 3-23. Magnetization versus field at 70 K and 35 K of spark-processed silicon (square and
round points, respectively).

We model the magnetization as followed:


Ms,-s = [X, ta Z para par (T) x H +M~yserets(T, H) ,where Xia is the diamagnetic


O~C`
susceptibility, Z ara is the temperature independent paramagnetic susceptibility, Z,ara (T) =T-


is the Curie-Weiss susceptibility and 2ysterests(T, H) is the Weiss magnetization presented in


Section 3.2.3. The Weiss magnetization is only temperature dependent near the Curie


temperature. At temperatures well below the Curie temperature (760 K for sp-Si), the Weiss

magnetization is almost temperature independent. For example, using the Weiss model, we

evaluated a magnetization decrease of 1.3% between 10 and 300 K using a Curie temperature of


2.0E-05


1.5E 05


1.0E-05


S5.0E-06


0j .0E+00


S-5.0E-06


S-1.0E-05


-1.5E 05


000


-2.0E 05
-1


-800 -600 -400 -200 0 200
Field (Oe)

-*-5.0 -5-0.0


400 600 800 1000










760 K. On the other hand, the Curie-Weiss susceptibility is strongly temperature dependent at

low temperature. The rotation of the hysteresis loop at low temperature is therefore interpreted to

be due to paramagnetic centers which follow the Curie-Weiss law.


5.0E 05

4.5E 05

4.0E 05

3.5E 05

& 3.0E-05 -i 02 phase transition

S2.5E 05





1.0E 05

5.0E 06


0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Temperature (K)

S10000e Tgoing down -0 Oe Tgoing down -Magnetization model


Figure 3-24. Magnetization versus temperature for spark-processed silicon at 1000 Oe (red
triangle) and 0 Oe bleuu squares). A model is fitted to the 1000 Oe magnetization
curve in solid red. The bump is magnetization near 40 K is an artifact caused by a
phase change of oxygen contamination in the measured chamber (see Appendix D).

If we set the magnetic field and consider the Weiss magnetization to be temperature


independent we can simplify our magnetization model to:Ms,s, = Me, +-, where
T-0


Me = [ ,0 + X~, j x H +M ,,, (H) and C' = C x H .Using this model on our magnetization


versus temperature data for sp-Si presented in Figure 3-24, we obtain the following fitting

parameters: Mo = 1.07 x10-5 emu, C' = 1.73 x10-4 emu. Oe and 6 = -3.16 K with a correlation










coefficient of 0.995. (Since oxygen has an influence on the data in the temperature range 20 to

60 K, we only use the data points outside this temperature range to fit our model). In addition,

Figure 3-24 also contains the remanence versus temperature of sp-Si. It should be noted that the

remanence does not change with temperature over the whole range, therefore validating the

temperature independence assumption from the Weiss model.


4.0E 05

-cr R2 =0.997 R2 =0.975
S3.5E 05

3.0E 05


S2.5E 05

2.E-05-- 0 phase transition




1.0E 05

c 5.0E 06


0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
1/(T+3.16K) and 1/T

r 1/(T3.16K) 1TT

Figure 3-25. Magnetization adjusted for diamagnetism and remanence as a function of inverse
temperature. The temperature has been shifted by 3.16 K to account for low
temperature exchange interactions. A linear trend is fitted to the low temperature data
(solid line). A green arrow marks the oxygen phase transition.

Since it is difficult to visualize the good correlation between our data and our proposed

model in Figure 3-24, another presentation of the data is proposed Figure 3-25. In Figure 3-25,


the magnetization at 1000 Oe is plotted as a function of [K ']. This method emphasizes
T +0









more the data points below 20 K and allows for a good visual correlation between our proposed


model and our data. For comparison the magnetization is also plotted as function of [K ']. It is


observe that in this case the model does not fit well the data.

3.4 Summary

From my research we learn the following:

* Sp-Si displays a magnetic hysteresis loop at room temperature under certain processing
conditions.

* A specific method was developed to measure the magnetization of sp-Si at high
temperature. From this method it was found that sp-Si magnetization as a function of
temperature follows the Weiss equation.

* A Curie temperature of 765 K as been evaluated from the Weiss equation applied to the
high temperature magnetic measurements for sp-Si.

* Annealing of sp-Si up to 800 K decreases the magnetization at 1000 Oe and the remanence
weakly .

* At low temperatures, sp-Si exhibits a large magnetization inversely proportional to the
temperature which is characteristic of paramagnets.









CHAPTER 4
INTERPRETATION OF QUASIFERROMAGNETISM IN SPARK PROCESSED SILICON

This chapter is dedicated to the study of the paramagnetic centers present in spark

processed silicon and how they are related to the observe quasiferromagnetism.

4.1 Model Concerning the Distribution of Paramagnetic Centers

In order to explain the magnetic hysteresis and the high Curie temperature in sp-Si we

propose that some paramagnetic centers, found in spark processed silicon, interact such that the

exchange integral is positive. First, to observe exchange interaction between electron spins, the

distance38 between them has to be smaller than 2 nm. It will be shown in a last section of this

chapter that the calculated average paramagnetic centers density in spark processed silicon is

about 2x1019 CA-3. Assuming that the paramagnetic centers are equally spaced from one another,

this would put an upper limit of 3.7 nm between them. We propose therefore that the inter-spin

distance is not homogeneous in sp-Si. That is, some paramagnetic centers could be less than 2

nm apart thus allowing exchange interaction between them. Figure 4-1 schematically depicts this

proposed distribution of paramagnetic centers in spark-processed silicon. Some spins are

assumed to form clusters (small inter-spin distance) and others are isolated (large inter-spin

distance) such that they do not participate in exchange interaction. Our results presented in the

previous chapter support such a model since the independent spins lead to paramagnetism which

we found to be present and the interacting spins within a cluster lead to a hysteresis which we

also found in sp-Si. In addition, to support our model we characterize the paramagnetic centers

using electron paramagnetic resonance. But first, we need to explain a few concepts using this

technique.




Note: we use spin or paramagnetic center interchangeably throughout this chapter.











** e
***
9
**
**
**


Paramagnetic centers


Clusters Diamagnetic matrix


Figure 4-1. Proposed paramagnetic centers distribution.

Energy


hu


gCLBBo


Microwave Absorbance


Bo


Figure 4-2. Energy levels of an electron at the resonance field.


Field









4.2 Electron Paramagnetic Resonance (EPR) Concepts

To perform an electron paramagnetic resonance experiment, we place a sample containing

unpaired spins in a resonant cavity which itself sits in the center of a large electromagnet. In

addition to being exposed to a magnetic field, microwaves are directed towards the sample inside

the cavity (Figure E-1 in Appendix E). The microwaves have a very specific frequency of

9.75GHz for X-band EPR while the field is swept around 3.5 kG. The field splits the electron

energy in two, El= +V/2 g CLBBo and Et= /2 g CLBBo, where g is the Lande factor, CLB is a constant

called the Bohr magneton, and Bo the magnetic field. When the magnetic field is such that the

difference between the two energy levels is equal to the microwave energy we have resonance,

i.e. the electron absorbs the microwave photon. The resonance condition leads to the following

equation, AE = Ez Et =CBRB~o = hU, where h is the Planck constant and v is the microwave

frequency. The absorption is maximal at the resonant condition, Bo = hU/gCRB. Since, CLB, h and v

are constants; the resonant field depends on the g-factor. This factor depends on the environment

of the paramagnetic center studied. It is used as an identifier for a particular type of magnetic

center. Figure 4-2 shows the resonance conditions.

In practice, modern EPR instruments use field modulation to record a spectrum. Field

modulation adds a small alternating field to the large static field. This small field is about 1

Gauss in our case while the large field is in the 3000 to 4000 Gauss range. The modulation

allows better sensitivity by using lock-in amplification. In addition, instead of directly observing

the absorption we measure its first derivative.

In the next section we explain how spectra are decomposed into independent factors which

are then analyzed individually to characterize the studied material.










4.3 Characterization of Continuous Wave Electron Paramagnetic Resonance Spectra

The EPR spectrum of spark-processed silicon is complex. It contains several features

which need to be separated before each individual component is studied. To study sp-Si EPR

spectra we use a mathematical function to model the absorption. But first, we need to explain the

mathematical function. Figure 4-3 schematically depicts our deconvolution scheme.

1 type of paramagnetic 2 types of paramagnetic
Microwave center centers
Absorbance











1st derivative
(Observed) Maue

Deconvolute











A I 'B
Field Field
Bo



Figure 4-3. Lorentzian distribution and 1st derivative of electron microwave absorbance as a
function of the magnetic field. A) one type of paramagnetic center. B) two different
types of paramagnetic centers (red curves) and their deconvolution (blue and green
curves).









When only one type of paramagnetic center is observed the model is simply the first

derivative of a single line. The term line refers to a very sharp peak characteristic of one

paramagnetic center. In addition, when two or more types of paramagnetic centers are observed

simultaneously, the model will be the sum of the first derivatives of two or more lines which is

due to the independent physical origin of the electron resonance for each type of center. Each

line is characterized by a mathematical function. In the case of sp-Si we use a Lorentzian

distribution but other functions are also commonly used such as Gaussian or Dysonian

distributions. The type of distribution is characteristic of the excited spins. For example highly

oriented pyrolitic graphite displays a Dysonian behavior, which is discussed in the next chapter.



The equation for a normalized Lorentzian distribution is: fo-r (x) = 1 2weeEi
(~x -x)2+ )2

the full width at half maximum, and xo is the center of the line. This distribution is normalized


using the following condition: /xo-(w)r (xd= 1. Our model for one line is y=Axf(x), where A is

the area under the curve. We call it the amplitude. Under specific conditions, it is proportional to

the number of paramagnetic centers. The first derivative of the Lorentzian distribution is defined

S1 F(x-xo)
as: fxo~r (x) = 2. In Spark processed silicon we observe two types of
(x -xo>2 +(2

paramagnetic centers and therefore our full mathematical model for the absorption is:

y = A, f ~, (x)+ A2 x]2 2 (X) Where x is the magnetic field. Each type of paramagnetic center is

characterized by an amplitude (A), a center field (xo) and a line width (T). We call our model

"two-Lorentzian". Figure 4-4 displays an EPR spectrum for spark processed silicon measured at

room temperature and a two-Lorentzian model. We found a very good agreement between the











model and the experimental data, where the coefficient of correlation is better than 0.98. The full


justification of our model will be discussed later in this chapter. First we need to identify each of


the paramagnetic centers observed in the spectrum. This is done by calculating the g-factor from

the Lorentzian model and comparing it with literature data. For a precise identification, a known


standard, DPPH (2,2-Diphenyl-1 -Picrylhydrazyl), is used as a reference point for the center field.


The standard and a sp-Si sample were measured at the same time in the EPR system thus


virtually eliminating instrumental errors.


1200

1000 -

800-

600 -
Proportional
40- defect densii

200-



-200-

-400-

-600 -

-800-

-1000
3350 3355


Proportional to line width
'M ~


Inversly proportional to g-factor


Sample name:
NSP12E 001


3360 3365 3370 3375 3380
Field (Gauss)

-Data -Model -Deconvolution


3385 3390 3395 3400 3405



1 -Deconvolution 2


Figure 4-4. Electron paramagnetic resonance spectrum of spark-processed silicon (back line) at
room temperature with its double Lorentzian 1st derivative model (red). For clarity the
deconvoluted curves are plotted in green and blue. Experimental parameters, power =
0.6331 mW, power attenuation = 25 dB, modulation field = 1 G, time constant = 10
ms, detector gain = 60 dB, temperature = 300 K.



































































Figure 4-5. Electron paramagnetic spectra of spark-processed silicon along with DPPH reference
standard (black line). Its model plotted in red is deconvoluted in three sub-models
(green, yellow and blue curves). Experimental parameters, power = 0.6331 mW,
power attenuation = 25 dB, modulation field = 1 G, time constant = 40 ms, detector
gain = 70 dB, temperature = 300 K.


Figure 4-5 displays the spectrum of sp-Si along with the DPPH standard. Using a three-

Lorentzian model (correlation coefficient = 0.986) we obtain three resonant fields, two from sp-


Si and one from DPPH. The published g-factor39 for our standard is 2.0036. From the resonant


condition equation presented in the previous section (gCLBBo = hU), we calculate the microwave


frequency to be ucal= 9.75044GHz. Then, using the same resonance condition equation with the

calculated frequency and the resonant field found for spark processed silicon from our


Lorentzian model we calculate two g-factors, gl = 2.0050 and g2 = 2.0013.


4000 -


3000 -

2000 -


1000 -


0-

-1000 -


-2000 -


-3000 -


-4000 -

-5000 -


345(


0 3455 3460 3465 3470 3475 3480 3485 3490 3495
Field (Gauss)

-Data Deconvolution 1 Deconvolution 2 Deconvolution 3 model


3500









Using the extensive literature40-47 On paramagnetic centers in silicon-based material, we

identify the first paramagnetic center with a g value of 2.0050 to stem from silicon unpaired

bond, backboned by three silicon atoms as schematically represented in Figure 4-6; it is called D

center. From literature41-4 the D center g-value varies between 2.0050 and 2.0055. In addition

the paramagnetic center with a g-value of 2.0013 is attributed to a silicon unpaired bond,

backboned by three oxygen atoms; it is called E' center. The E' center has many variations40

stemming from different precursors in SiO2 based material, but they all have g values between

2.0000 and 2.0018. Spark processed silicon is a nonstoiechiometric silicon dioxide doped with

nitrogen28 (SiOx:N) and therefore finding E' and D center is acceptable.



Si I O



Si Si n l~Si O



Si IO


g-factor = 2.0050 g-factor = 2.0013


Figure 4-6. Nature of spark-processed silicon paramagnetic centers.

It is to be noted that any impurities such as iron, nickel, or cobalt, which could cause a

magnetic hysteresis may absorb microwaves as well and therefore may be identified using the

same method as in the identification of paramagnetic centers in sp-Si. They would possess,

however, different g-values than those found here. No characteristic absorption from these

elements was found in spark processed silicon.










The resonant field has helped us to identify the paramagnetic centers but we have not

justified yet why our model is correct. To verify that the different types of paramagnetic centers

are truly independent from one another in sp-Si, we conducted a power saturation experiment.

The amplitude, as defined previously, is linearly dependent on the square root of the microwave

power44. This relationship is valid for small power values. When the power gets high enough the

amplitude saturates. Figure 4-7 displays the amplitude of the D centers versus the microwave

power.














O 0 1 1 6 1 02

Poe (W


Fiue47 mltd fDpaaantccnesa unto fmcoaepwr


In ore ofn h auainpitw is lo h mltd safnto ftesur











tgrend defne the saturation point. In the caeothDenters as poe greatr thn 0.2 mWroav (30










dB attenuation in our spectrometer) is enough to saturate the paramagnetic centers. Above the

saturation point, the amplitude is no longer proportional to the number of spins.


O 0.5 1 1 .5 2 2.5 3 3.5 4 4.5 5
Power1/2


Figure 4-8. Amplitude of D paramagnetic centers as a function of the square root of the
microwave power (dots). A linear trend is fitted for the lowest power data points
(R2=0.995).

We conducted a similar study for the E' centers as depicted in Figures 4-9 and 4-10. A

saturation power of 0.06 mW (35 dB attenuation in our spectrometer) was found. Knowing the

saturation point is not only important for comparing samples or spectra from the same sample at

different temperatures, it is also important to justify our two-Lorentzian model. Since the

saturation points are different for each of the observed features in a sp-Si spectrum, they are not

stemming from the same physical origin and therefore are independent. This independence

justifies that our model uses the sum of two independent lines. Figure 4-11 shows schematically











how the amplitudes of the D center and the E' center responded differently to the microwave


power.


04


0 35












0 00 4 00 8 01 01 4 01 8 02 02

Poe (mW


Fiuel 4-.Apiueo 'prmantccnesa ucto fmcoaepwr
Inadtoteln it fec ftetoosre etrsd o aetesm










beaioure with respliue tof te' aaantccnesa uci microwave power a eni iue41.Th etr'ln it




does not vary with microwave power, while the E' centers' line width is linearly dependent on

the log of the power which is explained in the next paragraph. The different behaviors of the E'

and D center are characteristic of their independent physical origin and justifies our two-

Lorentzian model.



















1.5







0.5







-0.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Power1/2



Figure 4-10. Amplitude of E' paramagnetic center as function of the square root of the
microwave power (dots). A linear trend is fitted for the lowest power data points
(R2=0.995).

Eaton and Eaton48 have developed a power saturation model which we apply to sp-Si. The

ax P1/2
saturation model48 is defined as: ampylitude = b/2 Where P is the microwave power, at is a
(c + P)

proportionality constant, c is a constant related to the power at half saturation and b is an

exponent which depends on the homogeneity of the line. The exponent constant b is an important

factor. In the extreme cases when b =1 we are in the inhomogeneous limit and when b=3 we are

in the homogeneous limit. In the case of sp-Si we plot and compare the models (b=1 and b=3) for

each of the paramagnetic centers in Figure 4-13 and 4-14. In the case of the D centers, the data is










very well describe (R2=0.998) by the inhomogeneous case while for the E' centers the model

matches the data well for the homogeneous case.

Amplitude
Paramagnetic center 1
Saturation point g-factor = 2.0050








Paramagnetic center 2
g-factor 2.0013








Microwave Power


Figure 4-11. Saturation effect observed for the two paramagnetic centers in spark-processed
silicon.

For comparison purposes we also plotted the other models on each of the graphs to visually

convince ourselves which model (i.e. which b value) works best. It can be added that this

conclusion is further confirmation that both EPR lines come from different paramagnetic centers.

Finally, the next figure is dedicated to confirm that the Lorentzian equation is the best

choice for modeling sp-Si EPR spectra. Figure 4-15 displays the comparison between sp-Si data

and two models best fit, Gaussian and Lorentzian. Both models were best fitted using the

software OriginPro 7.5.

In conclusion, we have presented several validation points to confirm the Lorentzian model

of sp-Si EPR lines and using this model we have identified the paramagnetic centers present.



























--
--
--


-3.5


0


-3 -2.5 -2 -1.5 -1

Log( Power (mV


-0.5 0 0.5 1 1 .5


9 D center line width E' center line width



Figure 4-12. Line width as a function of Log (power) for spark-processed silicon.


7.E+06


6.E+06


5.E+06


S4.E+06


Ei. 3.E+06


2.E+06


1.E+06


0.E+00
0 2 4 6 8 10 12

Power (mW)


14 16 18 20 22


+ Amplitude -Model b=1 Model b =3


Figure 4-13. Amplitude of D paramagnetic centers as a function of microwave power (dots).
Two saturation models are fitted to the data (solid lines).





30000


0002 004 006 008 01 012 014
Power (mW)

Amplitude -Modelb=1 -Modelb =3



Figure 4-14. Amplitude of E' paramagnetic centers as a function of microwave power for sp-Si
(dots). Two saturation models have been fitted to the data (solid lines).


-1500
3330


3340 3350 3360 3370
Field (Gauss)


3380 3390 3400


Data -Gaussian model -Lorentzian model



Figure 4-15. Electron paramagnetic resonance spectra of spark-processed silicon at 4.2K (black
line) and two possible models: Gaussian based (blue line) and Lorentzian based (red
line). Experimental parameters, power = 0.002 mW, power attenuation = 50 dB,
modulation field = 1 G, time constant = 20 ms, detector gain = 70 dB, temperature =
4.2 K.










We can now concentrate on characterizing the paramagnetic centers, compare the results

with the magnetization obtained from our SQUID and validate our quasiferromagnetic model.

4.4 Electron Paramagnetic Resonance Parameter versus Temperature

The temperature dependence of the sp-Si EPR spectra is very useful. First, the amplitude

of the EPR lines is proportional to the number of spins, as long as we are not saturating the

signal .


5 0E05
Settings Settings Settings
50dB-70dB; 40dB-60dB | 30dB-70dB









1 0 +05


1 0E+05




0 20 40608 10 2 106






Temperature (K)


Figure 4-16. Amplitude of D centers versus temperature. The data points above 40K have been
divided by 10 to account for the change in gain setting. The gain is changed to keep
the signal in the linear regime.

Since we have performed a saturation experiment we now know in which power range we

have to measure our data. Also, the magnetization of independent spins is proportional to the

number of spins. Thus, the amplitude of the EPR absorption line is proportional to the

magnetization as long as these two assumptions are met. In addition, the temperature dependence











of the line width will be useful for comparison with pulsed EPR experiments, which will be


presented in a later section. We present, now, the temperature dependence of the amplitude, line

width and g-factor all together of the D and E' centers present in sp-Si at low temperature and

then high temperature.


4 OE+05


3 5E+05


3 OE+05


2 5E+05


2 OE+05


<"1 5E+05


1 OE+05


5 OE+04


0 OE+00 iL
0 00


0 02 0 04 0 06 0 08 0 10 0 12 0 14 0 16 0 18 0 20 0 22 0 24 0 26
1/Temperature (K^1)


Figure 4-17. Amplitude of D centers versus inverse temperature (dots). The data points below
0.025K1 have been divided by 10 to account for the increased gain. A linear trend is
fitted to the data (solid line).

4.4.1 Low Temperature 5 to 300K

In order to study each paramagnetic center type we continue to use our two-Lorentzian

model and apply it at each temperature. Then the modeled amplitude, line width and g-factor can


be plotted as a function of temperature.

The amplitude versus temperature is plotted in Figure 4-16 for the D centers. One can

observe that the amplitude increase as the temperature decrease. In order to prevent saturation,











the microwave power was decreased and the detector gain increased. Three different settings


were used and the amplitude was multiplied by the proper coefficient to account for mismatches


between the microwave power and the signal gain scales. Furthermore, the amplitude is plotted


against the inverse temperature in Figure 4-17. A linear trend is fitted to the data with a

correlation coefficient of 0.99.


35E+04


Settings Settings
50dB-70dB, 40dB-60dB


Settings
30dB-70dB


3 OE+04



2 5E+04



ed2 OE+04



1 5E+04



1 OE+04



5 OE+03



O OF+On


20 40 60 80 100 120 140 160

Temperature (K)


Figure 4-18. Amplitude of E' centers versus temperature. The data points above 40K have been
divided by 10 to account for the increased gain.

In the case of independent spins, the magnetization is simply proportional to the measured


amplitude and therefore inversely proportional to the temperature. The experimental results


suggest that the EPR amplitude follows the Curie law. It could be argued that this relationship


demonstrates the independence of the paramagnetic centers and therefore deny our cluster


model. But, it has been calculated49 that for a ratio of independent spins over spins within











clusters of 50%, the magnetic susceptibility is almost observed as coming from independent


spins only. First, we believe that spins in sp-Si are mostly independent, as shown by the observed

Curie law. In addition, we suggest that the magnetization coming from the clusters of spins is


small in comparison to the magnetization from the independent spins. Similar conclusions are


drawn for the E' centers. Figure 4-18 and 4-19 present the amplitude of the E' centers as a


function of the temperature and inverse temperature, respectively.


3 5E+04



3 OE+04



2 5E+04



ed2 OE+04



S1 5E+04



1 OE+04



5 OE+03


0 OE+00 iL
0 00


0 02 0 04 0 06 0 08 0 10 0 12 0 14 0 16

1/Temperature (K^1)


0 18 0 20 0 22 0 24 0 26


Figure 4-19. Amplitude of E' centers versus inverse temperature (dots). The data points below
0.025 K1 have been divided by 10 to account for the increased gain. A linear trend is
fitted to the data (solid line).

Additionally, the line width for both centers is plotted versus the temperature in Figure 4-


20. In both cases the line width is essentially temperature independent. The line width depends










on different relaxation mechanism and a full account of that dependence will be presented in the

pulsed EPR section of this chapter.


14

***


10


60 80 100
Temperature (K)

4 Line width 1 m Line width 2


120 140 160


Figure 4-20. Line width of the two paramagnetic centers present in spark-processed silicon
versus temperature in the low temperature range. Line width 1 corresponds to the D
centers and line width 2 corresponds to the E' centers.

The characterization of the centers is completed with the temperature dependency of the g-

factors. Figure 4-21 presents the g-factor for each center as a function of temperature. For the D

centers the g-factor does not depend on the temperature while for the E' centers the g-factor has

a small temperature dependency. We believe that the main reason which explains this small

dependence is associated with the difficulty of fitting the Lorentzian equation. The signal from

the E' centers is much smaller than the D centers and therefore modeling is a more difficult

process since both signals are collected together and interfere with one another.










** *
,rr rr~ r r


....1.1;~ _~


2 007


-

-


2 006

2 005



O


60 80 10
Temperature (K)
g-factor 1 m g-factor 2


120 140


Figure 4-21. Spark-processed silicon paramagnetic centers g-factor (uncalibrated) versus
temperature. The g-factor 1 corresponds to the D centers while the g-factor 2
corresponds to the E' centers.
4.4.2. High Temperature 300 to 800K
While the low temperature EPR equipment was readily available, we were not equipped at

first for high temperature measurements. I designed and assembled a high temperature oven for

the EPR spectrometer which allows stable temperature up to 600 K. The temperature can be

pushed up to 700 K if precision is not essential. More details can be found in the Appendix B

about the design and working condition of this oven. For the highest temperature measurements

we collaborated with Dr. Causa from the Centro Atomico Bariloche in Argentina, who is

equipped with a commercial high temperature EPR cavity.







































700 750 800


Figure 4-22. Spark-processed silicon paramagnetic centers g-factor versus temperature. The g-
factor 1 corresponds to D centers while the g-factor 2 corresponds to E' centers. The
g-factor 1 was measured again after cooling back to room temperature (blue triangle)
and the same value was found as before the heating (green diamond).

The same analysis method for the high temperature EPR spectra as for the low temperature


spectra of sp-Si was used, meaning that we continue to use a two-Lorentzian model.


First, we look at the g-factor temperature behavior. Figure 4-22 displays g-factors for both


paramagnetic centers. The g-factor of the E' centers is temperature independent in this


temperature region. On the other hand the g-factor of D centers is affected by the temperature.


Both g-factors are deconvoluted from the same spectrum. If the temperature dependence was due


to the deconvolution method we would observe both g-factors to have the same temperature


dependency. But, it is not the case. The scatter around the average g-factor of the E' center give


Cooling direction


-


0


2 006 -





2 0044





2 0052



^2 0028
30l


Heating direction


350 400 450 500 550 600 650

Temperature (K)

g-factor 1 m g-factor 2 A g-factor 1 after cooling









an estimate of the error on the measurement. But a much larger variation of the D centers g-

factor is observed. Therefore, we conclude that the g-factor of the D centers is temperature

dependent. It should be noted that after cooling back to room temperature the g-factor of the D

centers reverts to its original value and therefore the process is reversible. Also, it only affects

the g-factor of D centers and not the g-factor of E' centers. We suggest that thermal expansion

could be one of the effects responsible for the g-factor temperature dependence. Since the E'

centers are related to oxygen rich defects we assume that they are located in the SiO2 matrix. The

D centers are only related to silicon atoms and therefore we suggest that they are likely to be

located in or at the surface of silicon clusters within the SiO2 matrix. Specifically, the thermal

expansion coefficient of each of these materials, that is, SiO2 and silicon are very different. The

thermal expansion coefficient of SiO2 is Very small compared to the one of silicon This could

induce changes on the bond length between silicon atoms, therefore affecting the electron

orbitals and consequently the g-factor of the D centers.

It should be noted in passing that the concept of silicon clusters imbedded in a SiO2 matrix

has been studied and documented by our group using comparison between optical properties and

computer molecular modeling'o as well as by direct transmission electronic microscopy

observation of silicon nanocrystals51

Secondly, the study of the line width as a function of the temperature does not show any

influence as displayed in Figure 4-23. For both centers the line width is temperature independent.

Finally, the amplitude variation of the EPR line intensity for each defect as a function of

the temperature is studied. Using our high temperature apparatus we observed a slight decrease

of the D and E' centers amplitude as a function of temperature in the 300 600 K range (results

not shown). Due to the strong decrease in sensitivity of our cavity at temperatures above 600 K










we felt like our data was not reliable above this temperature. This prompted the collaboration

with Dr. Causa who has measured the EPR spectra of sp-Si for us. Her EPR system is designed

to work at temperatures up to 1300K with no loss in sensitivity. Once the spectra were received,

I used the same two-Lorentzian model analysis to calculate the amplitude of the E' and D

paramagnetic centers.


WH


12


10


350 400 450 500 550 600
Temperature (K)

Line width 1 m Line width 2


650 700 750 800


Figure 4-23. EPR line width of the two paramagnetic centers present in spark-processed silicon
versus temperature in the high temperature range. The line width 1 corresponds to D
centers while the line width 2 corresponds to E' centers.

Figure 4-24 displays the amplitude of the D and E' paramagnetic centers (that is the A

factor in the Lorentzian model) as a function of the temperature. In the case of the D centers, the

amplitude is steady up to 500 K and then decreases down to almost zero at 700 K. On the other

hand, the E' paramagnetic centers amplitude is not affected by the temperature between 580 and











780 K. At temperatures below 580 K the deconvolution with the two-Lorentzian model is not


possible because the E' center is too weak compared to the D centers amplitude.


1800000-

1600000-

1400000-

1200000-

1000000 -

800000 -

600000 -

400000 -

200000--

0-
250


300 350 400 450 500 550

Temperature (K)


600 650 700 750 800


Figure 4-24. Amplitude of D (blue) and E' (red) centers versus temperature for spark-processed
silicon in the high temperature range.

These results confirm our previous suggestion that the D and E' centers are not related to

one another. In addition, we previously suggested that the E' centers are located in the SiO2


amorphous matrix while the D centers are located in silicon nanocrystals or clusters. Therefore,

we propose that these two types of centers are not close to one another, adding another argument

to our theory of non-random distribution of paramagnetic centers.

At low temperature, we observed that the magnetization as well as the amplitude of the D

and E' centers were characteristic of the Curie law. But, at high temperature (that is about 300 K)

the measurements do not suggest a Curie law behavior but rather a behavior modeled with the

Weiss equation. This is shown in Figure 4-24, where a Curie law model is plotted and one can










see that the data does not follow that law. We suggest that the deviation from the Curie law at

high temperature can be explained by the decoupling of the interacting centers within clusters.

When the temperature is near the Curie point, the thermal energy is large enough to overcome

the exchange interaction between two spins. When this happen the two spins become individual

spins and now behave like independent paramagnetic centers explaining the non-zero amplitude

above the Curie point.



1.2






S0.8


S0.6


a,0.4


E Samp e Names:
S MSP120 T 1

CD 0
250 300 350 400 450 500 550 600 650 700 750 800
Temperature at sample (K)



Figure 4-25. Amplitude of D centers (blue dots) and Magnetization at 1000 Oe (green dots)
versus temperature for spark-processed silicon in the high temperature range. A
Weiss equation is fitted through both data sets (solid curves). For comparison a Curie
law curve is plotted (black dash).

The amplitude data of the D centers was also compared to the Weiss equation to evaluate

the Curie temperature. We followed the same method previously described in chapter 3 (section

3.2.3). A Curie temperature of 710 K was found. Figure 4-25 displays the D centers amplitude as

a function of temperature along with its Weiss model curve. In addition, the magnetization of a










similar sp-Si sample as a function of temperature is plotted on the same graph along with its

Weiss model curve (previously presented in section 3.2.3). The comparison between the two sets

of data suggests that the D centers are at the origin of the magnetization behavior of sp-Si for

temperature above 300 K.

It could be argued that the Curie temperature evaluated from the Weiss model with the

magnetization data is too different from the one found with the data stemming from EPR, but, we

could attribute the differences to the type of instrument, which inevitably lead to some

discrepancies, and to the samples being prepared in a similar manner but not being exactly the

same. For example, the EPR technique is not sensitive to diamagnetism and species with an

integer total spins while the SQUID magnetometer is.

It should be noted in passing that the data obtained from Dr. Causa and our data obtained

with our own laboratory made equipment are consistent with one another for temperatures up to

600 K. Above that temperature our data on amplitudes of the E' and D centers is no longer

reliable.

In conclusion, the continuous wave EPR has allowed the identification and separation of

two paramagnetic centers. Also, the EPR spectral analysis and the comparison with the

magnetization of sp-Si at high temperature are consistent with our paramagnetic center

distribution model.

Continuous wave EPR allows the indirect measurement of the density of the paramagnetic

centers, but the direct method by pulsed EPR is preferred. The main reason for not using cw-EPR

is the need for a precise measurement of the sample volume, which turns out to be extremely

difficult for sp-Si. Pulsed EPR is a better technique for measuring the density which leads to the

distance between paramagnetic centers. But it requires the characterization of the observed










signals which is more complex, as this technique is more complex than cw-EPR. The next

section focuses on that method.

4.5 Characterization of Pulsed Electron Paramagnetic Resonance

Our goal in using pulsed EPR is to calculate the density of the paramagnetic centers at the

local level and therefore calculate the maximum separation distance between spins. This will

then be used to complement the model proposed to explain quasiferromagnetism. We separate

this part of the chapter into several sections to facilitate its understanding. In the first section, we

present the relaxation rates measured on sp-Si and information extracted from them. In a

subsequent section we propose to separate the centers by relaxation rates. Then, we measure the

relaxation rates leading to the local density of spins.

4.6 Relaxation Rates

In the pulsed EPR world there are many ways of acquiring a signal. In our case, we are

very much interested in the basic spin-lattice and spin-spin relaxation rates of sp-Si paramagnetic

centers.

4.6.1 Spin-Lattice Relaxation Rate

The spin-lattice relaxation rate is also known as T1 and longitudinal relaxation. In Figure 4-

26 we present the spectrum from which we measure T1. The detected intensity is plotted as a

function of time. In such experiments the intensity is expected to decay exponentially with time

at a rate of 1/T1. But, in the case of sp-Si bi-exponential decay functions are necessary for a good

match to our data, as seen in Figure 4-26. We called the exponential decay times T1 and T1'. The

model equation used is: Intensity(t) = Aze-tl + A e-"T' where Al and Al' are the exponential

amplitudes of each of the decays.











1000


500





500


E 1000


-1500


2000





-3000
0 2 4 6 8 10 12 14 16
Time (ms)



Figure 4-26. Intensity versus time for a spin-lattice relaxation rate experiment of spark-processed
silicon (black line), one-exponential decay model (green line) and bi-exponential
decays (red line). Experimental parameters (inversion recovery), center field =
3455.5 Gauss, shot repetition time = 408 ms, shot loop = 1, pulse length = 16 ns and
step is 16 ms.

In a subsequent experiment we measure T1 and T1' as a function of temperature. The

results are presented in Figure 4-27. In both cases the relaxation rate follows a direct process up

to 60 K. A direct process is characterized by the proportionality between T1 and the

temperatures. In addition above 60 K and according to the same authors, T1 and T1' follow a

hopping process. We are mostly interested in the T1 processes to help understand the physical

origin of the line width in the cw-EPR. It must be added in passing that the line width in cw-EPR

can have several origins and knowing the behavior of the spin-lattice relaxation rate as a function

of the temperature is necessary to meet this goal.





















-1 Direct process (slope = 1) Hopping process










S11 12 13 14 15 16 17 18 19 2 21 22 23 24
Log (temperature(K))

log(1/T1) log(1/T1')


Figure 4-27. Spin-lattice relaxation rates versus temperature for spark-processed silicon.

4.6.2 Spin-Spin Relaxation Rate

The spin-spin relaxation rate is very important to us as it is the first step towards measuring

the density of defects. This relaxation rate is also called T2 Or transverse relaxation rate. But T2 is

obtained indirectly from the phase memory time (Tm). By running an echo decay pulse EPR

experiments We Obtain intensity versus time curves. The exponential decay constant is Tm. The

relationship between Tm and T2 is given by the following equation:

1 1
-+ f(Power, concentration) where concentration is the density of spins in a given sample
T 72

and where the function of power and concentration is a constant for a given sample at a given

power. In this section, it is the case, that is, we use the same sample and use the same input

power setting for all measurements throughout this section, therefore the relationship becomes










1 1
simply: + constant Figure 4-28 displays the intensity as function of time of sp-Si. Once
To T2

again, the data can only be fitted with bi-exponential decays.


12000



10000



8000


6000


4000



2000 .




0 100 200 300 400 500 600 700 800 900 1000
time (ns)



Figure 4-28. Intensity versus time for a spin-spin relaxation rate experiment on spark-processed
silicon (black line), one-exponential decay model (green line) and bi-exponential
decays (red line). Experimental parameters for the 2 pulses echo decay, center field =
3467 Gauss, shot repetition time = 51 ms, shot loop = 2, pulse length = 16 ns and
step = 4ns.

For information, the model equation used is: Intensity(t) = A~et-t + A ~e-t"" where A2 and


A2' are the exponential amplitudes of each of the decays. If we use only one exponential decay

the fit is poor as can be visually observed in the graph.

In the next experiment, we measured Tm and Tm' as a function of temperature. The results

show essentially no temperature dependence, as seen in Figure 4-29. According to Eaton and






































*11


Eaton54 the line width can be calculated from the following equation:


7 T2 2


and y the electron gyromagnetic ratio. In the case of sp-Si the second term is much smaller than

the first one and therefore the line width depends only on T2. Since T2 is directly related to Tm,

the line width depends on Tm only. This is confirmed experimentally since the line width and Tm

have the same temperature dependency.


150 175 200 225


25 50 75 100 125
Temperature (K)
T2 m T2'


Figure 4-29. Spin-spin relaxation rates versus temperature for spark-processed silicon.

In brief, we have found two spin-lattice relaxation rates as well as two spin-spin relaxation

rates. It is of great interest to figure out which rate is related to the D centers and which one is

related to the E' centers. This is of maj or importance since this will allow us to perform the

separate measurement of the density for each type of centers.





















































3430 3440 3450 3460 3470 3480 3490 3500
Field (Gauss)
--Serles1 Model Deconvolution 1 --Deconvolution 2


Figure 4-30. Field sweep pulsed electron paramagnetic resonance of spark-processed silicon
(black curve). A two-Lorentzian model is fitted to the data (red curve) and each of its
individual components (green and blue curves). Experimental parameters, power
attenuation = 10 dB, shot repetition time = 20 ms, shot loop = 30, pulse length = 30
ns.


4.7 Separation of Rates to Identify Paramagnetic Centers

The processes involved in the relaxation of the spins after being excited by microwaves are

strongly dependent on the pulse length and pulse power. Therefore, in order to assign the two

defects observed with cw-EPR according to their own relaxation rates, we use several

experiments. First we measured an echo detected field sweep pulse spectrum. The data for sp-Si

is presented Figure 4-30. This is similar in principle to the concept presented at the beginning of

this chapter in Figure 4-3. A double Lorentzian line model is used to deconvolute the data,

showing again that two paramagnetic centers are present in the EPR signal. The characteristic

values (center field, line width) are presented in Table 4-1.

80000

70000

60000

50000


:S~a3b~-~' /


1000


~





On the other hand, when fitting the bi-exponential decay model to the phase memory time

experiment we are capable of extracting the exponential proportionality parameters (A2 and A2 ).

Since these parameters are related to the relaxation rates and we want to assign them, we

measured these parameters as a function of the magnetic field in order to compare them with the

field sweep curve obtain previously (Figure 4-30).




::I:: 5


5 OE+04


3440 3445 3450 3455 3460 3465 3470 3475 3480 3485 3490
Field (Gauss)
A2 m A2' A2 model A2' model


Figure 4-31. Amplitude of exponential decays in spin-spin relaxation rate experiments versus
field for spark-processed silicon (dots). Lorentzian distribution models have been
fitted to the data (solid lines) with long pulse (200 ns equivalent to 1.8 Gauss).

Figure 4-3 1 displays A2 and A2' aS a function of the external magnetic field. Lorentzian

line models are fitted to validate the data. Their characteristic values are summarized in the Table

4-1. If we compare them with the field sweep experiment we are able to assign the A2 with the D

centers and A2' with the E' centers.









Table 4-1. Characteristic values of echo detected Hield sweep and amplitude of exponential decay
as a function of magnetic Hield.
Echo detected Hield sweep Exponential decay amplitude
Con
stan

HD" 3462 3463
[Ga
uss]
MHD 10 12.5

[Ga
uss]
HE' 3467 3465
[Ga
uss]
MHE' 9 11

[Ga
uss]
Note: Ha is the center Hield and MH is the line width.

In conclusion, we are able to separate the paramagnetic centers using pulsed EPR which

allows the calculation of the density of centers for each type of defects (D and E') as described in

the next section.

4.8 Spin Density

The concept used to calculate the spin concentration was presented by Eaton and Eaton54

and was applied to y-irradiated Sio2, a very close cousin of sp-Si (composition and structure

wise). We have found this method to be more reliable than other methods such as the

"comparative technique" using cw-EPR for example. The comparative technique has been found

to be a lot less accurate than the method applied by us due to great difficulties in measuring the

volume of the sp-Si material.

























































---------- -------*1 I


The calculation of the concentration is based on the following relationship


-+ ~i2g~, sin2 Pw r Where the only constant which has not been
Tm T2 9 25 Poweg,


1 1
presented yet is C, the density of spins. Figure 4-32 shows and as function of the power
T Tm



andFiure4-3 dspay versus sin2 Poer). The slope of the curve is proportional
Tm 2 Power,


to the concentration of defects and the y-intercept is the inverse of T2. In the case of sp-Si, we

found the concentration of D centers to be 1.4 x 1019 Cm-3 and the concentration of the E' centers


to be 0.5 x 1019 CA-3. The total density of paramagnetic centers is therefore 1.9x 1019 Cm-3


0.021


0.018


0.015


S0.012

-1-



0.006


0.003


0


0.025


0.075


0.1
Power (W)

* 1/Tm a 1/Tm'


0.125


0.175


Figure 4-32. Phase memory time for each paramagnetic center measured as a function of the
input power of spark-processed silicon.










We have measured this density on different samples to investigate the repeatability and we

found all these values to be within 20% of the average (Figure 4-34). The D center average

density is 1.6 x1019 Cm-3 while the E' center average density is 0.5 x1019 Cm-3, leading to an

average total density of 2.1 x1019 Cm-3

It should be noted that in Chapter 3 we reported that the magnetization was dependent on

the spark frequency (Figure 3-6). Because we only measured an average density of paramagnetic

centers, no link can be drawn between the magnetization and the density. Only the knowledge of

the distribution would allow a comparison between the magnetization and the density of spins.


0.005

0.0045

0.004

0.0035

0.003

S0.0025

0.002

0.0015

0.001

0.0005


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1


rPower,
2Powero~


Figure 4-3 3. Inverse phase memory time (1/Tm') versus sin2(x/2 x(power/powero)1/2) Of spark-
processed silicon (dots). A trend line is run through the data with a correlation
coefficient of 0.998.









If we assume that all the paramagnetic centers are equidistant from one another, then the

inter-spin distance is equal to the cubic root of the inverse of the total density. This way, we

found a maximum inter-spin distance of 3.7 nm (or 3.6 nm if we use the average density

calculated from Figure 4-34). This result is very much within the range of values reported by

Eaton and Eaton on y-irradiated quartz54. As mentioned in the first section, it is usually assumed

that the maximum distance between spins which allows exchange interactions is 2 nm. But, it has

been shown52 that sp-Si is composed of silicon nanocrystals embedded in the SiO2 matrix.

Therefore, we suggest at first, that the distribution of paramagnetic centers is not homogeneous

which is also suggested but the heterogeneous structure. Secondly, we suggest that the D centers

are located on the border or inside the silicon nanocrystals. These nanocrystals observed by

Shepherds1 have sizes ranging from a few to tens of nanometers. If the paramagnetic centers are

located in or around such nanocrystals it is possible for their inter-spin distance to be less than 2

nm and therefore exhibit exchange interaction leading to the observed magnetic hysteresis.


































6 8 10 12 14 16 18 20 22 24
Spark frequency (kHz)
Total Density D centers Density A E' centers density


E 2.5




.2

Tj 1.5


Or


0


Figure 4-34. Density of paramagnetic centers as a function of the spark frequency for spark-
processed silicon. The density of D centers is represented by squares while the
density of E' centers is represented by triangles. The total density is represented by
diamonds.

It should be added in passing that a technique known as double quantum coherence EPR

which allows the measurement of the spatial distribution of paramagnetic centers developed by

Freed48 was tried on sp-Si but we were unsuccessful due to limitation of the technique itself.

Still, it may be possible in the future, once the EPR sensitivity has been improved, to measure the

distribution of centers.

It should be noted in passing that hydrofluoric acid etching (49% pure) for several minutes

did not change the EPR signal shape or amplitude. We concluded that the measured

paramagnetic centers are not surface related.










4.9 Summary

In this chapter we successfully identified two paramagnetic centers believed to be present

in sp-Si, namely the E' centers and the D centers (Figure 4-6). Also, we successfully measured

the densities of each of the two centers to be 1.4x 1019 Cm-3 for the D centers and 0.5 x1019 Cm-3

for the E' centers. In addition, we have measured a Curie temperature of 710 K from the

amplitude of the D centers to be compared with a Curie temperature of 765 K measured from the

magnetization at 1000 Oe (Chapter 3). Finally, we presented a cluster model consistent with the

magnetization results and the paramagnetic centers distribution (Figure 4-1). Our arguments can

be summarized as followed:

* Sp-Si is not homogeneous, it is composed of Si nanocrystals embedded in the SiO2 matrix,

* D paramagnetic centers are likely to be located in or around silicon nanocrystalline regions,

* E' paramagnetic centers are likely to be located in the SiO2 matrix,

* The structure suggests an inhomogeneous distribution of inter-spin distances,

* Paramagnetic centers are less than 3.7 nm apart but they could be less than 2 nm apart,

* Exchange interaction is possible between paramagnetic centers if they are closer than 2 nm,

* The paramagnetic centers are not surface related,

* Positive exchange interaction explains the observed magnetic hysteresis in sp-Si.

* The magnetic response at high and low temperatures of the D centers and the magnetization

at 1000 Oe (Chapter 3) have a very similar behavior. They both follow the same laws.

In the next chapter we expand our model to other materials and therefore describe a full

class of materials as quasiferromagnets.









CHAPTER 5
FURTHER CONSIDERATIONS

While the two previous chapters deal with spark processed silicon magnetic properties and

its model, this chapter extends this model to other materials. Quasiferromagnetism was first

studied using spark processed silicon. Later, we found that other materials had similar magnetic

properties and therefore, we classified them as quasiferromagnets.

In this chapter we first present the work of Hack3 On the annealing effect of the magnetic

properties of spark processed silicon which further confirms the magnetic model proposed in the

previous chapter. Then, we discuss and present some of the magnetic properties of other

materials as well as why we classified them as quasiferromagnets. These materials include ion

implanted silicon into silicon, argon implanted into silicon; neutron irradiated silicon and highly

oriented pyrolitic graphite (HOPG).

5.1 Annealing of Spark Processed Silicon

In this section we report on the annealing effect of the magnetization as well as the

annealing effect of the electron paramagnetic resonance spectrum of spark processed silicon.

This work was performed by Jonathan Hack during his masters' thesis at UF. It was published

in 1997. This work proposed to link the magnetic hysteresis to paramagnetic centers.

Hack measured the magnetization of sp-Si at 0 and 1000 Oe as function of cumulative

annealing. First, he measured the magnetization of sp-Si as processed, and then after annealing at

500 K for 30 min in a nitrogen atmosphere and subsequently, at higher temperatures, up to 1300

K. The results are normalized to the as prepared samples (Figure 5-1). The magnetization

decreases as the cumulative annealing increases. Furthermore, the decrease is more pronounced

around 700 K. Finally, in the high temperature range (i.e. above 900 K) the remanence

magnetization decreases to zero at 0 Oe and the saturation magnetization (at field of 1000 Oe)










also decreases down to the diamagnetic value of the substrate. The hysteresis is destroyed (non-

reversible process) at the cumulative annealing temperature of 900 K while a small but not

negligible paramagnetic magnetization remains at 1000 Oe.


O

-0.2
300


400 500 600 700 800 900 1000 1100 1200 1300 1400
Annealing Temperature (K)

SRemanence A Magnetization (1000 Oe)


Figure 5-1. Magnetization at 0 and 1000 Oe of spark processed silicon as a function of
cumulative isochronal (30 min) annealing temperature.

In addition, he measured the electron paramagnetic resonance spectrum at each annealing

temperatures and extracted the peak to peak amplitude of the main line. The results are shown

Figure 5-2. The peak to peak amplitude is proportional to the number of defects present in the

sample as long as we are in none saturated regime as explained in the Section 4.3. The

normalized amplitude decreases as the temperature is increased in a similar manner as the

magnetization. In addition, the largest slope (strongest relative decrease) is found at 700 K as for

the magnetization. Finally, the EPR peak to peak amplitude decrease almost to zero at the

highest temperature as does the magnetization.




















1 04










0.


300 400 500 600 700 800 900 1000 1100 1200 1300 1400
Annealing Temperature (K)



Figure 5-2. Electron paramagnetic resonance peak to peak spectra line of spark processed silicon
as a function of cumulative isochronal (30 min) annealing temperature.

Hack concluded that the paramagnetic centers were at the origin of the observed magnetic

hysteresis of sp-Si. The pioneering work of Hack is the origin of this dissertation.

In my quasiferromagnetic model, I suggest that some paramagnetic centers are clustered

and thus, have a positive exchange interaction. If one anneals sp-Si, thus removing paramagnetic

centers, the clusters would decrease in size and therefore the magnetization would decrease as a

result. Eventually, their number would approach zero, and the clusters would disappear (leading

to a vanishing of the hysteresis).

We conclude that the observations of Hack are in general agreement with our proposed

quasiferromagnetism model.









5.2 lon Implanted Silicon

lon implantation is a very common process used in the semiconductor industry. In the

seventies KhokhloV19 Studied the EPR spectra of paramagnetic defects produced by the ion

implantation process. Since, some others have continued to study the EPR spectra of ion

implanted silicon but the magnetization itself has been left out. I have published for the first

time on the magnetic hysteresis at room temperature of silicon implanted into silicon and argon-

implanted silicon. We will review in this section the most relevant results from this publication.

The samples were prepared using a very low implantation current density (less than 10CLA/

cm2) as well as high doses (greater than @=1016 ionS/cm2) while the silicon substrate were kept at

room temperature by water cooling the stage. We believe that such processing conditions favor a

large defect density (preventing self-annealing during implantation). We suggest that ion

implantation would be an interesting area for further investigations, for example, to produce

quasiferromagnetic silicon and allow potential application of this material in the spintronics area.

It should be re-emphasized that SIMS spectra were perform on each type of the processed

samples. No ferromagnetic elements (Fe, Ni, Co, Mn...) could be found35.

Below, we present the magnetization response and then the EPR spectra of this material.

5.2.1 Magnetic Response of lon Implanted Silicon

The magnetization as function of the field was measured for argon-implanted silicon. The

results are shown Figure 5-3. Two magnetic hysteresis curves are presented, one for the sample

implanted at a dose of 2x1016 Cm-2 and one for implantation at a dose of 2x1017 cm-2. Both

hysteresis are observed at room temperature. In addition a silicon wafer was implanted using

silicon ions with a dose of 5 x1016 Cm-2. Again a hysteresis was observed at room temperature as

shown in Figure 5-4. These results are not expected from the classical theory of magnetism.

Once again, a new concept is needed: quasiferromagnetism.














6E-06




4E-06 L, f--_5=~--C
r


r,
r
2E-06

~


OE+OO




2E-06
.C ,
L r

-4 E-06
~ars[--
r


-6 E-06


-1000 -800 -600 -400 -200 0
Field (Oe)


200 400 600 800 1000


Figure 5-3. Magnetization as a function of the magnetic field strength at 300 K for silicon

implanted with argon ions. The solid red curve corresponds to an argon dose of

2x1016 Cm-2 and the dash green curve to a dose of 2x10'7 cm-2. The magnetization has

been adjusted for the diamagnetism of the substrate.


























-1 0E 000 -0 -60 -0 -20 0 20 40 60 80 1 0









Field (Oe)




Figure 5-4. Magnetization as a function of magnetic field strength at 3 00 K for silicon implanted

with silicon ions. The dose was 5 x1016 Cm-2. The magnetization has been adjusted for

the diamagnetism of the substrate.





















8000


4000




E 00


84000


Vr
-12000
3320 3330 3340 3350 3360 3370 3380 3390 3400
Field (Gauss)

-Model .Data


Figure 5-5. Electron paramagnetic resonance spectra of argon implanted into silicon at a dose of
2x1016 CA-12 (blue squares) and its Lorentzian model (solid red). Experimental
parameters, power = 2 mW, power attenuation = 20 dB, modulation field = 1 G, time
constant = 80 ms, detector gain = 55 dB, temperature = 5 K.

The measurements were taken at 5 K to reduce thermal noise. A Lorentzian line is use to

model the data. We found a very good fit between the model and the experiment (correlation

coefficient is 0.998). Since one line was enough to model the data we conclude that there is only

one type of defect in this material. According to KhokhloV19 and Gerasimenko55 the pertinent

paramagnetic defects are "VV centers" (silicon dangling bonds around voids). Similarly the

electron paramagnetic resonance spectrum of silicon-implanted silicon with a dose of 1016 CM2 a


r2 =0.9


5.2.2 Electron Paramagnetic Resonance of lon Implanted Silicon

The electron paramagnetic resonance spectrum of argon-implanted silicon at 2x 1016 Cm-2 is

displayed Figure 5-5.


ILUUU










5 K was measured and analyzed (Figure 5-6). In this case a two-Lorentzian model was necessary

to match the data. The g-factors are 2.0054 and 2.0023 respectively.


5000


4000


3000


2000


1000


0


-1000


-2000


-3000
3445


3455 3465 3475 3485 3495 3505
Field (Gauss)

-Model Data


3515


Figure 5-6. Electron paramagnetic resonance spectra of silicon implanted into silicon at a dose of
1016 CA-12 (blue squares) and its two-Lorentzian model (solid red). Experimental
parameters, power = 50 mW, power attenuation = 6 dB, modulation field = 1 G, time
constant = 80 ms, detector gain = 60 dB, temperature = 5 K.

They allows the identification of the paramagnetic defects to be silicon dangling bonds40

(D centers) and E' centers44 TOSpectively. We believe that the E' centers are located on the

surface of the substrate in the oxide layer. On a silicon wafer there is a natural silicon oxide layer

forming as long as the substrate is left in an ambient atmosphere. In addition, Tomozeiu44 has

shown that the g-factor of E' centers is slightly dependant of the thickness of the silicon oxide

layer. In our case, the thickness corresponds to the natural oxide formed at the surface.









The ion implanted silicon samples which we characterized have similar magnetic

characteristic as sp-Si, that is, a magnetic hysteresis loop at room temperature and paramagnetic

centers. Once again, these samples do not contain elements with d or f shell electrons and

therefore fits well within the quasiferromagnetic materials point of view. Overall, we suggest

that ion-implanted silicon materials seem to have the same magnetic behavior as sp-Si and

therefore can be explained by the same quasiferromagnetic model.

5.3 Neutron Irradiated Silicon

Neutron irradiated silicon samples were prepared following the same general ideas as ion

implanted silicon. We tried to manufacture the material with the largest possible density of

paramagnetic defects hoping that they would form interacting clusters. In this section we present

magnetization curve of neutron irradiated silicon. I have already published this work in 2006.

Thus, only a brief summary will be given here.

A piece of silicon wafer was exposed to thermal neutrons in the University of Florida

nuclear reactor for 12 hours. A 12-hour exposure equate to a dose of 4x1016 Cm-2. The

magnetization curve was measured at 10K, to reduce large noise, see Figure 5-7.

According to Jung and Newell56 weak magnetic interaction are observed between closely

spaced dangling bonds in neutron irradiated silicon. Jung measured a distance of 0.5 nm between

two particular types of dangling bonds in neutron irradiated silicon using an electron

paramagnetic resonance technique.

Magnetic hysteresis and weak magnetic interaction between paramagnetic centers

contribute to classify neutron irradiated silicon as a quasiferromagnet. Similarly to ion implanted

silicon, neutron irradiated silicon has the same magnetic characteristic as sp-Si and therefore

should be in the same magnetic class.













4 E-06 I













-4 E-06

~O E+II

-10 80 -0 40 -00 020 40 60 80 10
~Fel (Oe)-

Fgre57Mantztovessmgeifelsteghonetoiraitdslcnaadoef
4x01 CA2 h antztini dutdfr h imgeimoftesbtae h







Oncu e 57 agaeiain, IM specrs a weeti taken d on et a neutron irradiated sampl and no magnticds




elements (such as Fe, Ni, Co...) were found.

5.4 Highly Oriented Pyrolitic Graphite

In this section we present another material which we classify as quasiferromagnet. This

material is not based on silicon. Highly oriented pyrolitic graphite (HOPG), an allotrope form of

carbon, was purchased from Mikromash57. This material is processed from pure graphite at

temperatures of 3,0000C under pressure. This material was previously known for its unusual

magnetic properties which triggered our interest. In this respect, we present the magnetization

measurements as well as electron paramagnetic resonance data which relate this material to


quasiferromagneti sm.












































-1500 -1 250 -1000 -750 -500 -250 0 250 500 750 1000 1250 1500

Field (Oe)



Figure 5-8. Magnetization as a function of magnetic field strength of HOPG graphite. The
magnetization is adjusted for the diamagnetism of the sample. The measurement
temperature was 300 K.


5.4.1 Magnetization Response of Highly Oriented Pyrolitic Graphite


The as-purchased material was measured with our SQUID magnetometer at room


temperature. A wide hysteresis is observed. Since the sample also exhibits strong diamagnetism,


its contribution was subtracted, see Figure 5-8. The coercive field is about 200 Oe, which is


much larger than in the case of silicon based quasiferromagnets. For example, sp-Si has a


coercive field of about 50 Oe and ion implanted silicon one of about 100 Oe.


5.4.2 Electron Paramagnetic Response of Highly Oriented Pyrolitic Graphite


The electron paramagnetic resonance of HOPG graphite is more involved than in the case


of silicon-based materials. HOPG is a conductor and therefore the EPR line do follow a rather


complex model call Dysonian lines named after Dyson58,59 who theoretically studied the EPR of


t+OO



1 E-05



1E-05



j E-05


8 E-05


6 E-05



4 E-05



2 E-05


E
5
o




err
I


O

















































Field (Oe)

*Data Dyson Model

Figure 5-9. Electron paramagnetic resonance spectra of HOPG graphite (blue squares) and its
Dysonian line model (solid red). The coefficient of correlation is 0.99. Experimental
parameters, power = 0.6315 mW, power attenuation = 25 dB, modulation field = 1 G,
time constant = 5 ms, detector gain = 60 dB, temperature = 300 K.

A correlation coefficient of 0.98 is found between the data and model. This is a quite

reasonable match considering that we approximated the Dysonian line using only one term. (The


g-factor = 2.0086


conductors and in particular of metals back in 1955. However, in the case of HOPG the EPR

intensity line can be reduced to an asymmetric Lorentzian line (only the first term of the


-0 H-H) -2(H-Ho)+1
A where
[1+ F (H H ,)


dP
Dysonian line) with the following equation:
dH


dP
-is the EPR intensity, A the amplitude, H the field, Ho the center field and r the full width.
dH

Figure 5-9 displays the comparison between the EPR data and Dysonian line model for HOPG

graphite at room temperature.


3320


-0.4


3322.5 3325 3327.5 3330 3332.5 3335 3337.5 3340 3342.5 3345 3347.5 3350









reader is referred to the original paper written by Dyson58 to see the complete equation). In

addition, according to Feher59 who confirmed the work of Dyson on different conductive

materials, any materials modeled with the equation used to model HOPG, contains paramagnetic

impurities distributed throughout the volume of the metal.

Once again, we found a material with paramagnetic impurities and a magnetic hysteresis at

room temperature. These characteristics are similar to the ones of sp-Si and to ion and neutron

irradiated silicon. Even if HOPG graphite is different from silicon-based material due to its

conductive nature, we suggest that it should also be classified as a quasiferromagnetic material.

5.5 Summary

In this chapter we looked at several different materials from the quasiferromagnetism point

of view. In brief:

* The original work started by Jonathan Hack is in line with our suggested
quasiferromagnetic model, that is, the paramagnetic centers observed by EPR are at the
origin of the observed magnetic hysteresis at room temperature.

* Ion-implanted silicon with either argon or silicon and neutron irradiated silicon contains
paramagnetic centers and display magnetic hysteresis at room temperature. Similarly to sp-
Si, we suggest that the macroscopic behavior is explained by the interaction of the
paramagnetic centers.

* HOPG graphite exhibits a magnetic hysteresis at room temperature in addition to a
Dysonian shaped EPR spectrum, characteristic of paramagnetic centers in conducting
materials. When compared with sp-Si, strong similarities suggest a quasiferromagnetic
behavior.









CHAPTER 6
CONCLUSION

The present investigations have been conducted to study in detail unknown magnetic

properties of non-magnetic materials. Because of their uniqueness we term them

"quasiferromagnetics" The experimental results and interpretations which have been observed

during this study are summarized below.

6.1 Macroscopic Magnetic Behavior of Spark-Processed Silicon

It has been confirmed that spark-processed silicon displays a magnetic hysteresis quite

analogous as Fe, Co, Ni and rare-earth metals. Once again, sp-Si does not contain magnetic

impurities at levels which would explain the magnetic hysteresis at room temperature.

The magnetization (remanent and at 1000 Oe) of sp-Si decreases as the temperature

increase. Applying the Weiss equation to the magnetization data, we evaluated a Curie

temperature of 765 K for sp-Si. It should be noted in passing that at such temperatures the

annealing effect is quite small but still noticeable. A new technique was developed to measure

the magnetization at such high temperatures.

On the other hand, at low temperatures (below 100 K), the magnetization at 1000 Oe of sp-

Si follows the Curie-Weiss law, characteristic of paramagnetic materials.

6.2 Electron Paramagnetic Resonance of Spark-Processed Silicon

The electron paramagnetic resonance of sp-Si allowed the identification and

characterization of paramagnetic centers within the material. Two type of centers were identified

namely, the D centers, (silicon dangling bond back-boned by three other silicon atom) and the E'

centers, (silicon dangling bond back-boned by three oxygen atoms.) The D centers amplitude

decrease as function of the temperature in a similar manner as the magnetization measured with

the SQUID magnetometer. Applying the Weiss equation to the EPR data, we evaluated a Curie










temperature of 710 K for the sp-Si D centers. In contrast, the E' centers amplitude is essentially

independent of temperature in the range 300 to 800 K. A new heating system was built for the

EPR system in the process leading to these results (Appendix E).

At low temperatures, both the D and E' center amplitudes follow the Curie-Weiss law,

characteristic of paramagnetic materials. This is a similar behavior as the magnetization

measured with the SQUID magnetometer.

In addition, the pulse EPR technique allowed the measurement of the local average spin

concentration. We measured a concentration of 1.4x1019 Cm-3 for the D centers and

0.5 x 1019 CA-3 for the E' centers. This translates into a maximum spin to spin distance of 3.7 nm.

6.3 Quasiferromagnetic Model for Spark-Processed Silicon

In order to explain the origin of the magnetic hysteresis loop observed at room temperature

in sp-Si we have developed a model based on our experimental results. Figure 4-1 illustrates the

most important assumption, that is, the distribution of paramagnetic centers (D and E') is not

homogeneous. Using this assumption leads to the possibility of having spin-spin distances of less

than 2 nm which is the commonly accepted upper limit for exchange interaction to occur

between spins.

It has been shown from previously published"" work from our group that sp-Si does not

have a homogeneous structure. Furthermore, sp-Si was also shown to have nanocrystals of

silicon embedded into an amorphous SiO2 matrix. Due to the physical nature of the D centers

(that is, containing only silicon atoms) they can only be located in silicon rich domains while the

physical nature of the E' centers (that is, containing both silicon and oxygen atoms) they can

only be located in the SiO2 matrix. Therefore, we suggests that D centers are forming clusters in

or around silicon nanocrystals leading to a high local density of spins and subsequently leading

to possible exchange interactions between them.









In addition to the distribution model, our experimental data suggest that D centers are

responsible for the observed magnetic hysteresis. Using two different techniques (SQUID

magnetometry and EPR) we found that the magnetization of the D centers (i.e. amplitude) and

the macroscopic magnetization have close Curie temperatures (765 K and 710 K respectively) in

addition to a similar temperature response. At low temperatures, they both follow the Curie-

Weiss law and at higher temperatures they both follow the Weiss equation.

6.4 Other Quasiferromagnetic Materials

In addition to sp-Si, we have found several other materials which we classified as

quasiferromagnetic materials. We classified them as such because similarly to sp-Si they display

a magnetic hysteresis at room temperature and contain paramagnetic defects. These materials

are:

* Ion implanted silicon with silicon at a dose of 5 x 1016Cm-3,
* Ion implanted silicon with argon at a dose of 2x 1016Cm-3,
* Neutron irradiated silicon at a dose of 4x1016Cm-3,
* HOPG graphite.

Similarly to sp-Si, we suggest that the macroscopic magnetic behavior is explained by the

interaction of the paramagnetic centers.

6.5 Future Work

We presented experimental work done on ion-implanted silicon; neutron irradiated silicon

and highly oriented pyrolitic graphite and how they are related to sp-Si and quasiferromagnets.

We suggest that all material with a high density of interacting paramagnetic centers with a

magnetic hysteresis and no magnetic elements (atoms containing d-shell and/or f-shell electrons)

should be called a quasiferromagnet.

First, we believe that there are many other techniques (such as plasma processing,

evaporation, sputtering...) which under specific condition could create materials with unpaired










bonds, which could contain magnetically interacting paramagnetic centers. This present a great

area of engineering research where new material could be discovered and where such materials

could lead to application such as spintronics transistors.

In addition, the materials presented in this study should be investigated further. For

example a more complete EPR study could be done and in particular pulse-EPR studies. Such a

study would allow the confirmation or distinction between these materials and sp-Si. We think

that conductors such as HOPG and semiconductor-based quasiferromagnets are slight variation

of one another and we should qualify them type 1 and type 2 quasiferromagnets according to

their conductivity. More research should be done toward understanding the link between the

conductivity and the magnetic properties as there are the bases for building future spintronics

devices.

Finally, even if the materials which we presented in this dissertation could not be used

directly for the manufacturing of devices it should be noted that the fundamental understanding

of local magnetism (cluster of spins) is necessary to further the engineering of new spintronic

devices.

Magnetism is an exciting research topic as evidenced by the recent Nobel Prize. This

dissertation has led me to grow and learn basic research principles which I will use throughout

my life. In the mean-time, working on this topic has allowed us to advance it through the

discovery of quasiferromagnetism.

Before we invented the concept of quasiferromagnetism and before we start to study

consistently the magnetic properties of spark-processed silicon very little was known on the

magnetization of materials containing large amount of paramagnetic centers. In addition, only a










restricted amount of information was known about the characteristic of such materials at the

electron level.

I believe that this work is the first step in the direction of understanding magnetism not

stemming from d or f-shell magnetism. It should be pursued further.









APPENDIX A
SPARK PROCESS POWER SUPPLY

I designed and fabricated a power supply which was used for the fabrication of spark-

processed silicon. In this Appendix, I describe how the power supply works and needs to be

operated.

A.1 Power Supply Principles of Operation

First, we describe how the power supply circuit works. Its schematic is plotted in Figure A-

1. The 110V AC coming from the wall outlet is transformed into 24V DC. Then the voltage is

again decreased to 12V DC corresponding to the pink subsection of the circuit only. This

subcircuit creates a pulsed DC waveform with a low current (typically 2 mA). The pulsed signal

is obtained by charging a capacitor (C1, C2, C3 Of C4) through a resistor (R1+F) for the high state

(V = 12V) and discharging the same capacitor through another resistor (R2+G) for the low state

(V = OV). A NAND gate is used to square the signal. Then, the output of this gate is inversed and

amplified (3 times) by feeding the signal through three other NAND gates. The output of the

pink subcircuit can be visualized on an oscilloscope using the outlet labeled E. Figure A-2

displays schematically what is seen on the oscilloscope. The length of the low and high states

can be calculated from the product of the capacitor by each of the respective resistors. Since we

use variable resistors (F and G) we can vary the duty cycle and the frequency. The frequency is


equal to the inverse of the sum of the low and high state ( fr~equency = ). The duty
(G,+F)C,

P: R,+ F
cycle is equal to: The frequency and duty cycle range which are limited by the
P, R + G

capacitor Ci can be expanded by using a selection of four capacitors (C1, C2, C3 and C4).

The second subcircuit, in green on the schematic, uses a BJT transistor (T1) to pre-amplify

the pulsed DC signal from a 2 mA to 200mA.







110V AC to 24V DC~rnfre
A Top Fan OV24V


O
4


/ h


To sample stage


To spark electrode


Figure A-1. Power supply schematic.










Then, the signal is amplified even more using a power MOSFET transistor (T2). The

current flowing through the orange subcircuit is about 2 Amps. Finally, the high current (2

Amps) low voltage (24V) pulsed DC signal is transformed into a high voltage (several kV) low

current (few mA) pulsed signal through the flyback transformer. The spark tip is connected to the

high voltage output of the flyback transformer while the stage is connected to the ground. In

addition, a variable resistor is placed in series with the flyback transformer to increase or

decrease the output high voltage.


P = P, + P










P1 = (R1+F) xC, P2 = (R +G) xC,


Time


Figure A-2. Typical waveform observed at the read out (E) on the screen of an oscilloscope.

A.2 Power Supply Inner Components

Practically, several cooling devices were added. Heat sinks were used to cool down the

voltage regulator and the high power transistor (T2). In addition to the heat sink, the high power

transistor (T2) WAS cooled by a large fan. Two other fans were positioned at the back of the

power supply to cool down the flyback transformer and one on the top of the box to cool down

the entire circuit. A previous bad experience with an uncooled circuit taught me to be on the safe

side by adding more fans than probably needed. Figure A-3 displays a picture of the built circuit

as described.




































Figure A-3. Power supply without its top cover.

To complete the description of the power supply, a picture of the front panel is included in

Figure A-4. The front panel allows the variation of the controls A G. Below is the list of the

controls with their meaning and labels:

* A, main switch
* B, high voltage switch
* C, high voltage power control (variable resistance 0 to 3000)
* D, frequency range selector
* E, waveform read out
* F and G, frequency and duty cycle fine adjustment (variable resistance 0 to 75kO).

A list of component is included for a full description:

* C1 = 10 nF (1.6 12k * C2 = 3.5 nF (5 40k * C3 = 1 nF (12 100k * C4 = 0.6 nF (25 125Hz)
* D1, IN4148 diode










D2, IN4148 diode
R = 10kO
R2 = 10kO
R3 = 1kO
R4 =1kO
CMOS 4093, quad 2 input NAND
Voltage regulator 7812, Vout = 12V DC
T1, 2N2222 NPN BJT transistor
T2, IRFPS43N50K HEXFET power MOSFET transistor
Flyback transformer from high voltage circuit of television set
Fuse 110V, 0.75Amp.


Figure A-4. Front side of the spark machine. The labels A
the schematic (Figure A-1).


G designate the same control as in


Finally, it is to be noted that the sparks do not occur under all conditions. The power

supply will only creates a spark when specific conditions of frequency, power, duty cycle and

sparking gap are met.









APPENDIX B
HgCo(SCN)4 MAGNETIC REFERENCE

B.1 SQUID Magnetometer Verification

This reference material is used to verify that the SQUID magnetometer is properly

functioning. Several references can be used to validate magnetization measurements with the

SQUID magnetometer at very low temperature (2-100K). The cobalt mercury cyanide is a

widely used reference for this range and was readily available to us. This material comes in a

powder form and special handling is required due to its toxicity and potential to contaminate the

magnetometer. A special sample holder was designed to prevent loss or scattering of the material

during the measurement process. We are describing the sample holder here at first.

The measurement process in the SQUID magnetometer is done in a helium atmosphere,

thus requiring pumping the chamber to a vacuum and then backfilling with helium. Since

pumping down could move HgCo(SNC)4 particles outside the holder, into the pump system and

onto the detector, we prepared a quartz ampoule under argon gas. The quartz ampoule is made of

a 5 mm outside diameter (4 mm inside diameter) quartz tube closed on each end. The ampoule

was back filled with argon just below one atmosphere before it was closed. In order for the

reference material to be positioned in the center of a symmetric holder, it was placed inside a

plastic straw, normally used as a sample holder, but seating on another piece of quartz tube such

that the ampoule seats in the middle of the straw. This not only places the sample properly but

also virtually eliminates the magnetization from the quartz ampoule. The SQUID magnetometer

is a differential technique and as such, makes differential measurements between the area above

the sample, the sample itself, and the area below the sample. The design of our holder, placing

quartz above, at the sample and below by adding a support tube underneath, creates a net











difference of zero. Therefore the quartz holder does not appear as a component of the observed

magnetization. Only the magnetization from the sample is observed.


0.004


0.003


0.002





- 0.001





-0.002


-0.003


-0.004
-1000


-800 -600 -400 -200 0
Field (Oe)


200 400 600 800 1000


Figure B-1. Magnetization versus field at room temperature for HgCo(SNC)4 (Square). A linear
curve has been fitted to the data points (solid line).

The magnetization as a function of magnetic field at room temperature for HgCo(SNC)4


prepared as described is displayed in Figure B-1. The typical positive linear trend is observed

between the magnetization and the field as it is expected for a paramagnetic material. A very


good correlation is found between the data and the linear fit (R2 = 0.999997). The sample mass is

calculated from the accepted magnetic susceptibility31 meaSured at 200C. A magnetization of

0.003162 emu at 1000 Oe and 200C (293K) leads to a calculated mass of 191 mg. This

calculated mass is useful for comparing the susceptibility constants in the gram unit system.

The magnetization versus temperature of HgCo(SNC)4 is plotted in figure B-2.












0.28

0.25

0.23

0.20

S0.18

S0.15

0.13

P 0.10

0.08

0.05

0.03

0.00
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
Temperature (K)



Figure B-2. Magnetization versus temperature at 10000e for HgCo(SNC)4.

The magnetization increase as the temperature is decreased. The magnetization is modeled


using the sum of three terms define as: X(T) = ydra ra, + r X,(T) Where


Magnetization.
X(T) = Xdr/Si the diamagnetic susceptibility independent of temperature,
Field


X",,a is the temperature independent paramagnetic susceptibility and Zwro (T) is the temperature


dependent paramagnetic susceptibility, which is also called the Langevin paramagnetic


susceptibility and is a function of the temperature as follows: Zwra (T) = where C is the
T-0


Curie constant, and 6 is temperature constant.


We apply the Curie-Weiss law to our data set; the fitting constants are presented in Table B

1. To visualize the good correlation between our measured data and the Curie-Weiss law, we plot










the temperature dependent part of the magnetization as function of inverse temperature minus

theta. The temperature dependent part of the magnetization is proportional C/(T-6) and is

presented Figure B-3.


0.30



E 0.25


0.20
0 ,


S0.15



P0.10



( 0.05


0.00 i"
0.00


0.05 0.10 0.15 0.20 0.25
1/(T+1.95K)


Figure B-3. Magnetization adjusted for diamagnetism as a function of the inverse temperature
(squares). The temperature is shifted by 1.95K. A linear trend is fitted to the data
(solid line).

Using these equations I modeled my measurements and the one of O'Connor32 USing their

published data. The values are presented in Table B-1. The analysis of O'Connor contains errors

and a detailed treatment of the magnetic susceptibility of HgCo(SNC)4 is the following sections.

Nevertheless, the measurement of the data by O'Connor is considered to be excellent33

Table B-1. Constants from susceptibility model.

Xd, + X7 [10-6 g-1] C [10-' g- ] 6 [K]
This work -3.05 5056 1.95
O'Connor32 -7.82 5433 1.98










A good agreement between our measurements and the one from O'Connor is observed. If

we compare directly our modeled constants to the ones of O'Connor, it does not seem that we

have a very good match. But if we look at the correlation between the susceptibility as function

of temperature, which we are ultimately interested in, we find an excellent match with a

correlation coefficient of 0.9999. This coefficient was calculated using the data of Table B-2,

which displays the susceptibility values calculated from our measurement and the susceptibility

values from O'Connor.

We conclude that HgCo(SNC)4 is a good reference for very low temperature magnetic

measurements and that our SQUID magnetometer is working properly in the 2 to 100K range

since we had a very good correlation between our data and previously published ones.

HgCo(SCN)4 is commonly used as a magnetic reference thanks to its ease of preparation

and stability31-34. In the following sections, we present several issues encountered during the

magnetic properties review of HgCo(SCN)4. First, we take a look at why some discrepancies can

be found between a proposed model (for example Curie-Weiss law) and measured data. Then,

we will review the models proposed to explain the magnetic properties of this standard and

discuss their validity.

B.2 Model Weighting

The Curie-Weiss model is widely used to model paramagnets. But as computer modeling

evolved the method employed to compare a set of data to a model changed. We show here that

using a classical technique leads to slightly different fitting parameters than using a more direct

approach. Let' s use the Curie-Weiss law as an example for our purpose of showing these


differences. We will use the following equation to represent the Curie-Weiss law:M~ =,


where T is the temperature and M the magnetic susceptibility, C and 6 are fitting parameters.











Table B-2. Magnetic susceptibility [10-6 g-1] as function of temperature of HgCo(SNC)4 Of OUT
data set and O'Connor's data set.
T[K] O'Connor32 This work
102.6 46.4 45.4
96.85 49.9 48.1
91 53.5 51.2
82.85 57.9 56.3
75.72 62.8 62.0
68.88 69.7 68.5
61.66 78.0 76
53.76 89.8 88
45.64 105 103
37.58 128 124
31.43 153 148
27.87 170 166
25.77 185 179
24.72 193 187
23.66 202 195
22.83 209 201
22.21 214 207
21.56 220 213
20.91 227 219
20.27 235 225
19.62 241 232
18.89 251 241
18.06 262 251
17.26 273 262
16.5 285 273
15.64 300 287
14.2 329 314
13.15 353 336
11.92 386 367
10.56 430 408
9.23 484 456
8.02 544 511
6.91 613 573
5.91 691 642
5.21 758 702
4.5 838 775
4.202 862 815
3.911 904 853
3.611 954 898
3.226 1025 966
2.9 1093 1033
2.39 1232 1165
1.99 1379 1299










The classical fitting method would be to plot as function of T. The equation is rewritten



as: -T+- In this case we expect the data to have a linear trend with a slope of and a
M~C C C


y-intercept equal to-. This classical method can be done quickly without computer help. On the


other hand, the more direct method of fitting the equation requires a computer' s help. To

illustrate our point we plot the data according to each method in Figure B-4. The A graph

illustrates the direct method while the B graph illustrates the classical one. In addition the data

used for these two graphs are shown in table B-3.

Table B-3. Data example.
T M 1

0 8.131 0.123
0.5 2.544 0.393
1 1.352 0.739

Both models lead to excellent correlation coefficient of 0.999 with the direct method and

0.995 with the classic one. Even with very good correlation coefficient, the fitting parameters

can have large discrepancies up to 18% in our case as show in table B-4.

Table B-4. Fitting parameters.
Constants Direct Method Classic Method Discrepancy
C 1.780 1.620 9%
9 0.218 0.178 18%

We use the same data, the same equation but the fitting parameters were evaluated

differently leading to large discrepancies! Our quantification of "large" is due to the fact that we

expected very small differences in our fitting parameters since the correlation coefficients are so

high. Therefore, one must be careful when using the coefficient correlation alone as a judging

factor for a good model fit.



































0 02 04 06 08
T

4 M-Model M


02


04


06
T

* 1/M -Model 1/M


08


12


Figure B-4. Example of the Curie law model. A) M-T plot and its model. B) M-1/T plot and its
model .


The discrepancies in fitting parameters between the classic and direct method comes from


the weighting of the data points. The direct method will weight each data point equally where the


classic method will decrease the weight of the data point with high M values and increase the











weight of the data point with low M values. In physics terms: the direct method considers each

data point to have the same precision while the classic method assumes that the large M data

point have less precision and should account for less. In the case where we know which data

point have more precision we can weight the model accordingly. But in the case of the classic

method the weighting is, in most cases, unrelated to the precision of the data and therefore does

not account properly for it.


2000

1800
R2 = 0.9998
-^ 1600



14000

8200


E 400


200


20

0 10 20 30 40 50 60 70 80 90 100 110

Temperature (K)

SMeasured data -Direct Method


Figure B-5. Magnetic susceptibility of HgCo(SNC)4 and its model using the direct method.

On the other hand the direct method (as presented here) does not account for the precision

either but conceder the data point to be equal. If no information is known about the precision,

one should use the direct method and not the classic one. If one knows the precision of each data

point, it is possible to take this information into account in the direct method and obtain more










trustworthy fitting parameters. Historically, the classical method has been used because

computers were not available. When high resolution is not required the classical method can be

used but since computers are so widely used nowadays we believe that the direct method should

always be used.


0.024


0.021


0.018


0.015


0.012




0.006


0.003



0 10 20 30 40 50 60
Temperature (K)

1/(Measured susceptibility+0.288)


70 80 90 100 110


-Classic Method


Figure B-6. Inverse magnetic susceptibility of HgCo(SNC)4 adjusted for diamagnetism versus
temperature and its model using the classic method.

Now we compare the direct and classic method on physical data. For our purpose we use

the magnetic susceptibility data provided by O' Connor32 and the model

C 1 1
equation: X = Zo +-~ for the direct method and (T 6) for the classic method. The
T-0 X-Zo C`

data with its model using the direct method is plotted Figure B-5. In addition, the inverse

susceptibility adjusted for diamagnetism (using a value proposed by O'Connor32) and its model









using the classical method is plotted Figure B-6. In both cases the model and data match very

well (correlation coefficients better than 0.999). But the fitting parameters do not mach that well

as we discuss now.

The diamagnetic susceptibility ( Zo) must be set to use the classic method. First, we use the

value found using the direct method. This allows observing only the effect of weighting on the

model and not the effect of choosing a set value. The fitting parameters are presented in Table B-

5 for comparison. A large discrepancy is found for the value of theta between the methods and a

moderate discrepancy is found for the Curie constant. Applying these two methods on physical

data reveals that weighting the data can be an important issue. Once again, since we do not know

the precision, we can only assume that all measurements have the same precision and therefore

we must weight equally our data points when applying the model. Now let' s see what happens to

the fitting parameters when the diamagnetic susceptibility is changed.

Table B-5. Comparison of the direct and classic method of O'Connor data set. For both methods
the diamagnetic constant is set and equal to the value found through the direct
method.
Constants Direct Method Classic Method Discrepancy
Zo [10-6 -1] -7.86 -7.86 0%
C [10-6 g-1] 5389 5621 4.3%
6 [K] -1.82 -2.62 44%
r2 0.9998 0.9991 N/A

O'Connor used an empirically calculated value32 for the diamagnetic susceptibility of

HgCo(SNC)4. If We USe that value we obtain the fitting parameters in Table B-6. When

comparing the direct and classic method we obtain large discrepancies. In particular the

diamagnetic susceptibility is twenty times larger when using the direct method than when we use

the proposed value by O'Connor. In addition the discrepancies for the other fitting parameters

are larger than when we use the same diamagnetic constant. We conclude that setting the









diamagnetic constant in the classic method leads to additional variation in the fitting parameters.

This is another reason why one should use the direct method rather than the classic one.

Table B-6. Comparison of the direct and classic method with O'Connor data set. For the classic
method the diamagnetic constant is set and equal to the value proposed by O'Connor.
Constants Direct Method Classic Method Discrepancy
Zo [10-6 -1] -7.86 -0.288 96%
C [10-6 g-1] 5389 4902 9%
6 [K] -1.82 -1.02 44%
r2 0.9998 0.9997 N/A

B.3 Temperature Independent Susceptibility

The previous section led us to see that the diamagnetic constant is an important factor in

the model of the magnetic susceptibility of HgCo(SNC)4. In this section we will discuss what has

been previously done regarding temperature independent susceptibility. It includes the

diamagnetic constant and the paramagnetic temperature independent constant, also sometimes

called Van Vleck magnetism38,60. The Van Vleck susceptibility is given by:


N 0 IO(L +g-Sz) nj12 2'j Z~~,wh
Zo = IU 2p hr is the spin density,
V E,, Eo 6me V=



2pU / is the temperature independent paramagnetic term and
E,,- E

e2~u 0y2 IS the diamagnetic term. In the first term, Lz is the orbital angular momentum
6me =,

operator proj ected on the z-axis, Sz is the total spin angular momentum proj ected on the z-axis, g

is the Lande factor, E is the energy, n designates the electron number and CLB is the Bohr

magneton. In the second term, e is the electron's electric charge, CLo is the vacuum magnetic

permeability, me is the electron mass, r is the electron radius and Z is the total number of

electrons. In practice, the full calculation has only been performed on monoatomic gases and









small molecules with high symmetry due to complexity of electron orbital's. In a large molecule

like HgCo(SNC)4, the simplest approach is to use a linear combination of individually calculated

temperature independent susceptibilities for an atom or small group of atoms. Selwood61 and

Pascal62 prOposed values presented in Table B-7 for the diamagnetic term. From the

stoichiometric composition we found ~,a = -37 12 4 x 3 5 = -189 x 10-67720/- according to

Selwood and Zizo = 4 x (-33.26 4.85 10.3) 12 32.3 1= -23 8 x 10-67720/- according to

Pascal's method. It must be added in passing that Selwood [61] recognized that these

diamagnetic corrections are not to be taken as absolute values.

Table B-7. Diamagnetic correction per mol.
Speci es Selwood6 Xa [10- mO1-1] Pascal62 Xza [10- mOl-1
CNS- -35 -33.26
C-N 0 -4.85
C-S 0 -10.3
Co2+ -12 -12*
Hg2+ -37 -32.31
HgCo(SNC)4 -189 -23 8
* Pascal's value was not available therefore it was taken to be equal to Selwood's.

In addition to the diamagnetic correction a temperature independent paramagnetic

correction may be required. According to Nelson63 CO2+ has a non-zero paramagnetic

susceptibility of Z ~ma = 430 x10-67O/-1. This value is similar to the calculation of Cotton64

based on optical measurements. But according to Selwood, Cobalt-cyanide salts, [Co(CN)x]- do

not have a temperature independent paramagnetic susceptibility if they are coupled with a non-

magnetic element such as Hg. Therefore no temperature independent susceptibility should be

added in our model.

Nelson's method includes, first, measuring the magnetic susceptibility from 40 to 300 K.

This is done in order to avoid the low temperature effect which will be discussed in the next










C
section. Then modeling the data using the equation: X = Zo +-~ where Zo = X,, am Zo~ In
T-0

addition, Nelson calculates the temperature independent susceptibility (Z ara,) from the previous


equation. Using thi s method on my data I obtained Z ara = 270 x 1 0-6 O/-1 and


Z ara = 302 x 10- "mol USing O' Connor' s data. This is far from what Nelson found


( o, = 430 x 10-6 MO/ ).


N


1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

S-0.2

- b.84


0.6 f
0 4


Y


-0.2
X


Figure B-7. Three dimensional representation of HgCo(SNC)4. X,Y,Z are the fractional
coordinates.


Hg Co


Ce









Finally, according to Selwood, the higher the symmetry of a molecule the better the

correction agree with experiment. In the case of HgCo(SNC)4 the molecule has a complex

symmetry65 and therefore the temperature independent corrections are not accurate. A three-

dimensional plot of a section of HgCo(SNC)4 is presented in Figure B-7.

In conclusion, the suggested values for the HgCo(SNC)4 temperature-independent

susceptibility corrections need to be taken with a grain of salt. We found many publications on

this topic but there were lots of inaccuracies or contradictory explanations and therefore we

suggest that the full calculation of the temperature independent susceptibility using electron

orbital's be performed before an improved analysis is proposed.

B.4 Zero Field Splitting and Exchange Interaction

I would like to finish this appendix with effects seen at very low temperature in the case of

this standard material, namely zero field splitting and exchange interaction. Nelson63,

O'Connor32 and Hatfield66 all agree that below 20 K both zero field splitting and exchange

interaction must be taken into account to properly model the magnetic susceptibility of this

cobalt salt. But none of them agree on the model. Hatfield66 Seems to have the most accurate

model for zero field splitting as he uses both measurements as a function of temperature and field

to validate his equation. He proposes the following set of equations:

(z. +2 2
X = Zo +



sinh( sinh(~2
2 +9e- 3y

Np, g2 2 2
Xo' kT coshi +ex cosh
\2 \2











sinh (y) 3 3
2 ~+ cosh(y)ez -z -xe
N pe g 2y 2x 2x
Zi=k,T ez cosh (y)+ e-x -




D gpu,H 3y2
x = ,y = and z =
k,T k,T 4x

The constants are defined as follows: D is the zero field splitting constant, kB the Boltzman

constant, T the temperature, g the Lande factor, H the magnetic field and CLB the Bohr magneton.


3.0E-04



2.5E-04



2.0E-04



1.5E-04



1.0E-04



5.0E-05



0.0E+00


10000


20000


30000


40000


50000


Field (Oe)



Figure B-8. Magnetic susceptibility of HgCo(SNC)4 aS function of magnetic field at 2 K (square)
and its model (solid line).

Using Hatfield's equations applied to the susceptibility versus field measurements at 2 K

we found a zero field splitting constant of 7 cml (Figure B-8). This value is at the same order of










magnitude to the one calculated by Hatfield (19 cm )~. In addition Hatfield66 TOCOgnize that he

did not have a precise value for the zero-field splitting.

The zero-field splitting effect has been shown before and we successfully reproduced the

measurement and modeling technique used. This confirms that our SQUID magnetometer is

properly calibrated.

Finally the model proposed for the exchange interaction occurring at very low temperature

can be reviewed in the work by Nelson on HgCo(SNC)4 CryStals. The measurement of the

exchange interaction in this material is well beyond the scope of this work and a good

presentation of this effect and model is presented63 On a HgCo(SNC)4 CryStal.

B.5 Conclusions

This appendix was aimed at showing several issues which have occurred during the study

of magnetism. First, it is a complicated topic as shown by the contradictory experiments and

models proposed by several leading authors in this field on a "standard" material. Secondly, we

were able to reproduce accurately the results produced by others. It demonstrates that our

methods and equipment are in good working conditions. Also, we wanted to raise awareness on

the difficulty of modeling as different authors use different techniques which add confusion to an

already difficult topic. Finally, we suggest that this material be studied further using optical

absorption measurements for example, to compare with zero field splitting value from magnetic

measurements or that its temperature independent susceptibility be fully modeled using quantum

theoretical calculation.











APPENDIX C
ALUMINUM MAGNETIC REFERENCE FOR TEMPERATURE RANGE 50 300 K

Aluminum has been well studied in the 50-300K temperature range and is a well suited


magnetic reference in that range due to its large temperature dependence. This Appendix details

the results and conclusions presented in section 3.3.2.


4.E-05


3.E-05


2.E-05


E 1.E-05

o
' 0.E+00


c~-1.E-05


-2. E-05


-3. E-05


-4. E-05
-1000


200 400 600 800 1000


Figure C-1. Magnetization versus field at room temperature of 99.999% pure aluminum
(squares). A linear curve is fitted to the data (solid line).

First, we measured the magnetization of an aluminum piece as function of magnetic field

at room temperature to evaluate the magnetic susceptibility. The data are plotted in Figure C-1.


The magnetization is linearly proportional to the field as expected for a paramagnet. The


measured magnetic susceptibility at room temperature is 3.3 77 x10-s emu for the aluminum


sample. Using the measured weight of the sample (53.4 +0. 1 mg) we calculated a sample volume


-800 -600 -400 -200 0

Field (Oe)











of 0.0198 10.00004 cm-3 leading to a volume susceptibility of 1.7010.03 x 10-6 Cm-3. This value is


very close to the published Value Of 1.65 x10-6 Cm-3


4.35E-05


4.20E-05


4.05E-05 4


3.90E-05


c* 3.75E-05


S3.60E-05

I 3.45E-05


3.30E-05


3.15E-05


3.00E 05
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300
Temperature (K)



Figure C-2. Magnetization versus temperature at 1000 Oe for 99.999% pure aluminum.

Next, we measured the magnetization as function of temperature at 1000 Oe. The data are

plotted in Figure C-2. The magnetization decreases as the temperature increases but not like the

Curie law. Rather, aluminum magnetization is linearly dependant on the square of temperature

according to Hedgcock34. A linear trend is fitted through our magnetization measurement versus


temperature square as seen in Figure C-3.

Table C-1. Comparison of model constants for aluminum.

Xda n wu~ [10-6 Cm-3] B [10-" K' cm]
This work 18.8 -3.96
Hedgcock34 19.2 -3.70











Using the calculated volume of our sample we obtained fitting parameters displayed in

Table C-1 in cm-3 units for direct comparison with Hedgcock's work34. For modeling our data we


use the following equation: X = Xdm Z m~, + B xT2 We found a correlation coefficient of 0.997


between our data and the model.



4.4E-05


50K 100K


150K


200K


300K


4.2E-05

R2 =0.997
4.0E-05



3.8E-05



S3.6E-05



3.4E-05



3.2E-05


3.0E-05
0 10000 20000 30000 40000 50000 60000 70000

Temperature# (K2


80000 90000 100000


Figure C-3. Magnetization as function of temperature square at 10000e for 99.999% pure
aluminum (diamonds). A linear trend is fitted to the data (solid line).

The results from HgCo(SNC)4 and Aluminum reference lead us to conclude that our


SQUID is properly calibrated from 50 to 300 K.

































































- e N


APPENDIX D
OXYGEN CONTAMINATION AT LOW TEMPERATURES

This Appendix is aimed at giving all the details necessary to visualize the oxygen


contamination problem.


As stated in section 3.3.3 oxygen is paramagnetic in its gas and liquid phases, becomes


antiferromagnetic when solid below 54.3 K, and changes its crystal structure (P to y at 43.8 K).


The magnetic transitions of oxygen at 54.3 K and 43.8 K generate a noticeable change in the


measured magnetic susceptibility of a sample while some gaseous oxygen is left in the sample


chamber. For example Figure D-1 displays the magnetization of a piece of plastic straw as a


function of temperature at 500 Oe. A very large peak around 50 K is observed above a broad flat


magnetization (equal to the diamagnetic susceptibility of the piece of straw).


-2.8E-05

-2.9E-05

3.0E 05

-3.1E-05

-3.2E-05

-3.3E 05

-3.4E-05

3.5E 05

-3.6E-05

-3.7E-05

-3.8E 05


0 25 50 75 100 125

Temperature (K)


150 175 200 225


Figure D-1. Magnetization versus temperature for a piece of plastic straw at 5000e.































I


r


In our SQUID magnetometer, a sample is normally measured in a Helium gas atmosphere.

Following the sample loading, the load lock (or the entire chamber) is purged with Helium gas.

But due to pumping and Helium quality there is still oxygen left in the chamber. To find out

what was the oxygen residual limit, we measured the magnetization versus temperature of

another piece of straw for several different numbers of purges. The data is presented in Figure D-


2.E-05


1.E 05



0. 10


S-1.E-05

2.-0


-3.E-05


I


-4.E-05
30 35 40 45 50 55
Temperature (K)

-*-0 purge -H 1 purge x 7 -A- purges x 30


60 65



+3 purges x 50


Figure D-2. Magnetization at 1000 Oe of a piece of straw as a function of temperature for several
different purges. The 0 purge magnetization has been shifted by -15K. The 1,2 and 3
purge magnetization has been multiplied by 7, 30 and 50 at 40, 45 and 50K.

For better visibility the magnetization at and around the oxygen peak has been multiplied


by a scalar listed in the Figure D-2 legend. When no purge is performed a large peak is observed

as expected since we leave a large amount of oxygen gas from air in the chamber. But, even

when we purged 3 times the oxygen peak is still visible. Plotting the oxygen peak height as a










function of the number of purges done during the loading of the sample helps us better visualize

the decrease of oxygen amount present in the SQUID magnetometer chamber. Figure D-3

displays such a graph.


O 0.5 1 1 .5 2 2.5 3 3.5
Number of purges


Figure D-3. Oxygen magnetization peak height versus number of purges (diamonds). An
exponential decay model is fitted to the data in solid.

An exponential decay model is used to model the decrease of oxygen amount as function

of the number of purge. The model has the following form:M2 = Mo, + A x e-nino, where Mo is the

residual magnetization due to oxygen, A is the exponential amplitude and no is the exponential

decay constant. Applying this model to our data, we found Mo = 0.059x10-5 emu, A = 4.44x 10-5

emu and no = 0.42. We found that a small but visible residual amount of oxygen is present and

further purging would not decrease it. This small trace of oxygen could be explained by the









limiting pumping capability of the mechanical pump and the presence of trace oxygen within the

helium gas use to cool down the sample.

It is to be noted that the magnetic oxygen peak position depends on the rate at which the

temperature is changed. For example, this is observed on our zero purge experiment, and this is

why we shifted our curve accordingly to better visualize the peak height as function of the

number of purges.

Finally, this "oxygen" effect is only visible in samples with magnetization in the 10-5 10-6

emu range. Therefore we recommend, in addition to multi-purging, using samples as large as

possible to decrease the relative effect due to oxygen magnetic transition.









APPENDIX E
ELECTRON PARAMAGNETIC RESONANCE SYSTEM OVEN APPARATUS

The design and construction of an oven was required for above room temperature

measurements of electron paramagnetic resonance. In this appendix we will describe how it is

designed and how it works.

To simplify the explanations, Figure E-1 is presented. In this figure, the left side is a

picture of the oven apparatus including the resonant cavity and the waveguide, while on the right

side a schematic representation of the cross cut is plotted.

First, at the bottom of the oven apparatus, room temperature nitrogen gas is introduced into

the hot quartz ampoule. Nitrogen was used because of its wide availability, none corrosive nature

and its zero background signal in the EPR cavity. The temperature range of the ampoule can be

varied from 200C to 10000C by adjusting the current in the heating element with a Variac. An E-

type thermocouple is built in the outside of the ampoule to monitor the quartz temperature. The

nitrogen is slowed down in the ampoule due to the increase in cross section and small quartz

piece making the molecular path length longer. Another thermocouple can also be inserted at the

output to monitor the temperature of the nitrogen. Typically high temperatures of near 6000C

have been utilized.

Since we only want to heat the sample and not the cavity, we used an insulating double

wall quartz tube to prevent heat from warming up the cavity and thus affect the measurements.

The insulation in the quartz tube is obtained by pumping the space between the walls down to 10-

Storr with a turbo-pump. The stainless steel metal casing was designed with an inner groove to

accommodate two viton o-rings. These o-rings are very critical for high vacuum quality. To

prevent fast degradation as the temperature rise in the column, only viton o-rings, specially

designed for high temperature were used.











Microwave wave-guide


< ,


Cap with Viton seal -


Hot N2 Output 4 -



Microwave cavity


Z
I
I


- Sample


To vacuum pump



Double wall quartz


, y


- -- -- -- -- -Ceramic insulation


Translation stage


- -Heating element


Quartz ampoule


'' ; ~ -- Broken quartz pieces

-Cold N2 input - -' Power from Variac


Figure E-1. Picture and schematic cross section of the oven apparatus for the electron
paramagnetic resonance system.





159


lit~P~n









The hot nitrogen gas flows through the cavity warming up the quartz sample holder and is

then released in the air through the exit port. Once in the air, the gas cools down very rapidly.

The design of the top part allows the variation of the viton o-ring inner diameter by

screwing in or out the cap (squeezing or releasing the o-ring). Since the sample holder passes

through the o-ring, simply screwing in the cap will lock the holder in place. The sample position

can be adjusted by sliding the sample holder through the o-ring when the cap is unscrewed. To

accommodate various sizes of quartz holder diameters, three inserts have been manufactured.

This allows the use of 3, 4 and 5 mm quartz tubes.

A thermocouple can be inserted in the quartz holder and positioned a few millimeters away

from the sample without perturbation of the spectrum acquisition. This method allows a very

accurate sample's temperature measurement.

In addition, a translation stage is used to adjust the waveguide and cavity position in the

center of the magnet. For practical reasons, the moving part of the stage is made of plastic. It will

melt if the experiment is conducted for too long (more than 2 hours).

Finally, the sample temperature is controlled by varying the power to the heating element

and the flow of nitrogen. At temperatures below 3000C at the sample, the cavity stays at room

temperature which allows a high quality resonance. But, when high temperatures are reached

(5000C) the cavity warms up just enough to modify to resonance condition and affect the

observed spectrum. To properly acquire EPR spectra at elevated temperature, a water cooling

system would be necessary to maintain the cavity at room temperature. But, such modifications

are beyond our capabilities. Broker, the manufacturer of the EPR system which we use sell a

high temperature (up to 1300 K) cavity for $50,000. I manufactured our system for less than

$1,300.









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BIOGRAPHICAL SKETCH

Thierry Dubroca was born in France in 1977. He attended Notre Dame high school at

Fontenay-le-Compte where he graduated with honors in 1995. After attending competitive

classes in mathematics and physics for three years at the preparatory school St. Joseph in La

Roche-sur-Yon, he was successfully admitted to the National School of Engineering Physics in

Grenoble, France. He graduated with honors in June 2001 with an engineering degree in applied

physics and a minor in entrepreneurship. Thierry concurrently earned a master's degree in

semiconductor physics from University Joseph Fourier and the Grenoble National Polytechnic

Institute in September 2001.

In 2000, while completing his engineering degree in France, Thierry moved to Gainesville,

FL where he was an exchange student at the University of Florida. He continued on and earned a

master' s degree in material science and engineering in 2002.

He started as a teaching assistant for Dr. John Ambrose and the Maj or Analytical

Instrumentation Center. During the fall 2001, he j oined Prof. Rolf Hummel's group where he

worked as a research assistant on infrared spectrometry. Thereafter, while he began his doctoral

research on magnetic properties of materials, he studied management, and, in 2004, received a

Master of Science in management from the Warrington College of Business and Administration

at the University of Florida. Thierry finishes his education earning a Ph.D. in material science

and engineering from the University of Florida while still being under the supervision of

Professor Rolf Hummel. That same year, he won the Rugby South conference championship

with the Gainesville Hogs.





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1 QUASIFERROMAGNETISM By THIERRY DUBROCA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2007

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2 2007 Thierry Dubroca

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3 To Jonathan Hack

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4 ACKNOWLEDGMENTS I m ust confess that I was pretty nave when I chose the topic of my dissertation. My decision to study the magnetic properties of se miconductor materials came very quickly after attending a seminar on spintronics, a related field. I felt passionate about semiconductor magnetic properties right away. Professor Rolf Hummel, who has been my advisor during the full length of my graduate studies has fully supported my decision for the topic. It was only after a couple years of studying this subject that I deeply understood the real difficulties of choosing ones own topic. Then, during the most difficult times, when a critical equipment of my work caught on fire and was destroye d, he reassured me by giving me his full support a second time. Without him, I most probably would have not co mpleted my doctorate work. This is why my deepest appreciation goes to Prof essor Hummel. He has been the best advisor a student could ever dream of. In addition, I am very grateful to Dr. Al exander Angerhofer for his generosity. Dr. Angerhofer has not only given me a lot of his tim e to teach me how to use the EPR system, he also amply advised me throughout my doctoral wor k. The main experiments of this dissertation could not have been conduc ted without his supervision. Our laboratory was not equipped with the magne tometer required to develop my work. Dr. Arthur Hebard has been very kind in letti ng me use his SQUID magnetometer for many years and I am very thankful to him for it. I would also like to thank Dr. William Vernets on for letting us use the nuclear reactor in order to prepare the neutron irradiated silicon samples. I feel very lucky to have studied here in the Materials Science department at the University of Florida, where I found very supportive and caring professors. In particular, I would like to

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5 thank my committee members from this depart ment, Dr. Paul Holloway, Dr. David Norton and Dr. Wolfgang Sigmund for their continuing support. Jonathan Hack discovered the magnetic hysteresis of spark processed silicon at UF several years before I became a graduate student. Jona than was very helpful and spent countless hours discussing my experimental resu lts and ideas. Jonathan will always hold a special place in my heart and will never be forgotten. His sudden death came to all of us as a shock. I am also very grateful to my colleague s and friends, Kwanghoon Kim, Anna Fuller, Julien Gratier and Max Lemaitre who had to put up with my incisiveness during our weekly group meetings. Their pertinent remarks have grown in me a way of thinking which, I am sure, will help me all through my life. I would like to express my grat itude to my long time friends Anne Charmeau and Fabien Gerard for their unconditional s upport, express my sincere appreci ation to my friend Courtney Allen for her patience and thank Orlando Rios fo r his support and help in preparing a magnetic standard. I will conclude my acknowledgement by thanki ng my parents, Michel and Christiane Dubroca who deserve my deepest love for th e support they have given me all along my schooling and in particular during my doctoral work.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES.......................................................................................................................10 ABSTRACT...................................................................................................................................16 CHAPTER 1 WHY STUDY QUASIFERROMAGNETISM?....................................................................18 1.1 Definition of Quasiferromagnetism..................................................................................18 1.2 Motivation for Studying Quasiferromagnetism................................................................20 1.3 Could Quasiferromagnetics Be Used in Spintronics?......................................................21 1.4 Understanding the Fundamental Physics of Quasiferromagnetism..................................21 2 WHERE DOES QUASIFERROMAGNETISM STAND WITHIN CLASSICAL MAGNETISM?..................................................................................................................... .23 2.1 Diamagnetism............................................................................................................... ....23 2.2 Paramagnetism..................................................................................................................24 2.3 Ferromagnetism............................................................................................................. ...27 2.4 Unclassified Magnetic Materials......................................................................................32 2.5 Summary...........................................................................................................................38 3 MANUFACTURING, MACROSCOPIC CHARACTERIZATION AND EXPERIMENTAL RESULTS OF Q UASIFERROMAGNETIC MATERIALS..................40 3.1 Room Temperature Study of Spark-Processed Silicon....................................................40 3.1.1 Production of Spark-Processe d Silicon for Magnetic Studies................................40 3.1.2 Magnetic Characterization Process Parameter Influence.......................................42 3.2 Magnetic Characterization of Spark-Pr ocessed Silicon at High Temperature.................46 3.2.1 Magnetic Characterization Me thod at High Temperatures....................................47 3.2.2 Verification of the M odified Magnetometer..........................................................55 3.2.3 High Temperature Spark-Processed Silicon Magnetization...................................58 3.2.4 Annealing Effect on the Magnetization..................................................................62 3.3 Low Temperature Magnetization.....................................................................................64 3.3.1 Magnetic Reference Material HgCo(SNC)4 for the 2-100K Temperature Range...........................................................................................................................65 3.3.2 Aluminum Reference for the 50-300 K Temperature Range.................................65 3.3.3 Oxygen Effect at Low Temperature.......................................................................66 3.3.4 Spark-Processed Silicon Low Temperature Magnetization...................................67 3.4 Summary...........................................................................................................................71

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7 4 INTERPRETATION OF QUASIFERROMAGNETISM IN SPARK PROCESSED SILICON.................................................................................................................................72 4.1 Model Concerning the Distribut ion of Paramagnetic Centers..........................................72 4.2 Electron Paramagnetic Resonance (EPR) Concepts.........................................................74 4.3 Characterization of Continuous Wave El ectron Paramagnetic Resonance Spectra.........75 4.4 Electron Paramagnetic Resonance Parameter versus Temperature..................................87 4.4.1 Low Temperature 5 to 300K..................................................................................88 4.4.2. High Temperature 300 to 800K.............................................................................92 4.5 Characterization of Pulsed Electron Paramagnetic Resonance........................................99 4.6 Relaxation Rates...............................................................................................................99 4.6.1 Spin-Lattice Relaxation Rate..................................................................................99 4.6.2 Spin-Spin Relaxation Rate...................................................................................101 4.7 Separation of Rates to Identify Paramagnetic Centers...................................................104 4.8 Spin Density....................................................................................................................106 4.9 Summary.........................................................................................................................111 5 FURTHER CONSIDERATIONS........................................................................................112 5.1 Annealing of Spark Processed Silicon............................................................................112 5.2 Ion Implanted Silicon.....................................................................................................115 5.2.1 Magnetic Response of Ion Implanted Silicon......................................................115 5.2.2 Electron Paramagnetic Resonance of Ion Implanted Silicon...............................117 5.3 Neutron Irradiated Silicon..............................................................................................119 5.4 Highly Oriented Pyrolitic Graphite................................................................................120 5.4.1 Magnetization Response of Highly Oriented Pyrolitic Graphite.........................121 5.4.2 Electron Paramagnetic Response of Highly Oriented Pyrolitic Graphite............121 5.5 Summary.........................................................................................................................123 6 CONCLUSION................................................................................................................... ..124 6.1 Macroscopic Magnetic Behavior of Spark-Processed Silicon........................................124 6.2 Electron Paramagnetic Resonance of Spark-Processed Silicon.....................................124 6.3 Quasiferromagnetic Model for Spark-Processed Silicon...............................................125 6.4 Other Quasiferromagnetic Materials..............................................................................126 6.5 Future Work................................................................................................................ ....126 APPENDIX A SPARK PROCESS POWER SUPPLY................................................................................129 A.1 Power Supply Principles of Operation...........................................................................129 A.2 Power Supply Inner Components..................................................................................131 B HgCo(SCN)4 MAGNETIC RE FERENCE...........................................................................134 B.1 SQUID Magnetometer Verification...............................................................................134 B.2 Model Weighting...........................................................................................................1 38

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8 B.3 Temperature Indepe ndent Susceptibility .......................................................................145 B.4 Zero Field Splitting a nd Exchange Interaction ..............................................................148 B.5 Conclusions....................................................................................................................150 C ALUMINUM MAGNETIC REFERENCE FOR TEMPERATURE RANGE 50 300 K. 151 D OXYGEN CONTAMINATION AT LOW TEMPERATURES .......................................... 154 E ELECTRON PARAMAGNETIC RESONANCE SYSTE M OVEN APPARATUS.......... 158 LIST OF REFERENCES.............................................................................................................161 BIOGRAPHICAL SKETCH.......................................................................................................165

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9 LIST OF TABLES Table page 4-1 Characteristic values of echo detected field sweep and am plitude of exponential decay as a function of magnetic field.............................................................................. 106 B-1 Constants from susceptibility model................................................................................ 137 B-2 Magnetic susceptibility [10-6 g-1] as function of temperature of HgCo(SNC)4 of our data set and OConnors data set..................................................................................... 139 B-3 Data example............................................................................................................... ....140 B-4 Fitting parameters......................................................................................................... ...140 B-5 Comparison of the direct and classic me thod of OConnor data set. For the classic m ethod the diamagnetic constant is set and equal to the value found through the direct method...................................................................................................................144 B-6 Comparison of the direct and classic me thod wi th OConnor data set. For the classic method the diamagnetic constant is se t and equal to the value proposed by OConnor.........................................................................................................................145 B-7 Diamagnetic correction per mol....................................................................................... 146 C-1 Comparison of model c onstants for alum inum................................................................ 152

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10 LIST OF FIGURES Figure page 2-1 Magnetization of silicon as a function of m agnetic field (own measurements)................ 24 2-2 Magnetization as a function of magnetic field for a param agnetic material...................... 25 2-3 Magnetic susceptibility versus temp erature for a param agnetic material.......................... 26 2-4 Electronic configuration of Aluminum.............................................................................. 26 2-5 Magnetization as function of magnetic field for ferrom agnetic materials......................... 28 2-6 Magnetization as a function of temperatur e at 1000 Oe for a nickel thin film on a silicon substrate.. ................................................................................................................29 2-7 Magnetization process...................................................................................................... .30 2-8 Magnetic phases as a func tion of particle diam eter........................................................... 31 3-1 Spark-processing of silicon................................................................................................40 3-2 Scanning electron micrograph of spark-processed silicon. A) large top view. B) zoom -in view................................................................................................................... ..41 3-3 Magnetization as a function of magnetic fi eld strength m easured at room temperature for spark-processed silicon (sparking time = 6 hours, frequency = 22.5 kHz).................. 43 3-4 Secondary ion mass spectrum of spark-pr ocessed silicon. The largest peaks have been labeled accordingly. See also 3-5.............................................................................. 44 3-5 Secondary ion mass spectrum of spark-pr ocessed silicon zoom ed in around the iron atomic number. An arrow marks the positi on of where the iron isotope with an atomic mass of 54 should be if it was present in the sample............................................. 45 3-6 Spark-processed silicon magnetization at 0 Oe (i.e. rem anence) and 1000 Oe as a function of the spark frequency (sparking ti me was set at 12 hours for all samples)........ 46 3-7 Spark-processed silicon magnetization at 0 Oe (i.e. rem anence,) 1000 Oe and hysteresis area as a function of the sparki ng time (spark frequency was set at 16 kHz for all samples)............................................................................................................... ....47 3-8 Super quantum interference device ma gnetom eter with oven insert and sample holder......................................................................................................................... ........49 3-9 Simulated detector voltage (a.u.) as a function of the position.. ........................................ 51

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11 3-10 Simulated detector voltage (a.u.) as a function of the position (blue diam onds) zoomed in around the sample located 7 cm away from the end of the holder. The computer model is plotted in solid orange......................................................................... 52 3-11 Simulated detector voltage (a.u.) as a function of the position.. ........................................ 53 3-12 Simulated detector voltage (a.u.) as a function of the position (blue diam onds) zoomed in around the sample located 3.5 cm away from the end of the holder. The computer model is plotted in solid orange......................................................................... 54 3-13 Magnetization of pure nickel as func tion of tem perature at 1000 Oe. A Curie temperature of 625 K is found as indicated by the arrow.................................................. 55 3-14 Magnetization versus magnetic field for a silicon sam ple weighting 10.3 mg, measured at 300K.............................................................................................................. 56 3-15 Magnetization versus temperature (grey dots) for a 10.3 m g silicon wafer measured at 10,000 Oe. The plotted magnetization is divided by 10, equivalent to magnetization at 1000 Oe. The aver age (solid line) is -2.8-6 emu............................... 57 3-16 Magnetization as a function of temper ature upon heating (blue diam onds) at 1000 Oe for spark-processed silicon (sparking tim e = 6 hours, frequency = 22.5 kHz) and the field cooled magnetization (red square)............................................................................. 58 3-17 Magnetization as a function of the magneti c field strength before (blue curve) and after field co oling (red curve) measured at room temperature for spark-processed silicon (sparking time = 6 hour s and frequency = 22.5 kHz)............................................ 59 3-18 Normalized magnetization as a function of tem perature for spark-processed silicon measured at 1000 Oe repr esented by red diamonds........................................................... 60 3-19 Normalized magnetization as a function of tem perature for spark-processed silicon measured at 500 Oe represented by red diamonds............................................................. 61 3-20 Remanent magnetization of spark-pro cessed silicon (sparking tim e = 6 hours, frequency = 22.5 kHz) measured as a f unction of temperature upon heating (blue dots) and cooling (red dots)............................................................................................... 62 3-21 Magnetization as function of magnetic fi eld for a spark-p rocessed silicon sample (sparking time = 6 hours and frequency = 22.5 kHz) at room temperature after each heating cycle (heating up to 800 K and cooling down to 300 K in a 1000 Oe field)........63 3-22 Magnetization at 1000 Oe (blue diamonds) a nd 0 Oe (red squares) versus annealing tim e for spark-processed silicon (sparki ng time = 6 hours and frequency = 22.5 kHz).... 64 3-23 Magnetization versus field at 70 K and 35 K of s park-processed silicon (square and round points, respectively).................................................................................................68

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12 3-24 Magnetization versus temperature for spark-processed silicon at 1000 Oe (red triangle) and 0 Oe (bleu squares).. .....................................................................................69 3-25 Magnetization adjusted for diamagnetism and rem anence as a function of inverse temperature.................................................................................................................... ....70 4-1 Proposed paramagnetic centers distribution. ..................................................................... 73 4-2 Energy levels of an elect ron at the resonance field............................................................ 73 4-3 Lorentzian distribution and 1st derivative of electron microwave absorbance as a function of the magnetic field. A) one type of paramagnetic center. B) two different types of paramagnetic centers (red curves ) and their deconvolu tion (blue and green curves)........................................................................................................................ ........75 4-4 Electron paramagnetic resonance spectrum of spark-processed silicon (back line) at room temperature with its double Lorentzian 1st derivative model (red).......................... 77 4-5 Electron paramagnetic spectra of spark-pr ocessed silicon along with DPPH reference standard (black line). ......................................................................................................... .78 4-6 Nature of spark-processed silicon paramagnetic centers................................................... 79 4-7 Amplitude of D paramagnetic centers as a function of m icrowave power........................ 80 4-8 Amplitude of D paramagnetic centers as a function of the square root of the m icrowave power (dots). A linear trend is fitted for the lowest power data points (R2=0.995)..........................................................................................................................81 4-9 Amplitude of E paramagnetic centers as a function of m icrowave power....................... 82 4-10 Amplitude of E paramagnetic center as f unction of the square root of the m icrowave power (dots). A linear trend is fitted for the lowest power data points (R2=0.995)...........83 4-11 Saturation effect observed for the two param agnetic centers in spark-processed silicon.................................................................................................................................84 4-12 Line width as a function of Log (power) for spark-processed silicon. .............................. 85 4-13 Amplitude of D paramagnetic centers as a function of m icrowav e power (dots). Two saturation models are fitted to the data (solid lines).......................................................... 85 4-14 Amplitude of E paramagnetic centers as a function of m icrow ave power for sp-Si (dots). Two saturation models have been fitted to the data (solid lines)........................... 86 4-15 Electron paramagnetic resonance spectra of spark-processed sili con at 4.2K (black line) and tw o possible models:........................................................................................... 86

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13 4-16 Amplitude of D centers versus temperat ure. The data points above 40K have been divided by 10 to account for the change in gain setting. The gain is changed to keep the signal in the linear regim e............................................................................................ 87 4-17 Amplitude of D centers versus inverse tem perature (dots). The data points below 0.025K-1 have been divided by 10 to account for the increased gain. A linear trend is fitted to the data (solid line)............................................................................................... 88 4-18 Amplitude of E centers versus temperat ure. The data points above 40K have been divided by 10 to account for the increased gain. ...............................................................89 4-19 Amplitude of E centers versus inverse tem perature (dots). The data points below 0.025 K-1 have been divided by 10 to account for the increased gain. A linear trend is fitted to the data (solid line)............................................................................................... 90 4-20 Line width of the two paramagnetic centers present in spark-processed silicon versus tem perature in the low temperature range. Line width 1 corresponds to the D centers and line width 2 corresponds to the E centers.................................................................. 91 4-21 Spark-processed silicon paramagnetic cen ters g-f actor (unc alibrated) versus temperature. The g-factor 1 corresponds to the D centers while the g-factor 2 corresponds to the E centers............................................................................................. 92 4-22 Spark-processed silicon paramagnetic centers g-f actor versus temperature...................... 93 4-23 EPR line width of the two paramagnetic cen te rs present in spark-processed silicon versus temperature in th e high temperature range............................................................. 95 4-24 Amplitude of D (blue) and E (red) centers v ersus temperature for spark-processed silicon in the high temperature range................................................................................. 96 4-25 Amplitude of D centers (blue dots) and Magnetization at 1000 Oe (green dots) versus tem perature for spark-processed silic on in the high temperature range............................ 97 4-26 Intensity versus time for a spin-lattice re laxation rate experiment of spark-processed silicon (b lack line), one-exponential decay model (green line) and bi-exponential decays (red line).............................................................................................................. .100 4-27 Spin-lattice relaxation rates versus te mperature f or spark-processed silicon.................. 101 4-28 Intensity versus time for a spin-spin relaxation rate experim ent on spark-processed silicon (black line), one-exponential decay model (green line) and bi-exponential decays (red line)...............................................................................................................102 4-29 Spin-spin relaxation rates versus te mperature for sparkprocessed silicon. ....................103 4-30 Field sweep pulsed electron paramagnetic resonance of spar k-processed silicon (black curve). ................................................................................................................. ..104

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14 4-31 Amplitude of exponential decays in spin -spin relaxation rate experim ents versus field for spark-processed silicon (dots)............................................................................105 4-32 Phase memory time for each paramagnetic cen ter m easured as a function of the input power of spark-processed silicon.....................................................................................107 4-33 Inverse phase memory time (1/Tm) versus sin2( /2(power/power0)1/2) of sparkprocessed silicon (dots).................................................................................................... 108 4-34 Density of paramagnetic centers as a function of the spark frequency for sparkprocessed silicon. ............................................................................................................. 110 5-1 Magnetization at 0 and 1000 Oe of spar k processed silicon as a function of cum ulative isochronal (30 min) annealing temperature................................................... 113 5-2 Electron paramagnetic resonance peak to p eak s pectra line of spark processed silicon as a function of cumulative isochron al (30 min) annealing temperature......................... 114 5-3 Magnetization as a function of the ma gnetic field strength at 300 K for silicon implanted with argon ions................................................................................................ 116 5-4 Magnetization as a function of magnetic fi e ld strength at 300 K for silicon implanted with silicon ions.............................................................................................................. .116 5-5 Electron paramagnetic resonance spectra of argon im planted into silicon at a dose of 216 cm-2 (blue squares) and its Lore ntzian model (solid red).....................................117 5-6 Electron paramagnetic resonance spectra of silic on implanted into silicon at a dose of 1016 cm-2 (blue squares) and its two-Lo rentzian model (solid red).................................118 5-7 Magnetization versus magnetic field strength of neutron irradiated silico n at a dose of 416 cm-2..................................................................................................................120 5-8 Magnetization as a function of magnetic field strength of HOPG graphite. ...................121 5-9 Electron paramagnetic resonance spectra of HOPG graphite (blue squares) and its Dysonian line m odel (solid red).......................................................................................122 A-1 Power supply schematic................................................................................................... 130 A-2 Typical waveform observed at the read out (E) o n the screen of an oscilloscope........... 131 A-3 Power supply without its top cover..................................................................................132 A-4 Front side of the spark machine. The labe ls A G designate the sam e control as in the schematic (A-1).......................................................................................................... 133 B-1 Magnetization versus field at room temperature for HgCo(SNC)4 (square). A linear curve has been fitted to the data points (solid line)......................................................... 135

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15 B-2 Magnetization versus temper ature at 1000Oe for HgCo(SNC)4......................................136 B-3 Magnetization adjusted for diamagnetism as a function of the inverse tem perature (squares)...........................................................................................................................137 B-4 Example of the Curie law model. A) M-T plot and its m odel. B) M-1/T plot and its model................................................................................................................................141 B-5 Magnetic susceptibility of HgCo(SNC)4 and its model using the direct method............ 142 B-6 Inverse magnetic susceptibility of HgCo(SNC)4 adjusted for diamagnetism versus temperature and its model using the classic method........................................................ 143 B-7 Three dimensional representation of HgCo(SNC)4. X,Y,Z are the fractional coordinates.................................................................................................................... ...147 B-8 Magnetic susceptibility of HgCo(SNC)4 as function of magnetic field at 2 K (square) and its model (solid line).................................................................................................. 149 C-1 Magnetization versus fi eld at room temperatur e of 99.999% pure aluminum (squares)...........................................................................................................................151 C-2 Magnetization versus temperature at 1000 Oe for 99.999% pure alum inum.................. 152 C-3 Magnetization as function of temp er ature square at 1000Oe for 99.999% pure aluminum (diamonds). A linear trend is fitted to the data (solid line)............................. 153 D-1 Magnetization versus temperature fo r a piece of plastic straw at 500Oe. ....................... 154 D-2 Magnetization at 1000 Oe of a piece of stra w as a function o f temperature for several different purges................................................................................................................155 D-3 Oxygen magnetization peak height versus num ber of purges (diamonds)...................... 156 E-1 Picture and schematic cross section of the oven apparatus for the electron param agnetic resonance system....................................................................................... 159

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16 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy QUASIFERROMAGNETISM By Thierry Dubroca December 2007 Chair: Rolf E. Hummel Major: Materials Science and Engineering During the 20th century, the understanding of magne tic phenomena had a big breakthrough thanks to quantum physics. However, there ar e still many unanswered questions. The research work presented here attempts to answer th e following question: where does the magnetic hysteresis come from in semiconductors not containing magnetic elements, such as iron, nickel, cobalt or rare earth elements? We have found that materials composed of light elements, such as silicon, oxygen, or nitrogen possess a magnetic hysteresis in contradi ction to classical theo ry. In order to avoid confusion between ferromagnets and those materials, a new name was coined to describe them: quasiferromagnets. In our investigation we used two techniques, namely electron paramagnetic resonance, and magnetometric measurements. We found a Curie temperature of 765 K for sparkprocessed silicon. Further, we identified two pa ramagnetic centers called D and E in sparkprocessed silicon. We meas ured a density of 1.419 cm-3 for the D centers and 0.519 cm-3 for the E centers leading to an average inter-sp in distance of 3.7 nm. In addition, we present the magnetic properties including magnetic hysteres is of spark-processed silicon, argon implanted silicon as well as neutron irradiated silicon and highly oriented pyrolitic graphite.

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17 We propose a model to explain quasiferromagnetism based on the inhomogeneous distribution of paramagnetic de fects. Our distribution model is based on the inhomogeneous structure of the materials. Spark-processed silicon is known to have silicon nanoclusters embedded into a silicon dioxide matrix. The clus tering of paramagnetic centers allows positive exchange interactions between them. We suggest that this clustering explains the observed macroscopic magnetic behavior in particular the magnetic hysteresis at room temperature.

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18 CHAPTER 1 WHY STUDY QUASIFERROMAGNETISM? Magnetism has been a topic of interest since the discovery of ferromagnetism by the ancient Greeks from the city of Magnesia seve ral thousands of years ago. Much later, the compass was invented using the properties of a magnetized iron needle which orients itself toward the north direction. The first theori es of magnetism were developed in the 19th century, a magnetic field created by a current in a wire by Oersted and Ampere. Since, Weiss, Curie and Langevin, to name a few, deve loped theories to explain ot her magnetic phenomena such as antiferromagnetism, diamagnetism or paramagnetis m. This was the beginning of what we know today as the theory of magneti sm. Our study expands this theory with a new branch, which should be tentatively called quasiferromagnetism. 1.1 Definition of Quasiferromagnetism A crystal defines a m aterial that can be sort ed according to its cr ystallographic signature. Bravais, in 1845, mathematically defined the maximum number of po ssible crystallographic arrangements (lattices) to be 14. Therefore, for half a century, crystals were mathematically defined and there was no room for other type of periodic arrangements of atoms which did not correspond to the Bravais networks. Later, be tween 1970 and 1980, a researcher (D. Shechtman) measured what seemed to be periodic lattices that were outside the Bravais networks. Because the word crystal was so closely attached to the concept of the Bravais networks, newly discovered pseudo-periodic latti ces could not be named crystals even though from a logical point of view, they were like crystals. The very close similarities with the classical Bravais networks, these periodic lattices were then named quasi-crystals! A few years later, the scientists (among them D. Shechtman) who discovered the qua si-crystals received numerous awards for their intensive work in this field.

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19 A few years ago, I was telling this story to a dear friend, the late Jonathan Hack, after brainstorming magnetic properties of semiconductors He told me about his first time presenting a magnetic hysteresis loop obtained on spark-proce ssed silicon at a conference: the participants did not agree to let him call what he was presen ting ferromagnetism. At that time, in the midnineties, almost no one believed that one could observe ferromagne tic behavior in materials not containing d or f shell electrons. Right after this conversation, there was no doubt that what we were studying should not continue to be called ferromagnetism, in order to avoid further semantic opposition and confusion. Thus, we decided to name our research topic quasiferromagnetism which occurred naturally to us after discussing the origin of the word quasi-crystals. Moreover, it should be noted, that a gr oup of scientists working on ferromagnetic semiconductors (Si containing ferromagnetic trace elements) ran into a similar problem. They could not use the word ferromagnetism by itsel f to describe their work because it was not within the exact framework of classical ferroma gnetism. Therefore to avoid their new results being rejected from the strict ferromagnetism label they came up with th e word dilute magnetic semiconductors (DMS). We discuss (Chapt er 2) the differences between DMS and quasiferromagnetics. Quasiferromagnetics define materials disp laying a behavior similar to classical ferromagnetic materials, but without containing d or f shell electr ons. The difference in the type of electrons involved leads to large differences in observed ma gnetic behavior. For example, quasiferromagnetics exhibit a magnetic hysteresis at room temperature, despite the fact that they essentially do not contain domain walls in the commonly used sense.

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20 This work is the continuation of what Jona than Hack started 10 years ago when he discovered the magnetic hysteresis of spark-proc essed silicon. This was discovered in our lab, and back then, Dr. Hummel, suggested studying the magnetic properties of this material. He was expecting to find that the magne tic susceptibility would go to minus one, characteristic of superconductors. It turned out that sp-Si was not a superconductor but ra ther exhibited a new effect which we call today: quasiferromagnetism. My doctoral work focuses mostly on explaining the origin of this effect. 1.2 Motivation for Studying Quasiferromagnetism At first, we thought we would be able to use these m aterials, so that we could assemble them into a spintronic transistor. Spintronics are de vices that use the spin of electrons rather than their charge to store and transf er information. These devices are thought to be much faster than the classical electronic devices and therefore would further the improvement of the computer industry. However, as we advanced our studi es for explaining quasiferromagnetism, we understood that implementing quasiferromagnetic mate rials into Spintronics devices would very likely be a difficult task, at least before we fu lly understand how they behave. Therefore, we decided to limit the scope of this work to ma ke experiments which would allow us to explain where quasiferromagnetism originates from. Consequently, our motivation shifted. Our passion pushed us toward understanding the fundamental physics behind this newly discovered magnetic property. In addition, by broadening of our research scope, we hope to promote the understanding of physics by changing the way we saw magnetism as a whole. This is our goal and challenge. In short, quasiferromagnets arise from unpaired bonds produced during processing of materials. For example, silicon or (carbon,) whic h are ion implanted, neut ron irradiated, plasma

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21 sprayed or spark processe d yield a high density of unpaired bonds leading to quasiferromagnetism. 1.3 Could Quasiferromagnetics Be Used in Spintronics? Spintronics as a new branch of physics and e ngineering has a handful of applications. The most commonly known application is the read head of hard drives in personal com puters. But spintronics is mostly a research discipline in which engineers and physicists try to understand how they can control and tr ansport the spin of electrons in semiconductors. Early on, we thought that the materials we studied were part of the spintronic world, in particular the diluted magnetic semiconductors, bu t as we will show throughout this dissertation, this is not the case. They sh are a common semiconductor host, as well as similar magnetic hysteresis. Spintronics use classical ferromagneti c elements, such as Fe, Ni, Co, Gd, etc., all containing d and/or f shell electr ons which are at the origin of the observed magnetic behavior. On the other hand, quasiferromagnetics are only com posed of p and s shell electrons; therefore, they have a very different origin for explaining their magnetic behavi or. It is to be noted, as we will see in detail through Chapter 2, that quasiferromagnetism is not a subpart of ferromagnetism, paramagnetism, diamagnetism or other classical subf ields of magnetism. As a consequence, the significant di fferences between spintronics and quasiferromagnetism lead us to the introduction of a new category of magnetic materials: the quasiferromagnets. A new field of st udy in physics of magnetism is born. 1.4 Understanding the Fundamental Physics of Quasiferromagnetism As a field of physics, quasiferrom agnetism aims at describing the fundamental behavior of electrons to explain macroscopi c physical observation. Our goal is to develop a comprehensive model of electron spin behavior which explains the magnetic behavior of quasiferromagnetics.

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22 For example, we could try to describe the macroscopic hysteresis loop observed at room temperature by using our understanding on how elect ron spins interact at the atomic scale.

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23 CHAPTER 2 WHERE DOES QUASIFERROMAGNETISM STAND W ITHIN CLASSICAL MAGNETISM? Magnetism can be classified either through its response to a magneti c field or through its electronic interactions. In the first case, we can distinguish several classes: diamagnetism, paramagnetism, ferromagnetism, anti-ferromagnetis m, ferrimagnetism. On the other hand, the classification using electron behavior also separates the different classes of magnetic materials according to their exchange interactions whic h can be direct or indirect, such as double exchange, super exchange, anisotropic exchange or itinerant exchange. In this chapter we develop most of the concepts which lead to the classification of qua siferromagnetism within classical magnetism. 2.1 Diamagnetism Diam agnetic materials have a negative respons e to an applied extern al magnetic field. The magnetic moment (M) induced from an external applied magnetic field is opposed to the applied field. Furthermore, the magnetic moment of diam agnetic materials is lin early proportional to the applied magnetic field, where the coefficient of linearity, called the susceptibility, is negative. For example, silicon (Si) shows a diamagnetic behavior (Figure 2-1). Its susceptibility ( ) is -0.32-6 (unitless in the cgs system). In addition, the susceptibility as a function of temperature is another way to characterize the magnetic behavi or and classify materi als accordingly. In the case of diamagnetism, the susceptibility does not change as a functi on of temperature. Diamagnetism is commonly explained by postulating the motion of electrons orbiting around the nucleus within an atom. According to Ampere, the motion of an electron around its nucleus creates a current within a loop (the orbi t). This current, in a loop, creates an orbital magnetic moment. In addition, each electron possesses a spin. The sp in is a concept originating from the relativistic quantum theory. Hence, each electron has a magnetic moment stemming

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24 from its spin and its orbital motion. Each atom (except hydrogen) is composed of several electrons. To compute the magnetic moment per atom, one sums the contribution of each electron spin. When the net sum of the spin magnetic moment is zero and only orbital magnetic moment is left we have a diamagnetic material1,2. M = -3.18*10-9 H R2 = 0.99 Sample mass: 10 mg-4.E-06 -3.E-06 -2.E-06 -1.E-06 0.E+00 1.E-06 2.E-06 3.E-06 4.E-06 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu*) Figure 2-1. Magnetization of silicon as a func tion of magnetic field (own measurements). 2.2 Paramagnetism In the case of param agnetism, the magnetizati on is proportional to the applied external magnetic field, but the response is positive as shown in Figure 2-2 For example, Aluminum is a paramagnet and its susceptibility is +1.65-6 (unitless in the cgs system) at room temperature. In addition, the susceptibility is a function of temperature and can be used to classify materials into the paramagnetic behavior: the phenomenon can be seen in Figure 2-3. The susceptibility ( ) *emu: electro-magnetic unit, measure of the ma gnetization in the centimeter-gram-second (CGS) system.

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25 follows the Curie law; it is inversely proportional to the temperature: = C / T, where C is a constant depending on each materials a nd T is the temperature in Kelvin. Figure 2-2. Magnetization as a function of magnetic field for a paramagnetic material. Langevin explains the origin of paramagnetism. We present the essence of his theory, without going into the details of the quantum me chanical equations. We will continue with the example of Aluminum (Al). Figure 2-4 displays the electronic structure of Al. The electrons which compose the Al atom have different energy levels and spins. The possible energy levels are: 1s, 2s, 2p, 3s and 3p whereby the possible spins are up or down. Electron energies and spins can only take specific values, as displayed in Figu re 2-4. For example, there are two electrons in the 2s energy levels with opposite spins. Thei r magnetic moments cancel one another. This is true for all paired electrons. Al has one unpaired electron in the 3p energy level, which contributes to a positive atomic mo ment. It is oriented in the di rection of the external magnetic field and therefore explains the positive susceptibility. It is to be noted that the magnetic moments of unpaired electrons do not interact with one another in the case of Al. Magnetization Magnetic Field Strength

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26 Figure 2-3. Magnetic susceptibility versus temperature fo r a paramagnetic material. Figure 2-4. Electronic conf iguration of Aluminum. Electron spin 1 2 3 Energy Levels Al: 1s2 2s2 2p6 3s2 3p1 s p s s p d Temperature (K) Susceptibility (unitless)

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27 Why is the susceptibility temperature dependant ? For example, at room temperature and at zero field, Al atomic moments are randomly distri buted due to thermal energy and therefore the net magnetic moment is zero. When one applies an external magnetic field, the Al atomic moments tend to orient in the di rection of the field. Thermal fluc tuations are strong and tend to randomize the atomic moments. As the temperatur e is lowered, the thermal fluctuation decreases leading to a larger magnetic moment, which in creases the susceptibility. Similarly, when the temperature is increased the thermal fluctuation in creases and the susceptibility decreases. For a full description through equations of the relatio nship between the paramagnetic susceptibility and the temperature see Cullity1 or Hummel2. 2.3 Ferromagnetism In the pr evious section we introduced the Curie-Weiss law. This law stems from the Weiss molecular field theory. In order to explain ferrom agnetism, we will start w ith this theory which explains the macroscopic magnetic behavior. Then, we will discuss how this theory is deepened by quantum mechanics and gives an explanation for the magnetic behavior at the electronic level. Weiss introduced a new field in his theory. This field (Hm) is a local field seen by electrons which is added to the external applied field (He). This local field is postulated to be proportional to the magnetization of the material (Hm = M), where is a proportionality factor. Hence, the material under magnetic charac terization is excited by the total field (Ht) equal to Hm plus He. When there is no external magnetic field (He = 0) the material still experiences the internal field which aligns the electron spins. This alignment of spins without external field creates a remanent magne tization; therefore, when an extern al field is applied the magnetization changes. A typical magnetization re sponse is shown in Figure 2-5.

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28 Figure 2-5. Magnetization as function of magne tic field for ferromagnetic materials. The saturation magnetization (Ms) as well as the remanent magneti zation (Mr) are shown. Using the molecular field theory, we can bett er explain the Curie-We iss law starting with the Curie law ( = C / T) and the definition of the susceptibility ( = M / H), C / T = M / H. When replacing H by Ht (Hm + He) we obtain: C / T = M / (Hm + He). Since Hm = M, the previous equation becomes: C / T = M / (He + M). This expression can be derived and expressed as such: M / He = C / (T C). Using the definition of the susceptibility, we finally get the Curie-Weiss law: = C / (T ), where = C. In the case of ferromagnets, the temperature term is positive and is essentially identic al with the Curie temperature, Tc. Below this temperature the material is ferromagne tic while above the Curie temperature it is paramagnetic. For example, Figure 2-6 displays the magnetization measured as a function of temperature for a thin film of nickel on a silic on wafer. The measured Curie temperature is 625K for nickel, which is within 1% lower than previously published data2. Below 625K, Ni is Magnetization Ms Mr Magnetic Field Strength

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29 ferromagnetic, that is, the electron spins are interac ting together such that they align in the same direction within a domain. While above 625K, Ni is paramagnetic, the temperature is such that the thermal agitation randomizes the electron sp in orientations more than the exchange interaction aligns them. -2.E-04 0.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03 300350400450500550600650700750800 T (K)M (emu) Tc = 625K Ferromagnetic Phase Paramagnetic Phase Figure 2-6. Magnetization as a function of temper ature at 1000 Oe for a nickel thin film on a silicon substrate. The measured Curie temperature is 625K. Below the Curie temperature nickel is ferromagnetic and above it, nickel is paramagnetic (own measurements). It should be noted in passing that the s ilicon wafers magnetization is 2 orders of magnitude smaller than the Ni film and therefor e is not taken into account into our analysis. The magnetization can be zero at zero external field in the following cases: if the material has never been exposed to a magnetic field (then it is called a virgin material ) or if the material is de-gaussed (use of an alternating field to randomi ze the spins) or by heatin g the sample above its Curie temperature for example.

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30 In order to explain how the magnetization can be zero in a ferrom agnet Weiss introduced the concept of domains. Each domain contains only electrons having magnetic moments oriented in the same direction. Figure 2-7 schematically represents the different magnetic orientations which can be taken while exposed to an external magnetic field. Figure 2-7. Magnetization process. A) the magnetic field is zer o and the magnetizations from each domain cancel each other. B) under a small magnetic field the domain wall moves and increases the magnetic moment of a domain while decreasing the other one, the net magnetization is not zero. C) at a higher field there is only one domain left and the total magnetization depends on the angle between the magnetic field and the domain magnetic moment. D) at the saturation field the magnetization is maximum. In the example of Figure 27, at zero field the two do mains have opposite magnetic moment leading to a total magne tic moment of zero. Once we a pply an external field, the magnetic domain which is oriented the closest to th e direction of the field increases in size. Once A C D B Ms Ms M = 0 Ms Ms M > 0 Ms M = Ms cos Ms M = Ms H = 0 Oe H = 10 Oe H = 100 Oe H = 1000 Oe

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31 the magnetic field is high enough there is only on e domain left. Then as we continue to increase the external magnetic field the domain magnetic mome nt orients itself toward the field until it is completely aligned. At this point the total magnetiza tion is equal to the satu ration magnetization. The notion of magnetic domains is essential in order to understand a limiting phenomenon in ferromagnetic materials. This phenomenon is called superparamagnetism. It appears when the theoretical domain size is larger than the particle of a given material. To explain this important phenomenon, we will use the simple case where a material is formed of spherical, identical and independent particles (no magnetic coupling). At a critical size the thermal agitation randomly orients the magnetic moment of the entire par ticle. Within the particle, the electron magnetic moments stay coupled such that they all align in the same direction. Figure 2-8 shows the different magnetic states as a function of the size. Figure 2-8. Magnetic phases as a fu nction of particle diameter. For example, the critical particle diameter for Cobalt is 2 nm1 (measured at 76K) which equates to 380 atoms of cobalt. Above 2 nm co balt particles behaves as ferromagnets while for Particle diameter Superparamagnetism ferromagnetism Single-domain Multi-domain Coercivity (a.u.) Critical diameter 0

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32 particles smaller than 2 nm it behaves like a paramagnet. From this definition, we now understand why superparamagnetism is di fferent from quasiferromagnetism. In conclusion, ferromagnetism is originating from the positive exchange interaction from the electrons spins. It requires a minimum amount of unpaired spins grouped together in order to prevent going into the superparamagnetic state. What we have described so far is classical magnetism. Now, we are going to present recent results on magnetic phenomena which have not been forecasted by the classical theory of magnetism and in particular the theory of ferromagnetism. 2.4 Unclassified Magnetic Materials Our group has been active in m agnetic material research since the mid-nineties. In 1995 Hack3 discovered that spark-pr ocessed silicon had a magnetic hysteresis loop at room temperature and demonstrated that the magne tic behavior was not due to ferromagnetic impurities. He suggested that the magnetic behavior was due to defects present in the processed material. Later, our group investigated silicon irradiated by Si, Ar and neutrons4. We found that these Silicon-based materials have a high number of defects as well as similar magnetic behavior as spark-processed Si. More details about the pr ocess and the characteriza tion of these materials will be given in the following chapters. We can distinguish three main groups of materi als which could not be classified according to the pervious definitions of diamagnets, para magnets, ferromagnets, or other classical magnetic materials. These materials are not predic ted by the classical theory of magnetism. The first group of materials is based on carbon. Carbon in the form of graphite or diamond is diamagnetic, but carbon can be made para magnetic or ferromagnetic-like using specific processes. For example, Esquinazi5 showed in 2002 that highly oriented pyrolytic graphite (HOPG) has a magnetic hysteresis at room temper ature stemming from def ects in carbon rather

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33 than from magnetic impurities such as Iron (Fe) or Nick el (Ni). They postulate d that it is not a ferromagnet because the observed hysteresis does not originate from partially filled d or f shells like in Fe, Ni, Co or rare earth elements. In addition, HOPG graphite has topological defects such as grain boundaries and edge st ates. It is understood that thes e defects are of the dangling bonds type which provide unpaired spins. It is believed that these unpaired spins, when correlated, give rise to the hysteresis behavior. The magneti zation under a magnetic field only changes by 10% with temperatur e ranging from 300 to 500K. This is characteristic of a high Curie temperature. Also, it is to be noted that the HOPG graphite has a paramagnetic behavior at low temperatures. HOPG graphite has two magn etic components, one which is strongly temperature dependant at low temperatures, ch aracteristic of dangli ng bond defects and one which is weakly temperature dependant at high temperatures (well below the Curie Temperature). It is associat ed with the hysteresis loop at room temperature which is characteristic of ferromagnetism. HOPG graphite cannot be classified as a ferrromagnet since no domains could be shown. Furthermore, Esquinazi6 and Spemann7 use proton irradiation (i.e. ionized hydrogen) to increase the magnetization of the HOPG gr aphite leading to magnetic domains. They present magnetic force microscopic images (MFM) and scans where magnetic domains can be seen in or around the irradiated spot. Final judgment on their interpretations needs to await further experimental results. Sp ecifically, it is noted that they do not show magnetic domains in non irradiated HOPG even though it has a magnetic remanence. Also, proton irradiation of carbon changes the surface morphology and therefore affects the quality of the MFM images. It is possible that the magnetic domains presented could be artifacts due to the radiation damages. In addition, Spemann7 hypothesizes that magnetic ordering in HOPG is due to defects (i.e. dangling bonds) and the implanted hydrogen. Finally, no mechanism is

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34 proposed to explain the exchange interaction between the unpaired spins (i.e. dangling bonds). Esquinazis group has published many papers on this topic8-12. Carbon nanofoam also has unusual magnetic prope rties. This material is produced using laser ablation/evaporatio n of carbon from an ultra high purity target onto a glass substrate. Rode13-15 in 2004-2006 presents evidence of ferro magnetism in carbon nanofoam below 90K. Above this temperature the nanofoam behaves as a paramagnet. It is well demonstrated that ferromagnetism is not due to impurities such as Ni or Fe and that the paramagnetic behavior is not due to Oxygen. They observe a decrease in the magnetization ove r time. We call this behavior room temperature annealing. It is another evidence of lack of impurities in the nanofoam since impurities do not disappear or self a nneal at room temperature. In particular it is shown that carbon nanofoam has a coercive fiel d of 420 Gauss at 1.8K. This is evidence of ferromagnetism-like behavior. The authors explai n that the nanofoam has a large number of unpaired spins attributed to defects and they be lieve that it is at the origin of the observed magnetic behavior. Furthermore, they speculate th at the nanofoam is formed of metallic carbon clusters separated by non conduc tion carbon walls, which would e xplain its overall magnetic and electrical response. The nanofoam is a semi conductor (explained by the behavior of non conducting walls) and has ferromagnetic-like clus ters due to itinerant electrons which are responsible for the positive exchange in teraction between th e unpaired spins. The Carbon nanofoam as well as the HOPG graph ite are not true ferromagnetic materials. In addition, since the origin of the magnetic hysteresis and high Curi e temperature is attributed to defects we classify these ma terials as quasiferromagnets. Several research groups modeled the magnetic properties of carbon structures. Orellana16 demonstrated, through ab-inito calculations that carbon nanotubes with a monovacancies

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35 exhibits ferromagnetic ordering, while the same carbon nanotube with divacancies does not exhibit ferromagnetic character. Orellana us ed defects in carbon nanotubes to introduce undercoordinated carbon atoms. Furthermore, no mechanism is proposed to explain the positive exchange interaction between unpaired spins an d the unusually high Curie temperature of such carbon structures. Similarly, Park17 calculated the stability of T-shaped carbon nanotube structures which demonstrates the possibility of unpaired spins on carbon atoms specifically located at the junction of carbon na notubes. Park showed that curved graphite sh eets modify the electronic structure of certain carbon atoms leading to unpaired sp ins. We believe that these unpaired spins have a similar role as dangling bonds They are most probably at the origin of the magnetic hysteresis behavior. No mechanism was proposed by these authors to explain the exchange interaction betw een the unpaired spins. All authors (experimentalist or theorist) w ho have studied the car bon based ferromagneticlike materials agree that it stem s from defects allowing for unpaired spins. They disagree as to where these unpaired spins come fr om. For some, it is due to dangling bonds while for others it is due to a modified electronic structure of carbon atoms (curved sheets). None of these authors propose a mechanism to explain the exchange in teraction between the unpa ired spins. Similar work has been done on silicon-ba sed materials. We review here the work of the main-stream authors in this area. In 1993, Laiho18 prepared porous silicon using anodic etching. The porous Si which he manufactured presented a magnetic hysteresis response as well as a Curie temperature of 570K. Porous Si is only composed of Si with a surface oxide (SiO2). Laiho investigated the Si dangling bonds present in the material using Electron Paramagnetic Resonance (EPR). The EPR technique

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36 showed direct evidence of dang ling bonds. The dangling bonds crea te unpaired spins which are believed to be at the origin of the magnetic hysteresis loop observed. Another technique is used by Khokhlov19 in 1967 to prepare silicon samples with a high number of paramagnetic defects (i.e. dangling bonds). Ion implantation using Neon and Argon is used at high doses (up to 317 cm-2) to create large amount of defects. EPR is also used to investigate the paramagnetic cente rs. It is shown that the in tensity of the absorption of microwaves, which is directly related to the su sceptibility, does not follow a Curie law as it is always the case for paramagnetic materials. This is why Khokhlov suggests that such a material has a ferromagnetic phase. He measures a magnetic transition temperature of 150K using EPR. It is to be noted that no hysteresis curve is shown in his work. Our research furthers this work. It will be presented in Chapter 5 chapter. Spintronics is the study and use of electron sp ins in electronic devices Since it is a very recent field of study, the boundaries of this fiel d are not well defined. Spintronics regroup giant magnetic resistance materials (metal alloys), semiconductors doped with magnetic ions, such as Mn, Co, Gd. Authors utilizing magne tic carbon also claim to be part of this field. In order to be precise and clear, we will define the spintroni cs materials as containing magnetic elements, dshell or f-shell magnetic ions, like Gd, Mn, Co, Ni with a ferromagnetic behavior and a potential to be used as magnetically driven devices. Therefore, our definition excludes carbon-based materials and other materials not containing magnetic ions. More recently (2006) Bolduc20 investigated the structural properties of ferromagnetic Mn implanted Si. It is classified as a spintronics ma terial. Mn is implanted at doses ranging from 1015 cm-2 to 1016 cm-2 corresponding to peak concentration of 0.1 to 0.8 at. %. Hysteresis loops at room temperature are presented before and after annealing. A 5 min annealing at 800C

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37 increases the area of the hysteresi s. Bolduc suggests that the Mn implanted Si magnetic behavior is due to carrier mediated interactions. In other words, the Mn electron spins interacts together through the mediation of itinerant electrons. Even if we do not agree with the conclusions of Bolduc and the origin of ferromagnetism we do not dispute the facts presented in his paper. More arguments will be given in the discussion part of this dissertation as to why we disagree with Bolduc on the origin of the magnetic hysteresis. Another interesting material for its magnetic properties is CaB6. Lofland21 measured, in 2003, the magnetic response of CaB6 as a function of temperature and demonstrated that the magnetic response varies with the environmental condition (gas employed during the annealing). He explained these differences by an increased number of defect s due to gas-samples surface interaction and subsequen tly that the ferromagnetic-like behavior in CaB6 was due to dangling bonds. Finally in 2005, Coey22-24 proposed several mechanisms to explain the magnetic behavior of the different carbon polymorphs, CaB6 as well as the diluted magnetic semiconductors (DMS). DMS are semiconductors such as Si, GaN, GaAs or ZnO doped with magnetic ions such as Mn, Cr, Co, Ni or Gd. DMS are spintronic materials. First, Coey showed that the DMS behavior cannot be explained by th e magnetic responses of the dilu ted ions within the material. For example, magnetization of ferromagnetic doped ZnO films decay with time24. When magnetization is measured several times over a peri od of weeks, a clear decrease is observed due to self annealing (it is to be noted that this phenomenon is un related with superparamagnetism). These observations are not compatib le with the classical explanation given for DMS, i.e. that the magnetic behavior is due to the in teraction between itinerant electr ons and electrons in the d or f-

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38 shell of the magnetic ions. In addition Coey e xplained that DMS have a high number of crystal defects. Therefore, similarly to ferromagneticlike carbon, he suggested th at the origin of the magnetic hysteresis as well as the high Curie te mperature is defects related. Even though Coey conceptualized the field of ferromagnetic-like mate rials and spintronics, he did not demonstrate which model or mechanism explains the observed phenomena. In this dissertation we explore the origin of the magnetic hysteresis as well as the high Curie temperature associated w ith it in the case of materials for which explanations are incomplete or none existing. Quasiferromagnetism is characterized by a ma gnetic hysteresis stemming from defects rather than from magnetic ions. Usually, quasife rromagnets have high Curie temperatures. In conclusion, all the unclassified materials which are believe to have their magnetic behavior defects related are quasiferromagnetic. Th is includes HOPG and nanofoam carbon, spark processed silicon, ion implanted silicon and to some extend ZnO doped with Mn where it is demonstrated that defects rather than Mn i ons are responsible for the magnetic behavior. 2.5 Summary There are several clas ses of magnetism: Diamagnetism stems from the electrons orbita l moment. It is opposite to the field which created it. Paramagnetism originates from the spin of independent unpaired electrons. The magnetization is in the same direction as the field which created it. It is proportional to the inverse of the temperature. Ferromagnetism is characterized by its remanence and its Curie temperature. The remanence is due to the interaction of electr on unpaired spins. The Curie temperature is a critical parameter as it is related to the strengths of that interaction.

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39 Superparamagnetism is a limiting case of ferro magnetism. It is observed when the thermal agitation randomizes the domain magnetization in small particles. A new class of magnetic material is proposed as a way of labeling materials in order to better explain their non classical magnetic behavior. Quasiferromagnetism appears in materials, such as s-Si, with a high density of defects, i.e. dangli ng bonds. It is postulated that the observed remanence is stemming from the interaction between the unpaired spins. A Curie temperature similarly to ferromagnetism is observed.

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40 CHAPTER 3 MANUFACTURING, MACROSCOPIC CHARACT ERIZATION AND EXPERIMENTAL RESULTS OF QUASIFERROMAGNETIC MATERIALS 3.1 Room Temperature Study of Spark-Processed Silicon 3.1.1 Production of Spark-Processed Silicon fo r Magnetic Studies The manufacturing of spark-processed sili con (sp-Si) was firs t developed by Hummel25 with the intent of using the op tical properties (specifically lumi nescence) of this newly created material. This method consists of applying a high voltage (several t housand volts) at a high frequency (several tens of kilo -hertz) between a substrate and a counter electrode, typically made of tungsten. I made several modifications to the original process in order to manufacture quasiferromagnetic sp-Si. These modifications incl ude a change in the position of the substrate with respect to the stage and th e use of a laboratory made power supply with slightly different voltage and frequency ranges. A complete description of the power supply which I designed and assembled is available in Appendix A. Figure 3-1 illustrates how sp-Si is produced: a silicon substrate is glued on an alumin um stage with silver paint. Figure 3-1. Spark-processing of si licon. A power supply provides se veral kilo-volts between the electrode and the substrate. The substrate is hanging from the stage and glued with silver paint. The end of the substrate (i.e. the sparked area ) is subsequently cut at the mark to avoid any possible contamination of the sample. Pulsed DC Power supply Tungsten tip Spark Plasma Silicon wafer Stage Silver paint Cut

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41 Figure 3-2. Scanning electron micrograph of spar k-processed silicon. A) large top view. B) zoom-in view. A 3 mm wide spark area B

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42 The silver paint provides the necessary conduc tivity for the current to flow from the substrate to the stage. The substrate hangs from the stage in order to prevent contamination through diffusion (or sparking) between the stage a nd the substrate. Once the silicon is sparkprocessed the substrate is cut as shown in Figur e 3-1, to separate the potentially contaminated part (in contact with the stage) from the sample The sample can be made to sizes ranging from 2mm x 5mm to 5mm x 10mm. The size of the sa mple is an important parameter in the characterization process si nce each equipment has a different size requirement. To manufacture the samples, th e voltage, current, duty cycle and tip to substrate distance are set while the frequency and the sparking time are varied with the laboratory made power supply. Scanning electron microscope (SEM) micrographs of sp-Si were taken to show how our material looks like after being manufactured. Figure 3-2A is a large scale top view while Figure 3-2B is a zoomed-in picture of a small area of sp -Si. A large round sparked area is visible. It is composed of silicon, oxygen and up to 5% nitrogen, as previously shown elsewhere26. The close look at the surface reveals large porou s, and sphere-like particles. Note: I published a study on sp-Si27 in which I found a volume porosity of 43%. Now that we have described the spark pro cess technique, we can look how the process parameters influence the magnetic response. 3.1.2 Magnetic Characterization Process Parameter Influ ence Several samples of sp-Si were prepared under various processing conditions and their magnetizations were observed as a function of an external magnetic field at room temperature, i.e. 300 K. In this section, we will pres ent the results of these experiments. Figure 3-3 is a typical magnetization curve as a function of the magnetic field for sp-Si. We used a commercial super quantum interf erence device magnetometer (SQUID) to conduct

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43 the experiment. A hysteresis l oop is observed at room temper ature. The sample was sparkprocessed for 6 hours. -4.0E-05 -3.0E-05 -2.0E-05 -1.0E-05 0.0E+00 1.0E-05 2.0E-05 3.0E-05 4.0E-05 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) Figure 3-3. Magnetization as a function of magnetic field strength measured at room temperature for spark-processed silicon (sparkin g time = 6 hours, frequency = 22.5 kHz). It could be argued that the hysteresis loop is due to ferromagnetic impurities such as iron, nickel or cobalt. In order to investigate this Secondary Ion Mass Spectroscopy technique (SIMS) has been applied down to the resolution limit of the instrument. For example, SIMS maximum resolution for iron in silicon is 513 at.cm-3. Figure 3-4 displays the mass spectrum of sp-Si. For clarity a zoom in around the area where the iron isotope with a mass of 54 amu should be, is displayed Figure 3-5. As observe d it iron is not detected. It should be concluded that ferromagnetic impurities cannot explained the observed magnetic hysteresis of sp-Si. It should be noted in passing that surface pa ssivation with hydrogen did not change the size or shape of the observed hysteresis.

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44 We use two parameters to characterize th e magnetic response: the remanence and the magnetization at 1000 Oe. The remanence is define as the magnetization at zero field after the sample has been exposed to an external fi eld equal to or greater than the saturation magnetization, taken to be 1000 Oe for sp-Si. Fi gure 3-6 displays the remanence (Mr) and the magnetization at 1000 Oe (Ms) as a function of the processi ng frequency. Both, Mr and Ms increase as a function of fr equency up to 22.5 kHz then decrease down to 25 kHz. Stora28 observe a similar behavior with the phot oluminescence of sp-Si. The photoluminescence intensity increases as a functi on of the frequency up to 10 kHz for the UV/blue band and 15 kHz for the green band and then decrease for high frequencies. It is to be noted that below 8 kHz there is no sparking. The frequency is too low to initiate a spark through the air between the tip and the substrate. 0 1 2 3 4 5 6 7 0 20406080100120140Atomic Numberlog(intensity)H O Si Si2Si3Si4Si5Si6Si7 Figure 3-4. Secondary ion mass spectrum of spar k-processed silicon. The largest peaks have been labeled accordingly. See also Figure 3-5.

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45 0 0.5 1 1.5 2 2.5 3 3.5 4 5051525354555657585960Atomic Numberlog(counts) Resolution limit Fe, isotope 54 Figure 3-5. Secondary ion mass spectrum of spar k-processed silicon zoomed in around the iron atomic number. An arrow marks the position of where the iron isotope with an atomic mass of 54 should be if it was present in the sample. Figure 3-7 displays the remanence and magnetiz ation at 1000 Oe as function of sparking time. The longer the substrate is proce ssed the larger the magnetization. Stora28 published a similar conclusion when studying the intensity of the photoluminescence of sp-Si as a function of the sparking time. Even though knowing the influence of the proc ess parameters are important information, more crucial information can be obtained by studying the magnetizati on as a function of temperature. Since we know that the samples prepared at a frequency of 22.5 kHz exhibit the strongest remanence (Figure 3-6), the next se ction will focus on studying sp-Si magnetization at high temperature (300 800 K) with samp les prepared at this frequency.

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46 0 1 2 3 4 5 6 7 0 5 10 15 20 25 30Frequency (kHz)Magnetization (10-6 emu) Mr (M at 0Oe) Ms (M at 1000Oe) Sparking commences here Figure 3-6. Spark-processed silic on magnetization at 0 Oe (i.e. remanence) and 1000 Oe as a function of the spark frequency (sparking time was set at 12 hours for all samples). 3.2 Magnetic Characterization of SparkProcessed Silicon at High Temperature In this section, we describe the tem perature dependence of the magnetic properties of spSi. Measuring the high temperature dependen ce in a SQUID magnetometer is by no means a trivial task for small signals as it is the case for spark-processed silicon. Therefore, we first describe a new measurement procedure to overc ome the limitation of the SQUID magnetometer for temperature ranging from 300 to 800 K. Sample Name: MSP03-12 Cut-off Frequency

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47 0 1 2 3 4 5 6 7 8 0 5 10 15 20 25 30Sparking time (hrs)Magnetization (10-6 emu) and hysteresis area (a.u.) Mr (M at 0Oe) Ms (M at 1000Oe) hysteresis area (a.u.) Figure 3-7. Spark-processed si licon magnetization at 0 Oe (i.e. remanence,) 1000 Oe and hysteresis area as a function of the sparki ng time (spark frequency was set at 16 kHz for all samples). 3.2.1 Magnetic Characterization Method at High Temperatures All of our high tem perature magnetization e xperiments were conducted in a commercial SQUID with an oven option. This oven insert al lows us to measure magnetization as a function of temperature in the range 300 800 K. The co mmercial software sold with the SQUID is designed to measure the magnetizati on with a maximum resolution of 10-7 emu without the oven insert and 10-5 emu with the oven insert while control ling the temperature with great accuracy (0.01 K). But the resolution limit of 10-5 emu was not acceptable for our purpose since our samples have typical magnetization in the 10-6 emu range. Therefore, I modified the measurement procedure in order to restore the magnetization resolution back to its 10-7 emu value. The drop in maximum resolution is due to the heating system within the oven. Figure 3-8 Sample Name: MSP03-12

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48 shows a schematic representation of the oven appa ratus installed in the SQUID magnetometer. It is important to notice that the oven is inserted in the detector loop. When the computer software controls the temperature of th e oven, it continuously adjusts the current in the heating element which causes the detector to acquire an additional unwanted signal. This unwanted signal decreases the resolution from 10-7 emu to 10-5 emu. In order to avoid this unwanted signal the temperature controller is turned off during the measurement. The measurement takes about 4 min and during this time the temperature drifts. Th e maximum drift is about 1 K at the highest temperature (800 K). This is down from the 0.01 K accuracy when the temperature controller is on but it is acceptable for our purpose. To su mmarize, the new meas urement procedure is: the temperature is set while the temperature controller is on, the temperature controller is turned off when the temperature is stable, the magnetization is measured, the temperature controller is turned back on. This improvement allows us to measure the magnetization as a functi on of the temperature of the samples with an acceptabl e loss of temperature accuracy. Other procedures were suggested by the ma nufacturer of the SQUID magnetometer but implementing them revealed to be extremely di fficult. To our knowledge, no one else has ever used this new procedure to measure small magnetiz ation with the oven insert It should be noted in passing that this procedure has been validated by the manufacturer befo re it was implemented to prevent any damages to our equipment. In a ddition to improvements in the computer software, a new sample holder was constructed. Indeed, th e two types of sample holders proposed by the SQUID manufacturer were not intended to work at such high resolution with the oven insert. The first type of holder is made of copper wires and has a limited resolution of about 10-4 emu (measurement not shown) due to magnetic impurities in the copper.

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49 Figure 3-8. Super quantum interference device magnetometer with oven insert and sample holder. Moving axis SQUID magnetometer Rod holder Copper hook Quartz holder Sample Detector Signal Moving stage Oven apparatus Sample position = 7cm from end of glass tube

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50 The second type made of quartz had to be modified to reduce the diamagnetic response added to the sample signal. We re-desi gned the quartz holder proposed by Lewis29. Lewis proposed a quartz sample holder composed of an outer quartz tube with two inner quartz rods fitted inside. In this case, the sample is being positioned between the two quartz rods. These two rods have a diamagnetic response which is supe rimposed to the signal coming from the sample. Such a holder reduces the accuracy of the magnetization measurement. Our new design includes a thinner outer tube wi th a wall of 0.4 mm (instead of 0.6 mm for Lewis design) leading to a 30% decrease in ma ss, allowing accommodation of larger samples (2.2 mm up from 1.8 mm). In addition, the rods were removed while a notch in the quartz tube was added to hold the sample in place as s hown Figure 3-8. These two modifications improved the magnetization signal coming from the sample while decreasing the in fluence of the signal generated by the holder. In addition to the general design of the samp le holder, the position of the sample with respect to the end of the holder is a critical para meter. It has been found30 that the end of the quartz holder creates an artifact in the measurem ent. Also, it has been shown how to position the sample with respect to the end of the holder to prevent this artifact from interfering with the sample signal. Similarly, with our new designed holder we came to the same conclusion. In order to understand how to remove the artifact stem ming from the end of the sample holder we now describe how the SQUID magnetometer calculates the magnetization from the detector voltage output signal. In a SQUID magnetometer the sample is moved up and down along the vertical axis (Figure 3-8). When the sample moves, the detector measures the change in the magnetic flux as a function of z (the sample position). Then, the detector outputs a voltage, proportional to the

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51 magnetic flux, which is plotted against z. Then, this curve is modeled by the computer to calculate the magnetization in emu units. The mode l, f(z), used by the software is define as followed: 223/2223/2223/2()2[][()][()] fzRzRzLRzL where R and L are instrument constants. The computer only uses da ta spanning over a 4 cm range to calculate the magnetization. -1 -0.5 0 0.5 1 1.5 2 2.5 1 08642024681 0Position (z) in cmSimulated voltage at detector Sample at 7cm from end of quartz holder End effect of quartz holder Figure 3-9. Simulated detector volta ge (a.u.) as a function of the position. The simulated function is define as:()0.1(7) fzfz In order to understand the ar tifact due to the end effect we show on Figure 3-9 the simulated output voltage from the detector includ ing both signals from the sample and the end of the holder. The simulated function is:()0.1(7) fzfz where f(z) is the signal coming from the end of the quartz holder while the second term 0.1(7) fz simulates the sample signal. Usually, the sample signal is one order of ma gnitude smaller than the artifact signal and

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52 positioned 7 cm away from the end of the holder. Figure3-10 shows the simulated function centered at 7 cm (the sample position) with a range of 4 cm along with the modeled curve from the software. -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 -9 -8.5 -8 -7.5 -7 -6.5 -6 -5.5 -5Position (z) in cmSimulated voltag e from detector and computer model Sample at 7 cm from end of quartz holder Figure 3-10. Simulated detector voltage (a.u.) as a function of the position (blue diamonds) zoomed in around the sample located 7 cm away from the end of the holder. The computer model is plotted in solid orange. When the sample is placed at 7 cm from the end of the holder the modeled curve is very close to the simulated one (the correlation coe fficient is greater than 0.9) and therefore the calculated magnetization is the correct value. On the other hand, when we position the sample at only 3.5 cm from the end of the holder the modele d curve does not fit with the detector voltage (the correlation coefficient is onl y 0.4). Therefore the calculated magnetization is an incorrect value. To illustrate this effect, Figure 3-11 shows the simulated curve when the sample is 3.5 cm

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53 from the end of the holder. We observe that the signal from the sample and the one from the end of the holder overlap. -1 -0.5 0 0.5 1 1.5 2 2.5 -8 -6 -4 -2 0 2 4 6 8Position (z) in cmSimulated voltage at detector Sample at 3.5cm from end of quartz holder End effect of quartz holder Figure 3-11. Simulated detector voltage (a.u.) as a function of the position. The simulated function is defined as:()0.1(3.5) fzfz Upon zooming on the 4 cm range around the samp le, as shown in Figure 3-12 we clearly notice the large discrepancy betw een the model curve used to calculate the magnetization and the simulated detector voltage curve whic h causes an incorrect measurement. Now, it becomes clear that the further the sample is located from the end of the quartz holder the more accurate the measurement. Unfortuna tely, the oven itself limits the length of the holder and therefore the maximum practical distance is 7 cm. With this design and proper sample position, the measurement accuracy is more than sufficient for our purpose.

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54 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 -5.5-5-4.5-4-3.5-3-2.5-2-1.5Position (z) in cmSimulated voltage from detector and computer model Sample at 3.5cm from end of quartz holder Figure 3-12. Simulated detector voltage (a.u.) as a function of the position (blue diamonds) zoomed in around the sample located 3.5 cm away from the end of the holder. The computer model is plotted in solid orange. To summarize, here are the modifications done to the SQUI D in order to measure the magnetization in the temper ature range 300 to 800 K: Add the oven insert, Use an ultra thin tube for the holder, Use a notch in the holder rather th an inner rods for sample support, Position the sample with respect to the end of the tube as far as possible, Turn off the temperature contro ller during each measurement, Turn back on the temperature contro ller and go to the next data point.

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55 3.2.2 Verification of the Modified Magnetometer In order to validate the SQUID modifications and before measuring the magnetization of sp-Si, three experiments were made. First, the magnetization as function of temper ature at 1000 Oe of a pure nickel sample was measured; the data is presented in Figure 3-13. We observe a Curie temp erature of 625 K to be compared with published value2 of 631 K. This is a very good agreement and corresponds to a discrepancy of less than 1%. 0.E+00 1.E-04 2.E-04 3.E-04 4.E-04 5.E-04 6.E-04 7.E-04 8.E-04 9.E-04 1.E-03 300350400450500550600650700750800Temperature (K)Magnetization (emu) Curie temperature = 625K Figure 3-13. Magnetization of pur e nickel as function of temp erature at 1000 Oe. A Curie temperature of 625 K is found as indicated by the arrow. Secondly, we measured the magnetization at room temperature of a piece of silicon wafer as function of the field. We us ed the newly designed sample holder without the oven. The result is plotted Figure 3-14. The very well known diam agnetic response of silicon is observed. In

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56 addition, the susceptibility (0.318-6) measured is less than 3% different from the published value2. This is acceptable and further validates the modification of the sample holder. In other words, our sample holder does not interf ere with the magnetization measurements. M = -3.18*10-9 H R2 = 0.99-4.E-06 -3.E-06 -2.E-06 -1.E-06 0.E+00 1.E-06 2.E-06 3.E-06 4.E-06 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) Figure 3-14. Magnetization versus magnetic fiel d for a silicon sample weighting 10.3 mg, measured at 300K. Finally, we measured the magnetization of the same piece of silicon wa fer as a function of the temperature at 10,000 Oe. The resulting data is plotted on Figure 3-15. It is to be noted that we measured the magnetization of the silicon sample at 10,000 Oe and then divided the measured value by ten. This was done in order to compare directly with the magnetization as function of temperature curves for sp-Si whic h we will present in the next section. The magnetization is independent of the temperature over the entire range (300-800 K) as expected for silicon. From the average magnetization we de rive the susceptibility; it is about 15% smaller

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57 than the susceptibility we obtained at room temp erature without the oven insert. Since we use the same holder in both measurements we attribute th e discrepancy to the oven itself. The design of the SQUID requires the oven to be inserted betw een the detector and the sample; therefore it induces a perturbation during measurements. It seems that 15% is a large disc repancy, but this is still better than what we initially observed before the modifications. -3.50E-06 -3.00E-06 -2.50E-06 -2.00E-06 -1.50E-06 -1.00E-06 -5.00E-07 0.00E+00 300350400450500550600650700750800Temperature (K)Magnetization (emu) Figure 3-15. Magnetization versus temperature (grey dots) for a 10. 3 mg silicon wafer measured at 10,000 Oe. The plotted magnetization is di vided by 10, equivalent to magnetization at 1000 Oe. The average (solid line) is -2.8-6 emu. The magnetization versus temperature of nickel and silicon are satisfactory and provide us with validation standards for our method of measurement. Sample name: SpSiH0

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58 3.2.3 High Temperature Spark-Processed Silicon Magnetization Using the improved high temperature SQUID oven, we measure the magnetization as function of temperature for sp-Si spark-processed for 6 hrs at a frequency of 22 kHz. Figure 3-16 displays the resulting curve upon heating and cool ing in an external magnetic field of 1000 Oe. We observe that the magnetization decreases as the temperature increases and increases as the temperature decreases. In addition, the magneti zation at room temperature is larger (by 35%) after cooling in the field than before going thr ough the heating cycle. Co oling of a ferromagnetic material in a magnetic field (field cooling) is kno wn to cause additional alignment of spins. This causes an increase in the remanence. 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05 300350400450500550600650700750800Temperature (K)Magnetization (emu) Heating cooling Figure 3-16. Magnetization as a function of temperature upon heating (blue diamonds) at 1000 Oe for spark-processed sili con (sparking time = 6 hours, frequency = 22.5 kHz) and the field cooled magnetization (red square). Sample name: MSP104 35% increase

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59 The effect of field cooling is better seen in Figure 3-17 where we plot the magnetization as a function of the field at room temperature before and after field cooling. After field cooling, the hysteresis loop is much larger than before. -4.0E-05 -3.0E-05 -2.0E-05 -1.0E-05 0.0E+00 1.0E-05 2.0E-05 3.0E-05 4.0E-05 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) before after Figure 3-17. Magnetization as a function of the ma gnetic field strength before (blue curve) and after field cooling (red curve) measured at room temperature for spark-processed silicon (sparking time = 6 hour s and frequency = 22.5 kHz). Using the Weiss model1 define as: 0 0tanhc M M M T M T where M is the magnetization at a given temperature, M0 is the magnetization at zero Kelvin and Tc is the Curie temperature, we find a very good agreement between the Weiss mol ecular field theory and our sp-Si data. Figure 3-18 and 3-19 display two measur ed samples along with their Wei ss models. For the first sample (spark time = 12 hours, frequency = 22.5 kHz) the Weiss model leads to a Curie temperature of 770 K while for the second sample (spark time = 6 hours, frequency = 22.5 kHz) the model leads 35% increase Sample name: MSP104 300% increase

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60 to a Curie temperature of 760 K. The correlation coefficient between the model and the measured data are very good, that is 0.983 for sample 1 and 0.988 for sample 2.The temperature dependence of the magnetization shows a str ong similarity between sp-Si and ferromagnetic behavior. 0 0.2 0.4 0.6 0.8 1 1.2 300350400450500550600650700750800Temperature (K)Normalized magnetization The Curie Temperature is about 770K M0 = 3.25 10-5 emu Si wafer average magnetization Weiss Model M/M0 = Tanh[ (M/M0) / (T/Tc) ] M0 = 3.8 10-5 emu Tc = 770K r2 = 0.983 Sample name: MSP104 Figure 3-18. Normalized magnetizat ion as a function of temperatur e for spark-processed silicon measured at 1000 Oe represented by red diamonds. The sample was processed for 12 hours at a frequency of 22.5 kHz. The blue line represents the Weiss model with a Curie temperature of 770 K. The average magnetization of a piece of silicon wafer comparable in size to the measured sp-Si sample is plotted for comparison (green dash line). The sample was processed for 6 hours at a frequ ency of 22.5 kHz. The blue line represents the Weiss model with a Curie temperature of 760 K. The aver age magnetization of a piece of silicon wafer comparable in size to the measured sp-Si sample is plotted for comparison (green dash line).

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61 The two most important parameters for descri bing the macroscopic magnetic behavior of a material are the remanence and the saturati on magnetization. In our study, we use the magnetization at 1000 Oe as satu ration point. In the previous section we presented the temperature dependence of the saturation magnetization. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 300350400450500550600650700750800Temperature (K)Normalized Magnetization Weiss Model M/M0 = Tanh[ (M/M0) / (T/Tc) ] Tc = 760K M0 = 0.92 10-5 emu r2 = 0.988 The Curie Temperature is about 760K Si wafer average magnetization M0 = 0.91 10-5 emu sample name: SpSiH11 Figure 3-19. Normalized magnetizat ion as a function of temperatur e for spark-processed silicon measured at 500 Oe represented by red diamonds. In the next section we briefly describe the effect of temperature on the remanence. Figure 3-20 displays the remanence of sp-Si (sparki ng time = 6 hrs and frequency = 22.5 kHz) as a function of temperature. We obser ve a decrease in the remanence as the temperature increases and an increase as the temperature decrease s, but the heating and cooling curve are not superimposed on one another (the cooling magne tization is smaller than the magnetization upon

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62 heating). Heating up at the Curie temperature randomizes the spins. Upon cooling a small but discernable spontaneous ma gnetization is observed. -4.E-06 -2.E-06 0.E+00 2.E-06 4.E-06 6.E-06 8.E-06 300350400450500550600650700750800Temperature (K)Magnetization (emu) Heating cooling Figure 3-20. Remanent magnetization of spar k-processed silicon (spa rking time = 6 hours, frequency = 22.5 kHz) measured as a f unction of temperature upon heating (blue dots) and cooling (red dots). The large erro r bars at high temperatures are caused by a lower sensitivity of the instrument in such temperatures. Note that these measurements were made at 0 Oe where as in Figure 3-16 they were made at 1000 Oe. In this section, we presented the magnetiz ation as a function of the temperature and concluded that the magnetic behavior of sp-Si is very similar to ferromagnetic materials. Now we investigate the effect of a nnealing on the magnetization. 3.2.4 Annealing Effect on the Magnetization The magnetization as a function of the field was measured after a number of heating and cooling cycle. A cycle included heating the sa mple at 800 K and cooling it down to room Sample name: MSP104

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63 temperature at a field of 1000 Oe A cycle takes 7 hours. The resu lting curves are plotted in figure 3-21. The area within the hys teresis loops, measured at room temperature, is observed to become smaller as the number of cycle increases. -4.E-05 -3.E-05 -2.E-05 -1.E-05 0.E+00 1.E-05 2.E-05 3.E-05 4.E-05 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) 1st 2nd 2nd 3rd 4th 5th Figure 3-21. Magnetization as func tion of magnetic field for a sp ark-processed silicon sample (sparking time = 6 hours and frequency = 22. 5 kHz) at room temperature after each heating cycle (heating up to 800 K and c ooling down to 300 K in a 1000 Oe field). The first two (grey and purple) were measured on the same day, while the others were measured at a later time. The relevant data, remanence and magnetiza tion at 1000 Oe as a function of annealing time, can be better seen in the next graph, figure 3-22. The remanence as well as the magnetization at 1000 Oe decrease slowly in a linear manner with annealing time. The magnetization at 1000 Oe decreases by about 15% ove r an annealing time range of 35 hrs. This is only a 3% decrease per heating cycle. The pr eviously presented data of magnetization as a Sample name: MSP104

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64 function of temperature is only marginally aff ected. Therefore, our conclusions on the magnetic behavior of sp-Si at high temperatures are unchanged. Ms = -10-7 Time + 3.5*10-5R2 = 0.997 Mr = -4*10-8 Time + 10-5R2 = 0.52 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05 0 5 10152025303540Annealing Time (Hours)Magnetization (emu) Ms (1000Oe) Mr (0Oe) Figure 3-22. Magnetization at 1000 Oe (blue diamonds ) and 0 Oe (red squares) versus annealing time for spark-processed silicon (sparki ng time = 6 hours and frequency = 22.5 kHz). Linear models are plotted as solid lines. The annealing was performed during heating at 800 K and cooling back to 300 K in a 1000 Oe field over a 7 hours heating-cooling cycle. 3.3 Low Temperature Magnetization In this section we present and analyze the magnetization as function of temperature of spark-processed silicon at low temperatures. But, similarly to high temper atures, proper control measurements need to be performed before doi ng experiments on unknown material such as spSi. Therefore, we will use HgCo(SNC)4 and aluminum as low temperature references. Also, we will discuss observed artifact caused by oxygen in the sample chamber. Sample name: MSP104

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65 3.3.1 Magnetic Reference Material HgCo(SNC)4 for the 2-100K Temperature Range This reference material is used to make su re that the SQUID magnetometer measurements are reliable. Several references can be used to validate magnetization measurements with the SQUID magnetometer at very low temperature (2-100K). The cobalt mercury cyanide is a widely used reference for this range and was readily available to us. This material comes in a powder form and special handling is required due to its toxicity and potential to contaminate the magnetometer. A special sample holder was designed to prevent loss or scattering of the material during the measurement process. A descripti on of the holder design can be found in the Appendix B. To evaluate the reliability of the SQUID magnetic measurements, we look at the correlation between the magnetic susceptibility of HgCo(SNC)4 as a function of temperature of our own data and the one published by OConnor32. We find an excellent match with a correlation coefficient of 0.9999. Our results are also consiste nt with the values published by Bunzli33. We concluded that HgCo(SNC)4 is a good choice of standard for very low temperature magnetic measurements and that our SQUI D magnetometer gives reliable magnetic measurements in the 2 to 100K range since we ha d a very good correlation between our data and previously published ones. This work is fully detailed in the Appendix B. 3.3.2 Aluminum Reference for the 50-300 K Temperature Range Aluminum has been well studied in the 50-300K temperature range and is a better suited magnetic standard than HgCo(SNC)4 in this range due to its large temperature coefficient. First, we measured a magnetic susceptib ility at room temperature of 3.377-8 emu for the aluminum sample. Using the measured weight of the sample (53.4 .1 mg) we calculated a

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66 sample volume of 0.0198 .00004 cm-3 leading to a volume susceptibility of 1.70.03-6 cm-3. This value is very close to the published value2 of 1.65-6 cm-3. Next, we measured the susceptibility as function of temperature. The aluminum susceptibility is linearly dependant on the square of temperature according to Hedgcock34. This dependence can be expressed by the following equation: 02 diapara B T where dia is diamagnetic susceptibility, 0 para is the temperature independent paramagnetic susceptibility and where B is a constant characteri stic of aluminum. We found a correlation coefficient of 0.997 between our data and this proposed model. The results from HgCo(SNC)4 and Aluminum reference lead us to conclude that our the magnetization measurements at low temperatures with our SQUID magnetom eter are reliable. In addition, to proper calibration, oxygen contamin ation could be an issue with high resolution magnetization at low temperature. In the next section, we will discuss the oxygen contamination. 3.3.3 Oxygen Effect at Low Temperature Oxygen contamination is a known problem with low temperature measurements with a SQUID magnetometer but not very publicized. I have published on this topic35 and found out that it was known to Quantum Design Inc., the manufacturer of our SQUID magnetometer but an application note has never been written to help users properly interpret their measurements. Therefore some clarifications are needed. Oxygen is paramagnetic in its gas and liqui d phases, becomes antiferromagnetic when solid below 54.3 K, and changes its crystal structure36,37 ( to at 43.8 K). The magnetic transitions of oxygen at 54.3 K and 43.8 K gene rate a noticeable change in the measured magnetic susceptibility of a sample while some gaseous oxygen is left in the sample chamber.

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67 Typically a large peak around 50 K is observe d in addition to the magnetization of the characterized sample. In our SQUID magnetometer, a sample is normally measured in a Helium gas. Following the sample loading, the load lock (or the entire chamber) is purged with Helium gas. But due to pumping and Helium quality there is still oxyge n left in the chamber. When no purge is performed a large peak is obser ved as expected since we l eave a large amount of oxygen gas from air in the chamber. But, even when we purged 3 times the oxygen peak is still visible. This small trace of oxygen could be explained by the limiting pumping capability of the mechanical pump and the presence of trace oxygen within th e helium gas use to cool down the sample. See Appendix D for more details. Finally, this oxygen effect is only visible in samples with magnetization in the 10-5 or 106 emu range. Therefore we recommend, in addition to multi-purging, using samples as large as possible to decrease the relative effe ct due to oxygen magnetic transition. Now that we have shown that our SQUID ma gnetometer works properly over the entire temperature working range and th at we have discussed the probl em associated with the oxygen, we can focus on spark-processed silicon. 3.3.4 Spark-Processed Silicon Low Temperature Magnetization We have previously shown that spark-processe d silicon had a magnetic hysteresis at room temperature. Upon cooling, this magnetic hysteres is loop remains present as seen in Figure 3-23. The magnetization versus field was measured at 35 and 70 K. The remanence is the same for both temperature but the magnetization at non zero field increases as the temperature is cooled down. The magnetization increases by 30% at 1 000 Oe. Further, the hysteresis loop rotates counterclockwise as the temperature is lowered. This can be explained using a complete model of the magnetization for sp ark-processed silicon.

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68 -2.0E-05 -1.5E-05 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) 35.0 70.0 Figure 3-23. Magnetization versus field at 70 K and 35 K of sparkprocessed silicon (square and round points, respectively). We model the magnetization as followed: 00() (,)spSidiaparapara Hysteresis M THMTH where 0 dia is the diamagnetic susceptibility,0 para is the temperature independent paramagnetic susceptibility, ()paraC T T is the Curie-Weiss susceptibility and (,)Hysteresis M TH is the Weiss magnetization presented in Section 3.2.3. The Weiss magnetization is only temperature dependent near the Curie temperature. At temperatures well below the Curie temperature (760 K for sp-Si), the Weiss magnetization is almost temperature independent. For example, using the Weiss model, we evaluated a magnetization decrease of 1.3% between 10 and 300 K using a Curie temperature of

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69 760 K. On the other hand, the Curie-Weiss suscep tibility is strongly temperature dependent at low temperature. The rotation of the hysteresis loop at low temperature is therefore interpreted to be due to paramagnetic centers which follow the Curie-Weiss law. 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05 4.0E-05 4.5E-05 5.0E-05 020406080100120140160180200220240260280300Temperature (K)Magnetization (emu) 1000Oe T going down 0 Oe T going down Magnetization model O2 phase transition Figure 3-24. Magnetization versus temperature for spark-processed silicon at 1000 Oe (red triangle) and 0 Oe (bleu squa res). A model is fitted to the 1000 Oe magnetization curve in solid red. The bump is magnetiza tion near 40 K is an artifact caused by a phase change of oxygen contamination in the measured chamber (see Appendix D). If we set the magnetic field and consider the Weiss magnetization to be temperature independent we can simplify our magnetization model to: 0spSiC MM T where 00 0()diapara Hysteresis M HMH and 'CCH Using this model on our magnetization versus temperature data for sp-Si presented in Figure 3-24, we obtain the following fitting parameters: M0 = 1.07-5 emu, C = 1.73-4 emu. Oe and = -3.16 K with a correlation

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70 coefficient of 0.995. (Since oxygen has an influen ce on the data in the temperature range 20 to 60 K, we only use the data points outside this te mperature range to fit our model). In addition, Figure 3-24 also contains the rema nence versus temperature of sp-Si. It should be noted that the remanence does not change with temperature ove r the whole range, therefore validating the temperature independence assumption from the Weiss model. R2 = 0.997 R2 = 0.975 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05 4.0E-05 0.000.050.100.150.200.250.300.350.400.450.501/(T+3.16K) and 1/TMagnetization adjusted for diamagnetism and remanance 1/(T+3.16K) 1/T O2 phase transition Figure 3-25. Magnetization adjusted for diamagne tism and remanence as a function of inverse temperature. The temperature has been shifted by 3.16 K to account for low temperature exchange interactions. A linear tr end is fitted to the low temperature data (solid line). A green arrow ma rks the oxygen phase transition. Since it is difficult to visualize the good co rrelation between our data and our proposed model in Figure 3-24, another pr esentation of the data is propos ed Figure 3-25. In Figure 3-25, the magnetization at 1000 Oe is plotted as a function of 11 [] K T This method emphasizes

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71 more the data points below 20 K and allows fo r a good visual correlati on between our proposed model and our data. For comparison the magne tization is also pl otted as function of 11 [] K T. It is observe that in this case the model does not fit well the data. 3.4 Summary From my research we learn the following: Sp-Si displays a magnetic hysteresis loop at room temperature under certain processing conditions. A specific method was developed to meas ure the magnetization of sp-Si at high temperature. From this method it was found that sp-Si magnetizati on as a function of temperature follows the Weiss equation. A Curie temperature of 765 K as been evalua ted from the Weiss e quation applied to the high temperature magnetic measurements for sp-Si. Annealing of sp-Si up to 800 K decreases th e magnetization at 1000 Oe and the remanence weakly. At low temperatures, sp-Si exhibits a large magnetization inversely proportional to the temperature which is characteristic of paramagnets.

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72 CHAPTER 4 INTERPRETATION OF QUASIFERROMAGNETI SM IN SPARK PROCESSE D SILICON This chapter is dedicated to the study of the paramagnetic centers present in spark processed silicon and how they are rela ted to the observe quasiferromagnetism. 4.1 Model Concerning the Distribution of Paramagnetic Centers In order to explain the magnetic hysteresis and the high Curie temperature in sp-Si we propose that some paramagnetic centers, found in spark processed silicon, in teract such that the exchange integral is positive. First, to observe exchange intera ction between elec tron spins, the distance38 between them has to be smaller than 2 nm. It will be shown in a last section of this chapter that the calculated average paramagnetic centers density in sp ark processed silicon is about 219 cm-3. Assuming that the paramagnetic centers are equally spaced from one another, this would put an upper limit of 3.7 nm between them. We propose therefore that the inter-spin distance is not homogeneous in sp-Si. That is, so me paramagnetic centers could be less than 2 nm apart thus allowing exchange interaction betw een them. Figure 4-1 schematically depicts this proposed distribution of parama gnetic centers in spark-proces sed silicon. Some spins are assumed to form clusters (small inter-spin distance) and others are isolated (large inter-spin distance) such that they do not participate in exchange interaction. Our results presented in the previous chapter support such a model since the independent spin s lead to paramagnetism which we found to be present and the in teracting spins within a cluster lead to a hysteresis which we also found in sp-Si. In addition, to support our model we characterize the paramagnetic centers using electron paramagnetic resonan ce. But first, we need to explain a few concepts using this technique. Note: we use spin or paramagnetic center in terchangeably throughout this chapter.

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73 Figure 4-1. Proposed paramagne tic centers distribution. Figure 4-2. Energy levels of an electron at the resonance field. Field B0 h = gBB0 0 E E E0 Microwave Absorbance Energy Paramagnetic centers Clusters Diamagnetic matrix

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74 4.2 Electron Paramagnetic Resonance (EPR) Concepts To perform an electron paramagnetic resonan ce experiment, we place a sample containing unpaired spins in a resonant cavity which itself si ts in the center of a la rge electromagnet. In addition to being exposed to a magnetic field, mi crowaves are directed to wards the sample inside the cavity (Figure E-1 in Appendix E). The micr owaves have a very specific frequency of 9.75GHz for X-band EPR while the field is sw ept around 3.5 kG. The field splits the electron energy in two, E= + g BB0 and E= g BB0, where g is the Lande factor, B is a constant called the Bohr magneton, and B0 the magnetic field. When the magnetic field is such that the difference between the two energy levels is equal to the microwave energy we have resonance, i.e. the electron absorbs the microwave photon. The resonance condition leads to the following equation, E = E E = g BB0 = h, where h is the Planck constant and is the microwave frequency. The absorption is maxi mal at the resonant condition, B0 = h/g B. Since, B, h and are constants; the resonant fiel d depends on the g-factor. This f actor depends on the environment of the paramagnetic center studied. It is used as an identifier for a particular type of magnetic center. Figure 4-2 shows the resonance conditions. In practice, modern EPR instruments use fi eld modulation to reco rd a spectrum. Field modulation adds a small alternati ng field to the large static fiel d. This small field is about 1 Gauss in our case while the large field is in the 3000 to 4000 Gauss range. The modulation allows better sensitivity by using lock-in amplifica tion. In addition, instea d of directly observing the absorption we measure its first derivative. In the next section we expl ain how spectra are decomposed into independent factors which are then analyzed individually to characterize the studied material.

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75 4.3 Characterization of Continuous Wave Electron Paramagnetic Resonance Spectra The EPR spectrum of spark-processed silicon is complex. It contai ns several features which need to be separated before each individual component is studied. To study sp-Si EPR spectra we use a mathematical function to model th e absorption. But first, we need to explain the mathematical function. Figure 4-3 schemati cally depicts our deconvolution scheme. Figure 4-3. Lorentzian distribution and 1st derivative of electron mi crowave absorbance as a function of the magnetic field. A) one type of paramagnetic center. B) two different types of paramagnetic centers (red curves ) and their deconvolu tion (blue and green curves). Field B0 1s t derivative (Observed) Microwave Absorbance Field 2 types of paramagnetic centers 1 type of paramagnetic center A B Measured D econvolute

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76 When only one type of paramagnetic center is observed the model is simply the first derivative of a single line. The term line refers to a very sharp peak characteristic of one paramagnetic center. In addition, when two or more types of paramagnetic centers are observed simultaneously, the model will be the sum of the fi rst derivatives of two or more lines which is due to the independent physical origin of the electron resonance for each type of center. Each line is characterized by a mathematical function. In the case of sp-Si we use a Lorentzian distribution but other functions are also commonly used such as Gaussian or Dysonian distributions. The type of distri bution is characteristic of the excited spins. For example highly oriented pyrolitic graphite displays a Dysonian behavior, which is discussed in the next chapter. The equation for a normalized Lorentzian distribution is: 0, 22 01 2 () ()() 2xfx xx where is the full width at half maximum, and x0 is the center of the line. This distribution is normalized using the following condition: 0,()1x f xdx Our model for one line is y=Af(x), where A is the area under the curve. We call it the amplitude. Under specif ic conditions, it is proportional to the number of paramagnetic centers The first derivative of the Lo rentzian distribut ion is defined as: 00 2 22 01 () ()() 2xxx fx xx In spark processed silicon we observe two types of paramagnetic centers and therefore our full mathematical model for the absorption is: 11 22'' 1,2,()()xxyAfxAfxwhere x is the magnetic field. Each type of paramagnetic center is characterized by an amplitude (A), a center field (x0) and a line width ( ). We call our model two-Lorentzian. Figure 4-4 disp lays an EPR spectrum for spark processed silicon measured at room temperature and a two-Lorentzian mode l. We found a very good agreement between the

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77 model and the experimental data, where the coeffi cient of correlation is better than 0.98. The full justification of our model will be discussed later in this chapte r. First we need to identify each of the paramagnetic centers observed in the spectrum This is done by calculating the g-factor from the Lorentzian model and comparing it with literature data. For a precise identification, a known standard, DPPH (2,2-Diphenyl-1-Picrylhydrazyl), is used as a reference point for the center field. The standard and a sp-Si sample were measured at the same time in the EPR system thus virtually eliminating instrumental errors. -1000 -800 -600 -400 -200 0 200 400 600 800 1000 1200 335033553360336533703375338033853390339534003405Field (Gauss)Intensity (a.u.) Data Model Deconvolution 1 Deconvolution 2 Proportional to defect density Proportional to line width Inversly proportional to g-factor Figure 4-4. Electron paramagnetic resonance spectrum of spark-processed silicon (back line) at room temperature with its double Lorentzian 1st derivative model (red). For clarity the deconvoluted curves are plotted in green a nd blue. Experimental parameters, power = 0.6331 mW, power attenuation = 25 dB, modulation field = 1 G, time constant = 10 ms, detector gain = 60 dB, temperature = 300 K. Sample name: NSP12E_001

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78 Figure 4-5 displays the spectrum of sp-Si al ong with the DPPH standard. Using a threeLorentzian model (correlation coefficient = 0.986) we obtain three resonant fields, two from spSi and one from DPPH. The published g-factor39 for our standard is 2.0036. From the resonant condition equation presented in the previous section (g BB0 = h), we calculate the microwave frequency to be cal = 9.75044GHz. Then, using the same resonance condition equation with the calculated frequency and the resonant field found for spark processed silicon from our Lorentzian model we calcu late two g-factors, g1 = 2.0050 and g2 = 2.0013. -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 34503455346034653470347534803485349034953500Field (Gauss)Intensity (a.u) Data Deconvolution 1 Deconvolution 2 Deconvolution 3 model Red = green + yellow + blue Figure 4-5. Electron paramagnetic spectra of spar k-processed silicon along with DPPH reference standard (black line). Its model plotted in red is deconvoluted in three sub-models (green, yellow and blue curves). Expe rimental parameters, power = 0.6331 mW, power attenuation = 25 dB, m odulation field = 1 G, time constant = 40 ms, detector gain = 70 dB, temperature = 300 K. Sample name: EPR05_047

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79 Using the extensive literature40-47 on paramagnetic centers in silicon-based material, we identify the first paramagnetic center with a g value of 2.0050 to stem from silicon unpaired bond, backboned by three silicon atoms as schematically represented in Figur e 4-6; it is called D center. From literature41-46 the D center g-value varies between 2.0050 and 2.0055. In addition the paramagnetic center with a g-value of 2.0013 is attribut ed to a silicon unpaired bond, backboned by three oxygen atoms; it is called E center. The E cen ter has many variations40 stemming from different precursors in SiO2 based material, but they all have g values between 2.0000 and 2.0018. Spark processed silicon is a n onstoiechiometric silico n dioxide doped with nitrogen28 (SiOx:N) and therefore finding E and D center is acceptable. Figure 4-6. Nature of spark-pro cessed silicon paramagnetic centers. It is to be noted that any impurities such as iron, nickel, or cobalt, which could cause a magnetic hysteresis may absorb microwaves as we ll and therefore may be identified using the same method as in the identification of parama gnetic centers in sp-Si. They would possess, however, different g-values than those found he re. No characteristic absorption from these elements was found in spark processed silicon. Si Si Si Si g-factor = 2.0050 Si O O O g-factor = 2.0013

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80 The resonant field has helped us to identify the paramagnetic centers but we have not justified yet why our model is corr ect. To verify that the differe nt types of paramagnetic centers are truly independent from one another in sp-Si, we conducted a power saturation experiment. The amplitude, as defined previous ly, is linearly dependent on the square root of the microwave power44. This relationship is valid for small power values. When the power gets high enough the amplitude saturates. Figure 4-7 displays the amplitude of the D centers versus the microwave power. 0 5 10 15 20 25 30 35 0246810121416182022Power (mW)Amplitude (a.u.) Figure 4-7. Amplitude of D paramagnetic cen ters as a function of microwave power. In order to find the saturation point we first plot the amplitude as a function of the square root of the input power, Figure 48. The point at which the amp litude is deviating from a linear trend, defines the saturation point In the case of the D centers a power greater than 0.2 mW (30

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81 dB attenuation in our spectrome ter) is enough to saturate the paramagnetic centers. Above the saturation point, the amplitude is no longe r proportional to the number of spins. 0 5 10 15 20 25 30 35 40 45 00.511.522.533.544.55Power1/2Amplitude (a.u.) Figure 4-8. Amplitude of D paramagnetic centers as a function of the square root of the microwave power (dots). A linear trend is fitted for the lowest power data points (R2=0.995). We conducted a similar study for the E centers as depicted in Figures 4-9 and 4-10. A saturation power of 0.06 mW (35 dB attenuati on in our spectrometer) was found. Knowing the saturation point is not only important for comparing samples or spectra from the same sample at different temperatures, it is also important to justify our two-Lorent zian model. Since the saturation points are different for each of the obs erved features in a sp-Si spectrum, they are not stemming from the same physical origin and therefore are independent. This independence justifies that our model uses the sum of two i ndependent lines. Figure 4-11 shows schematically

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82 how the amplitudes of the D center and the E ce nter responded differently to the microwave power. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 00.020.040.060.080.10.120.140.160.180.20.22Power (mW)Amplitude (a.u.) Figure 4-9. Amplitude of E paramagnetic centers as a function of microwave power. In addition, the line width of each of the two observed features do not have the same behavior with respect to the microwave power as seen in Figure 4-12. The D centers line width does not vary with microwave power, while the E centers line width is linearly dependent on the log of the power which is explained in the ne xt paragraph. The differe nt behaviors of the E and D center are characteristic of their inde pendent physical origin and justifies our twoLorentzian model.

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83 -0.5 0 0.5 1 1.5 2 2.5 00.050.10.150.20.250.30.350.40.450.5Power1/2Amplitude (a.u.) Figure 4-10. Amplitude of E paramagnetic cente r as function of the square root of the microwave power (dots). A linear trend is fitted for the lowest power data points (R2=0.995). Eaton and Eaton48 have developed a power saturation m odel which we apply to sp-Si. The saturation model48 is defined as: 1/2 /2 baP amplitude cP where P is the microwave power, a is a proportionality constant, c is a constant related to the power at half saturation and b is an exponent which depends on the homogeneity of the line. The exponent constant b is an important factor. In the extreme cases when b =1 we are in the inhomogeneous limit and when b=3 we are in the homogeneous limit. In the case of sp-Si we plot and compare the models ( b=1 and b=3) for each of the paramagnetic centers in Figure 4-13 and 4-14. In the case of the D centers, the data is

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84 very well describe (R2=0.998) by the inhomogeneous case whil e for the E centers the model matches the data well for the homogeneous case. Figure 4-11. Saturation effect observed for the two paramagnetic centers in spark-processed silicon. For comparison purposes we also plotted the other models on each of the graphs to visually convince ourselves which model (i.e. which b value) works best. It can be added that this conclusion is further confirmation that both EPR lines come from different paramagnetic centers. Finally, the next figure is dedi cated to confirm that the Lorentzian equation is the best choice for modeling sp-Si EPR spectra. Figure 4-15 displays the comparison between sp-Si data and two models best fit, Gaussian and Lorent zian. Both models were best fitted using the software OriginPro 7.5. In conclusion, we have presented several valid ation points to confirm the Lorentzian model of sp-Si EPR lines and using this model we have identified the paramagnetic centers present. MicrowavePower Amplitude Saturation point Paramagnetic center 1 g-factor = 2.0050 Paramagnetic center 2 g-factor = 2.0013

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85 0 2 4 6 8 10 12 14 -3.5-3-2.5-2-1.5-1-0.500.511.5Log( Power (mW))Line width (Gauss) D center line width E' center line width Figure 4-12. Line width as a function of Log (power) for spark-processed silicon. 0.E+00 1.E+06 2.E+06 3.E+06 4.E+06 5.E+06 6.E+06 7.E+06 0246810121416182022Power (mW)Amplitude (a.u.) Amplitude Model b=1 Model b =3 Figure 4-13. Amplitude of D pa ramagnetic centers as a functi on of microwave power (dots). Two saturation models are fitted to the data (solid lines).

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86 0 5000 10000 15000 20000 25000 30000 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14Power (mW)Amplitude (a.u.) Amplitude Model b=1 Model b =3 Figure 4-14. Amplitude of E paramagnetic centers as a function of microwave power for sp-Si (dots). Two saturation models have been fitted to the data (solid lines). -1500 -1000 -500 0 500 1000 1500 3330 3340 3350 3360 3370 3380 3390 3400Field (Gauss)Intensity (a.u.) Data Gaussian model Lorentzian model Figure 4-15. Electron paramagnetic resonance spectra of spark-processed silicon at 4.2K (black line) and two possible models: Gaussian base d (blue line) and Lorentzian based (red line). Experimental parameters, power = 0.002 mW, power attenuation = 50 dB, modulation field = 1 G, time constant = 20 ms, detector gain = 70 dB, temperature = 4.2 K.

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87 We can now concentrate on characterizing th e paramagnetic centers, compare the results with the magnetization obtained from our SQUI D and validate our quasiferromagnetic model. 4.4 Electron Paramagnetic Resonance Parameter versus Temperature The temperature dependence of the sp-Si EPR spectra is very useful. First, the amplitude of the EPR lines is proportional to the number of spins, as long as we are not saturating the signal. 0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05 3.0E+05 3.5E+05 4.0E+05 4.5E+05 5.0E+05 020406080100120140160Temperature (K)Amplitude (a.u.) Settings: 30dB-70dB Settings: 40dB-60dB Settings: 50dB-70dB Figure 4-16. Amplitude of D centers versus temp erature. The data points above 40K have been divided by 10 to account for the change in ga in setting. The gain is changed to keep the signal in the linear regime. Since we have performed a saturation experi ment we now know in which power range we have to measure our data. Also, the magnetizati on of independent spins is proportional to the number of spins. Thus, the amplitude of th e EPR absorption line is proportional to the magnetization as long as these two assumptions ar e met. In addition, the temperature dependence

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88 of the line width will be useful for comparis on with pulsed EPR experiments, which will be presented in a later section. We present, now, the temperature dependence of the amplitude, line width and g-factor all together of the D and E centers present in sp-Si at low temperature and then high temperature. y = 1E+06x R2 = 0.9886 0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05 3.0E+05 3.5E+05 4.0E+05 0.000.020.040.060.080.100.12 0.140.160.180.200.220.240.261/Temperature (K-1)Amplitude (a.u.) Settings: 40dB-60dB Settings: 50dB-70dB Settings: 30dB-70dB Figure 4-17. Amplitude of D centers versus inve rse temperature (dots). The data points below 0.025K-1 have been divided by 10 to account for the increased gain. A linear trend is fitted to the data (solid line). 4.4.1 Low Temperature 5 to 300K In order to study each paramagnetic center type we continue to use our two-Lorentzian model and apply it at each temper ature. Then the modeled amplitude line width a nd g-factor can be plotted as a function of temperature. The amplitude versus temperature is plotte d in Figure 4-16 for the D centers. One can observe that the amplitude increase as the temperature decrease. In order to prevent saturation,

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89 the microwave power was decreased and the detect or gain increased. Three different settings were used and the amplitude was multiplied by the proper coefficient to account for mismatches between the microwave power and the signal gain scales. Furthermore, the amplitude is plotted against the inverse temperature in Figure 4-17. A linear trend is fitted to the data with a correlation coefficient of 0.99. 0.0E+00 5.0E+03 1.0E+04 1.5E+04 2.0E+04 2.5E+04 3.0E+04 3.5E+04 020406080100120140160Temperature (K)Amplitude (a.u.) Settings: 50dB-70dB Settings: 40dB-60dB Settings: 30dB-70dB Figure 4-18. Amplitude of E centers versus temp erature. The data points above 40K have been divided by 10 to account for the increased gain. In the case of independent spins, the magnetization is simply proportional to the measured amplitude and therefore inversely proportional to the temperature. The experimental results suggest that the EPR amplitude follows the Curie law. It could be argued that this relationship demonstrates the independence of the parama gnetic centers and therefore deny our cluster model. But, it has been calculated49 that for a ratio of independent spins over spins within

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90 clusters of 50%, the magnetic susceptibility is almost observed as coming from independent spins only. First, we believe that spins in sp-S i are mostly independent, as shown by the observed Curie law. In addition, we suggest that the ma gnetization coming from the clusters of spins is small in comparison to the magnetization from the independent spins. Similar conclusions are drawn for the E centers. Figure 4-18 and 4-19 present the amplitude of the E centers as a function of the temperature and inverse temperature, respectively. 0.0E+00 5.0E+03 1.0E+04 1.5E+04 2.0E+04 2.5E+04 3.0E+04 3.5E+04 0.000.020.040.060.080.100.12 0.140.160.180.200.220.240.261/Temperature (K-1)Amplitude (a.u.) Settings: 50dB-70dB Settings: 40dB-60dB Settings: 30dB-70dB Figure 4-19. Amplitude of E centers versus inve rse temperature (dots). The data points below 0.025 K-1 have been divided by 10 to account for the increased gain. A linear trend is fitted to the data (solid line). Additionally, the line width for both centers is plotted versus the temperature in Figure 420. In both cases the line width is essentially temperature in dependent. The line width depends

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91 on different relaxation mechanism and a full account of that dependence will be presented in the pulsed EPR section of this chapter. 0 2 4 6 8 10 12 14 020406080100120140160Temperature (K)Line width (Gauss) Line width 1 Line width 2 Figure 4-20. Line width of the two paramagnetic centers present in spark-processed silicon versus temperature in the low temperature range. Line width 1 corresponds to the D centers and line width 2 co rresponds to the E centers. The characterization of the centers is comple ted with the temperature dependency of the gfactors. Figure 4-21 pres ents the g-factor for each center as a function of temperature. For the D centers the g-factor does not depe nd on the temperature while for th e E centers the g-factor has a small temperature dependency. We believe that the main reason which explains this small dependence is associated with the difficulty of f itting the Lorentzian equa tion. The signal from the E centers is much smaller than the D centers and therefore modeling is a more difficult process since both signals are collected togeth er and interfere with one another.

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92 2 2.001 2.002 2.003 2.004 2.005 2.006 2.007 02 04 06 08 01 0 01 2 01 4 01 6 0Temperature (K)g-factor (uncalibrated) g-factor 1 g-factor 2 Figure 4-21. Spark-processed silicon paramagnetic centers g-factor ( uncalibrated) versus temperature. The g-factor 1 corresponds to the D centers while the g-factor 2 corresponds to the E centers. 4.4.2. High Temperature 300 to 800K While the low temperature EPR equipment was r eadily available, we were not equipped at first for high temperature measurements. I desi gned and assembled a high temperature oven for the EPR spectrometer which allows stable temp erature up to 600 K. The temperature can be pushed up to 700 K if precision is not essential. More details can be found in the Appendix B about the design and working condition of this oven. For the highest temperature measurements we collaborated with Dr. Causa from the Centro Atomico Bariloche in Argentina, who is equipped with a commercial high temperature EPR cavity.

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93 2.002 2.0024 2.0028 2.0032 2.0036 2.004 2.0044 2.0048 2.0052 2.0056 2.006 300350400450500550600650700750800Temperature (K)g-factor (uncalibrated) g-factor 1 g-factor 2 g-factor 1 after cooling Cooling direction Heating direction Figure 4-22. Spark-processed silicon paramagnetic centers g-factor versus temperature. The gfactor 1 corresponds to D centers while the g-factor 2 corresponds to E centers. The g-factor 1 was measured again after cooling back to room temperature (blue triangle) and the same value was found as before the heating (green diamond). The same analysis method for the high temperature EPR spectra as for the low temperature spectra of sp-Si was used, meaning that we continue to use a two-Lorentzian model. First, we look at the g-factor temperature be havior. Figure 4-22 displa ys g-factors for both paramagnetic centers. The g-factor of the E centers is temperature independent in this temperature region. On the other hand the g-factor of D centers is affected by the temperature. Both g-factors are deconvoluted from the same spectrum. If the temperature dependence was due to the deconvolution method we would observe bo th g-factors to have the same temperature dependency. But, it is not the case. The scatter ar ound the average g-factor of the E center give

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94 an estimate of the error on the measurement. Bu t a much larger variation of the D centers gfactor is observed. Therefore, we conclude that the g-factor of the D centers is temperature dependent. It should be noted that after cooling back to room te mperature the g-factor of the D centers reverts to its original value and therefor e the process is reversible. Also, it only affects the g-factor of D centers and not the g-factor of E centers. We suggest that thermal expansion could be one of the effects responsible for the g-factor temperature de pendence. Since the E centers are related to oxygen rich defects we assume that they are located in the SiO2 matrix. The D centers are only related to silicon atoms and th erefore we suggest that they are likely to be located in or at the surface of silicon clusters within the SiO2 matrix. Specifically, the thermal expansion coefficient of each of these materials, that is, SiO2 and silicon are ve ry different. The thermal expansion coefficient of SiO2 is very small compared to the one of silicon2 This could induce changes on the bond length between silic on atoms, therefore affecting the electron orbitals and consequently the g-factor of the D centers. It should be noted in passi ng that the concept of silicon clusters imbedded in a SiO2 matrix has been studied and documented by our group usi ng comparison between optical properties and computer molecular modeling50 as well as by direct tran smission electronic microscopy observation of silicon nanocrystals51. Secondly, the study of the line width as a f unction of the temperature does not show any influence as displayed in Figure 4-23. For both centers the line wi dth is temperature independent. Finally, the amplitude variation of the EPR lin e intensity for each defect as a function of the temperature is studied. Using our high temper ature apparatus we obser ved a slight decrease of the D and E centers amplitude as a functi on of temperature in the 300 600 K range (results not shown). Due to the strong d ecrease in sensitivity of our cav ity at temperatures above 600 K

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95 we felt like our data was not re liable above this temperature. This prompted the collaboration with Dr. Causa who has measured the EPR spectra of sp-Si for us. Her EPR system is designed to work at temperatures up to 1300K with no loss in sensitivity. Once the spectra were received, I used the same two-Lorentzian model analysis to calculate the amplitude of the E and D paramagnetic centers. 0 2 4 6 8 10 12 14 300350400450500550600650700750800Temperature (K)Line width (Gauss) Line width 1 Line width 2 Figure 4-23. EPR line width of the two paramagnetic centers present in sp ark-processed silicon versus temperature in the high temperatur e range. The line width 1 corresponds to D centers while the line width 2 corresponds to E centers. Figure 4-24 displays the amplitude of the D and E paramagnetic centers (that is the A factor in the Lorentzian model) as a function of the temperature. In the case of the D centers, the amplitude is steady up to 500 K and then decrease s down to almost zero at 700 K. On the other hand, the E paramagnetic centers amplitude is not affected by the temperature between 580 and

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96 780 K. At temperatures below 580 K the deconvol ution with the two-Lorentzian model is not possible because the E center is too weak compared to the D centers amplitude. 0 200000 400000 600000 800000 1000000 1200000 1400000 1600000 1800000 250300350400450500550600650700750800Temperature (K)Amplitude of D and E' centers (a.u. ) A mplitude E' centers x10 sample name: MSP120 Figure 4-24. Amplitude of D (blue) and E (red) centers versus temperature for spark-processed silicon in the high temperature range. These results confirm our previo us suggestion that the D and E centers are not related to one another. In addition, we pr eviously suggested that the E centers are located in the SiO2 amorphous matrix while the D centers are located in silicon nanocry stals or clusters. Therefore, we propose that these two types of centers are no t close to one another, adding another argument to our theory of non-random distribu tion of paramagnetic centers. At low temperature, we observed that the magnetization as well as the amplitude of the D and E centers were characteristic of the Curie law. But, at high temperature (that is about 300 K) the measurements do not suggest a Curie law behavior but rather a behavior modeled with the Weiss equation. This is shown in Figure 4-24, where a Curie law model is plotted and one can

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97 see that the data does not follow that law. We suggest that the deviation from the Curie law at high temperature can be explained by the decoupling of the intera cting centers within clusters. When the temperature is near the Curie point, the thermal en ergy is large enough to overcome the exchange interaction between two spins. When this happen the two spins become individual spins and now behave like independent paramagnetic centers explaining the non-zero amplitude above the Curie point. 0 0.2 0.4 0.6 0.8 1 1.2 250300350400450500550600650700750800Temperature at sample (K)D center Amplitude and Magnetization at 1000 Oe (a.u.) Sample Names: MSP104 MSP120 Tc = 770 K Tc = 710 K Figure 4-25. Amplitude of D cen ters (blue dots) and Magnetiza tion at 1000 Oe (green dots) versus temperature for spark-processed silicon in the high temperature range. A Weiss equation is fitted through both data se ts (solid curves). For comparison a Curie law curve is plotted (black dash). The amplitude data of the D centers was also compared to the Weiss equation to evaluate the Curie temperature. We followed the same met hod previously described in chapter 3 (section 3.2.3). A Curie temperature of 710 K was found. Fi gure 4-25 displays the D centers amplitude as a function of temperature along with its Weiss model curve. In addition, the magnetization of a

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98 similar sp-Si sample as a function of temperat ure is plotted on the same graph along with its Weiss model curve (previously presented in sec tion 3.2.3). The comparison between the two sets of data suggests that the D centers are at the origin of the magnetization behavior of sp-Si for temperature above 300 K. It could be argued that the Curie temperatur e evaluated from the Weiss model with the magnetization data is too different from the one found with the data stem ming from EPR, but, we could attribute the differences to the type of instrument, which inevitably lead to some discrepancies, and to the samples being prepared in a similar manner but not being exactly the same. For example, the EPR technique is not sensitive to diamagnetism and species with an integer total spins while the SQUID magnetometer is. It should be noted in passing that the data obtained from Dr. Causa and our data obtained with our own laboratory made equipment are consis tent with one another for temperatures up to 600 K. Above that temperature our data on amp litudes of the E and D centers is no longer reliable. In conclusion, the continuous wave EPR has allowed the identifica tion and separation of two paramagnetic centers. Also, the EPR spectral analysis and the comparison with the magnetization of sp-Si at high temperature ar e consistent with our paramagnetic center distribution model. Continuous wave EPR allows the indirect meas urement of the density of the paramagnetic centers, but the direct method by pulsed EPR is pr eferred. The main reason for not using cw-EPR is the need for a precise measurement of the sa mple volume, which turns out to be extremely difficult for sp-Si. Pulsed EPR is a better technique for measuring the density which leads to the distance between paramagnetic centers. But it requires the characteri zation of the observed

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99 signals which is more complex, as this tec hnique is more complex than cw-EPR. The next section focuses on that method. 4.5 Characterization of Pulsed Electron Paramagnetic Resonance Our goal in using pulsed EPR is to calculate th e density of the paramagnetic centers at the local level and therefore calculate the maximu m separation distance between spins. This will then be used to complement the model proposed to explain quasiferromagnetism. We separate this part of the chapter into several sections to facilitate its understanding. In the first section, we present the relaxation rates measured on sp-Si and information extracted from them. In a subsequent section we propose to separate the ce nters by relaxation rates. Then, we measure the relaxation rates leading to the local density of spins. 4.6 Relaxation Rates In the pulsed EPR world there are many ways of acquiring a signal. In our case, we are very much interested in the ba sic spin-lattice and spin-spin rela xation rates of sp-Si paramagnetic centers. 4.6.1 Spin-Lattice Relaxation Rate The spin-lattice relaxation rate is also known as T1 and longitudinal relaxation. In Figure 426 we present the spectrum from which we measure T1. The detected intensity is plotted as a function of time. In such experiments the intens ity is expected to decay exponentially with time at a rate of 1/T1. But, in the case of sp-Si bi-exponential decay functions are necessary for a good match to our data, as seen in Figure 4-26. We called the exponential decay times T1 and T1. The model equation used is: 11 '// 11()tTtTIntensitytAeAewhere A1 and A1 are the exponential amplitudes of each of the decays.

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100 -3000 -2500 -2000 -1500 -1000 -500 0 500 1000 024681 01 21 41 6Time (ms)Intensity (a.u.) Figure 4-26. Intensity versus time for a spin-lattic e relaxation rate experime nt of spark-processed silicon (black line), one-exponential decay model (green line) and bi-exponential decays (red line). Experimental paramete rs (inversion recovery), center field = 3455.5 Gauss, shot repetition time = 408 ms, shot loop = 1, pulse length = 16 ns and step is 16 ms. In a subsequent experiment we measure T1 and T1 as a function of temperature. The results are presented in Figure 4-27. In both cases the relaxation ra te follows a direct process up to 60 K. A direct process is charact erized by the proportionality between T1 and the temperature52. In addition above 60 K and according to the same authors, T1 and T1 follow a hopping process. We are mostly interested in the T1 processes to help understand the physical origin of the line width in the cw-EPR. It must be added in passing that the line width in cw-EPR can have several origins and knowing the behavior of the spin-lattice relaxa tion rate as a function of the temperature is necessary to meet this goal.

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101 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 11.11.21.31.41.51.61.71.81.922.12.22.32.4Log (temperature(K))Log (1/T1) and Log (1/T1') log(1/T1) log(1/T1') Direct process (slope = 1) Hopping process Figure 4-27. Spin-lattice relaxa tion rates versus temperature for spark-processed silicon. 4.6.2 Spin-Spin Relaxation Rate The spin-spin relaxation rate is very important to us as it is the first step towards measuring the density of defects. This relaxation rate is also called T2 or transverse relaxation rate. But T2 is obtained indirectly from the phase memory time (Tm). By running an echo decay pulse EPR experiment53 we obtain intensity versus time curves The exponential decay constant is Tm. The relationship between Tm and T2 is given by the following equation: 211 (,)m f Powerconcentration TT where concentration is the density of spins in a given sample and where the function of power and concentration is a constant for a given sample at a given power. In this section, it is the case, that is, we use the same sample and use the same input power setting for all measuremen ts throughout this section, therefore the relationship becomes

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102 simply: 211 constantmTT Figure 4-28 displays the intensity as function of time of sp-Si. Once again, the data can only be f itted with bi-exponential decays. 0 2000 4000 6000 8000 10000 12000 01002003004005006007008009001000time (ns)Intensity (a.u.) Figure 4-28. Intensity versus time for a spin-spi n relaxation rate experi ment on spark-processed silicon (black line), one-exponential decay model (green line) and bi-exponential decays (red line). Experimental parameters for the 2 pulses echo decay, center field = 3467 Gauss, shot repetition time = 51 ms, s hot loop = 2, pulse length = 16 ns and step = 4ns. For information, the model equation used is: '// 22()mmtTtTIntensitytAeAe where A2 and A2 are the exponential amplitudes of each of the decays. If we use only one exponential decay the fit is poor as can be visually observed in the graph. In the next experiment, we measured Tm and Tm as a function of temperature. The results show essentially no temperature dependence, as seen in Figure 4-29. According to Eaton and

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103 Eaton54 the line width can be calcula ted from the following equation: 22 1 1 22 221 T HAB TT where A is a proportionality factor, B1 is the microwave magnetic field and the electron gyromagnetic ratio. In the case of sp-Si the second term is much smaller than the first one and therefore th e line width depends only on T2. Since T2 is directly related to Tm, the line width depends on Tm only. This is confirmed experime ntally since the line width and Tm have the same temperature dependency. 0 100 200 300 400 500 600 700 800 900 0255075100125150175200225Temperature (K)T2 and T2' (ns) T2 T2' Figure 4-29. Spin-spin relaxati on rates versus temperature fo r spark-processed silicon. In brief, we have found two spin-lattice relaxa tion rates as well as two spin-spin relaxation rates. It is of great interest to figure out which rate is related to the D centers and which one is related to the E centers. This is of major im portance since this will allow us to perform the separate measurement of the density for each type of centers.

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104 4.7 Separation of Rates to Id entify Paramagnetic Centers The processes involved in the relaxation of the spins after being excited by microwaves are strongly dependent on the pulse le ngth and pulse power. Therefore, in order to assign the two defects observed with cw-EPR according to th eir own relaxation rates, we use several experiments. First we measured an echo detected field sweep pulse spectr um. The data for sp-Si is presented Figure 4-30. This is similar in prin ciple to the concept pres ented at the beginning of this chapter in Figure 4-3. A double Lorentzian line model is used to deconvolute the data, showing again that two paramagnetic centers are present in the EPR signal. The characteristic values (center field, line width) are presented in Table 4-1. -10000 0 10000 20000 30000 40000 50000 60000 70000 80000 3430 3440 3450 3460 3470 3480 3490 3500Field (Gauss)Intensity (a.u.) Series1 Model Deconvolution 1 Deconvolution 2 Figure 4-30. Field sweep pulsed electron parama gnetic resonance of sp ark-processed silicon (black curve). A two-Lorentzian model is fitte d to the data (red curve) and each of its individual components (green and blue cu rves). Experimental parameters, power attenuation = 10 dB, shot re petition time = 20 ms, shot loop = 30, pulse length = 30 ns.

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105 On the other hand, when fitting the bi-exponential decay model to the phase memory time experiment we are capable of extracting the exponential proportionality parameters (A2 and A2). Since these parameters are related to the rela xation rates and we want to assign them, we measured these parameters as a function of the ma gnetic field in order to compare them with the field sweep curve obtain pr eviously (Figure 4-30). 0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 2.5E+05 3.0E+05 34403445345034553460346534703475348034853490Field (Gauss)A2 and A2' (a.u.) A2 A2' A2 model A2' model Figure 4-31. Amplitude of exponential decays in spin-spin relaxation rate experiments versus field for spark-processed silicon (dots). Lorentzian distribution models have been fitted to the data (solid lines) with long pulse (200 ns equivalent to 1.8 Gauss). Figure 4-31 displays A2 and A2 as a function of the external magnetic field. Lorentzian line models are fitted to validate the data. Their ch aracteristic values are summarized in the Table 4-1. If we compare them with the field sw eep experiment we are able to assign the A2 with the D centers and A2 with the E centers.

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106 Table 4-1. Characteristic values of echo detect ed field sweep and amplit ude of exponential decay as a function of magnetic field. Con stan ts Echo detected field sweepExponential decay amplitude 0 D H [Ga uss] 3462 3463 D H [Ga uss] 10 12.5' 0EH [Ga uss] 3467 3465'EH [Ga uss] 91 1 Note: 0His the center field and H is the line width. In conclusion, we are able to separate th e paramagnetic centers using pulsed EPR which allows the calculation of the density of centers fo r each type of defects (D and E) as described in the next section. 4.8 Spin Density The concept used to calculate the spin c oncentration was presented by Eaton and Eaton54 and was applied to -irradiated SiO2, a very close cousin of sp-Si (composition and structure wise). We have found this method to be more reliable than other methods such as the comparative technique using cw-EPR for exampl e. The comparative te chnique has been found to be a lot less accurate than the method applied by us due to great difficulties in measuring the volume of the sp-Si material.

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107 The calculation of the concentration is based on the following relationship54: 1/2 2 2 204 11 sin 2 93B mgC Power TT Power where the only constant which has not been presented yet is C, the density of spins. Figure 4-32 shows 1mTand '1mTas function of the power and Figure 4-33 displays '1mTversus 1/2 2 0sin 2 Power Power The slope of the curve is proportional to the concentration of defects and the y-intercept is the inverse of T2. In the case of sp-Si, we found the concentration of D centers to be 1.419 cm-3 and the concentration of the E centers to be 0.519 cm-3. The total density of paramagnetic centers is therefore 1.919 cm-3. 0 0.003 0.006 0.009 0.012 0.015 0.018 0.021 00.0250.050.0750.10.1250.150.1750.2Power (W)1/Tm and 1/Tm' 1/Tm 1/Tm' Figure 4-32. Phase memory time for each paramagnetic center measured as a function of the input power of sparkprocessed silicon.

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108 We have measured this density on different sa mples to investigate the repeatability and we found all these values to be w ithin 20% of the average (Fig ure 4-34). The D center average density is 1.619 cm-3 while the E center average density is 0.519 cm-3, leading to an average total density of 2.119 cm-3. It should be noted that in Ch apter 3 we reported that the magnetization was dependent on the spark frequency (Figure 3-6). Because we only measured an average density of paramagnetic centers, no link can be drawn between the magnetiz ation and the density. On ly the knowledge of the distribution would allow a co mparison between the magnetizati on and the density of spins. 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005 00.10.20.30.40.50.60.70.80.911.1Sin2( /2(Power/Power0)1/2)1/Tm' Figure 4-33. Inverse phase memory time (1/Tm) versus sin2( /2(power/power0)1/2) of sparkprocessed silicon (dots). A tr end line is run through th e data with a correlation coefficient of 0.998. 1/2 2 02 Power Sin Power

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109 If we assume that all the paramagnetic centers are equidistant from one another, then the inter-spin distance is equal to th e cubic root of the inverse of the total density. This way, we found a maximum inter-spin distance of 3.7 nm (or 3.6 nm if we use the average density calculated from Figure 4-34). This result is very much within th e range of values reported by Eaton and Eaton on -irradiated quartz54. As mentioned in the first section, it is usually assumed that the maximum distance between spins which allo ws exchange interactions is 2 nm. But, it has been shown52 that sp-Si is composed of silicon nanocrystals embedded in the SiO2 matrix. Therefore, we suggest at first, that the distribution of parama gnetic centers is not homogeneous which is also suggested but the heterogeneous stru cture. Secondly, we sugge st that the D centers are located on the border or inside the sili con nanocrystals. These nanocrystals observed by Shepherd51 have sizes ranging from a few to tens of nanometers. If the paramagnetic centers are located in or around such nanocrystals it is possible for their inter-spin distance to be less than 2 nm and therefore exhibit exchange interaction leading to the observed magnetic hysteresis.

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110 0 0.5 1 1.5 2 2.5 3 681012141618202224Spark frequency (kHz)Density of paramagnetic centers [1019 cm-3] Total Density D centers Density E' centers density Figure 4-34. Density of paramagnetic centers as a function of the spark frequency for sparkprocessed silicon. The density of D centers is represented by squares while the density of E centers is represented by tr iangles. The total density is represented by diamonds. It should be added in passi ng that a technique known as double quantum coherence EPR which allows the measurement of the spatial di stribution of paramagnetic centers developed by Freed48 was tried on sp-Si but we were unsuccessful due to limitation of the technique itself. Still, it may be possible in the future, once the EPR sensitivity has been improved, to measure the distribution of centers. It should be noted in passing th at hydrofluoric acid etching (49% pure) for several minutes did not change the EPR signal shape or am plitude. We concluded that the measured paramagnetic centers are not surface related.

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111 4.9 Summary In this chapter we successfully identified tw o paramagnetic centers believed to be present in sp-Si, namely the E centers and the D cente rs (Figure 4-6). Also, we successfully measured the densities of each of the two centers to be 1.41019 cm-3 for the D centers and 0.519 cm-3 for the E centers. In addition, we have m easured a Curie temperature of 710 K from the amplitude of the D centers to be compared with a Curie temperature of 765 K measured from the magnetization at 1000 Oe (Chapter 3) Finally, we presented a clus ter model consistent with the magnetization results and the paramagnetic centers distribution (Figure 41). Our arguments can be summarized as followed: Sp-Si is not homogeneous, it is composed of Si nanocrystals embedded in the SiO2 matrix, D paramagnetic centers are like ly to be located in or around silicon nanocrystalline regions, E paramagnetic centers are likely to be located in the SiO2 matrix, The structure suggests an inhomogeneous distribution of inter-spin distances, Paramagnetic centers are less than 3.7 nm apart but they could be less than 2 nm apart, Exchange interaction is possibl e between paramagnetic centers if they are closer than 2 nm, The paramagnetic centers are not surface related, Positive exchange interaction explains th e observed magnetic hysteresis in sp-Si. The magnetic response at high and low temperat ures of the D centers and the magnetization at 1000 Oe (Chapter 3) have a very simila r behavior. They both follow the same laws. In the next chapter we expand our model to ot her materials and therefore describe a full class of materials as quasiferromagnets.

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112 CHAPTER 5 FURTHER CONSIDERATIONS W hile the two previous chapters deal with sp ark processed silicon magnetic properties and its model, this chapter extends this model to other materials. Quasiferromagnetism was first studied using spark processed silicon. Later, we found that other materials had similar magnetic properties and therefore, we classi fied them as quasiferromagnets. In this chapter we first present the work of Hack3 on the annealing effect of the magnetic properties of spark processed silicon which furthe r confirms the magnetic model proposed in the previous chapter. Then, we discuss and pres ent some of the magnetic properties of other materials as well as why we classified them as quasiferromagnets. These materials include ion implanted silicon into silicon, ar gon implanted into silicon; neutron irradiated silicon and highly oriented pyrolitic graphite (HOPG). 5.1 Annealing of Spark Processed Silicon In this section we report on the annealing effect of the magnetization as well as the annealing effect of the electron paramagnetic re sonance spectrum of sp ark processed silicon. This work was performed by Jonathan Hack during his masters thesis at UF. It was published3 in 1997. This work proposed to link the magnetic hysteresis to paramagnetic centers. Hack measured the magnetization of sp-Si at 0 and 1000 Oe as f unction of cumulative annealing. First, he measured the magnetization of sp-Si as processed, and then after annealing at 500 K for 30 min in a nitrogen atmosphere and subsequently, at higher temperatures, up to 1300 K. The results are normalized to the as pr epared samples (Figure 5-1). The magnetization decreases as the cumulative anne aling increases. Furthermore, the decrease is more pronounced around 700 K. Finally, in the high temperature range (i.e. above 900 K) the remanence magnetization decreases to zero at 0 Oe and th e saturation magnetization (at field of 1000 Oe)

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113 also decreases down to the diamagnetic value of the substrate. The hysteresis is destroyed (nonreversible process) at the cumulative anneal ing temperature of 900 K while a small but not negligible paramagnetic magnetization remains at 1000 Oe. -0.2 0 0.2 0.4 0.6 0.8 1 1.2 30040050060070080090010001100120013001400Annealing Temperature (K)Magnetization (a.u.) Remanence Magnetization (1000 Oe) Figure 5-1. Magnetization at 0 and 1000 Oe of spark processe d silicon as a function of cumulative isochronal (30 min) annealing temperature. In addition, he measured the electron para magnetic resonance spectrum at each annealing temperatures and extracted the peak to peak am plitude of the main line. The results are shown Figure 5-2. The peak to peak amplitude is propor tional to the number of defects present in the sample as long as we are in none saturated re gime as explained in the Section 4.3. The normalized amplitude decreases as the temperat ure is increased in a similar manner as the magnetization. In addition, the largest slope (str ongest relative decrease) is found at 700 K as for the magnetization. Finally, the EPR peak to peak amplitude decrease almost to zero at the highest temperature as does the magnetization.

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114 0 0.2 0.4 0.6 0.8 1 1.2 30040050060070080090010001100120013001400Annealing Temperature (K)EPR line intensity (a.u.) Figure 5-2. Electron paramagnetic resonance peak to peak spectra line of spark processed silicon as a function of cumulative isochron al (30 min) annealing temperature. Hack concluded that the parama gnetic centers were at the or igin of the observed magnetic hysteresis of sp-Si. The pioneering work of Hack is the origin of this dissertation. In my quasiferromagnetic model, I suggest th at some paramagnetic centers are clustered and thus, have a positive exchange interaction. If one anneals sp-Si, thus removing paramagnetic centers, the clusters would decrease in size and therefore the magnetization would decrease as a result. Eventually, their number would approach zero, and the clusters would disappear (leading to a vanishing of the hysteresis). We conclude that the observations of Hack are in general agreem ent with our proposed quasiferromagnetism model.

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115 5.2 Ion Implanted Silicon Ion implantation is a very common process us ed in the semiconductor industry. In the seventies Khokhlov19 studied the EPR spectra of parama gnetic defects produced by the ion implantation process. Since, some others have continued to study th e EPR spectra of ion implanted silicon but the magnetization itsel f has been left out. I have published35 for the first time on the magnetic hysteresis at room temperatur e of silicon implanted into silicon and argonimplanted silicon. We will review in this section the most relevant results from this publication. The samples were prepared using a very lo w implantation current density (less than 10 A/ cm2) as well as high doses (greater than =1016 ions/cm2) while the silicon substrate were kept at room temperature by water cooling the stage. We believe that such processing conditions favor a large defect density (preventing self-anneali ng during implantation). We suggest that ion implantation would be an interesting area for fu rther investigations, for example, to produce quasiferromagnetic silicon and allow potential applicati on of this material in the spintronics area. It should be re-emphasized that SIMS spectra were perform on each type of the processed samples. No ferromagnetic elements (Fe, Ni, Co, Mn) could be found35. Below, we present the magnetization response an d then the EPR spectra of this material. 5.2.1 Magnetic Response of Ion Implanted Silicon The magnetization as function of the field was measured for argon-implanted silicon. The results are shown Figure 5-3. Tw o magnetic hysteresis curves are presented, one for the sample implanted at a dose of 216 cm-2 and one for implantation at a dose of 217 cm-2. Both hysteresis are observed at room temperature. In addition a silicon wafer was implanted using silicon ions with a dose of 516 cm-2. Again a hysteresis was observe d at room temperature as shown in Figure 5-4. These results are not expected from the classical theory of magnetism. Once again, a new concept is needed: quasiferromagnetism.

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116 -6.E-06 -4.E-06 -2.E-06 0.E+00 2.E-06 4.E-06 6.E-06 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) Figure 5-3. Magnetization as a function of th e magnetic field strength at 300 K for silicon implanted with argon ions. The solid red curve corresponds to an argon dose of 216 cm-2 and the dash green curve to a dose of 217 cm-2. The magnetization has been adjusted for the diamagnetism of the substrate. -1.5E-06 -1.0E-06 -5.0E-07 0.0E+00 5.0E-07 1.0E-06 1.5E-06 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) Figure 5-4. Magnetization as a function of magnetic field strength at 300 K for silicon implanted with silicon ions. The dose was 516 cm-2. The magnetization has been adjusted for the diamagnetism of the substrate.

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117 5.2.2 Electron Paramagnetic Resonance of Ion Implanted Silicon The electron paramagnetic resonance spect rum of argon-implanted silicon at 216 cm-2 is displayed Figure 5-5. -12000 -8000 -4000 0 4000 8000 12000 332033303340335033603370338033903400Field (Gauss)Intensity (a.u.) Model Data r2 = 0.998 Figure 5-5. Electron paramagnetic resonance spectra of argon implanted into silicon at a dose of 216 cm-2 (blue squares) and its Lorentzian model (solid red). Experimental parameters, power = 2 mW, power attenuati on = 20 dB, modulation field = 1 G, time constant = 80 ms, detector gain = 55 dB, temperature = 5 K. The measurements were taken at 5 K to reduc e thermal noise. A Lorentzian line is use to model the data. We found a very good fit betw een the model and the experiment (correlation coefficient is 0.998). Since one li ne was enough to model the data we conclude that there is only one type of defect in this material. According to Khokhlov19 and Gerasimenko55 the pertinent paramagnetic defects are VV centers (silic on dangling bonds around voids). Similarly the electron paramagnetic resonance spectrum of silicon-implanted silicon with a dose of 1016 cm2 at

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118 5 K was measured and analyzed (F igure 5-6). In this case a twoLorentzian model was necessary to match the data. The g-factors are 2.0054 and 2.0023 respectively. -3000 -2000 -1000 0 1000 2000 3000 4000 5000 34453455346534753485349535053515Field (Gauss)Intensity (a.u.) Model Data Figure 5-6. Electron paramagnetic re sonance spectra of silicon implan ted into silicon at a dose of 1016 cm-2 (blue squares) and its two-Lorentzi an model (solid re d). Experimental parameters, power = 50 mW, power attenua tion = 6 dB, modulation field = 1 G, time constant = 80 ms, detector gain = 60 dB, temperature = 5 K. They allows the identificati on of the paramagnetic defects to be silicon dangling bonds40 (D centers) and E centers44 respectively. We believe that the E centers are located on the surface of the substrate in the oxide layer. On a silicon wafer there is a natural silicon oxide layer forming as long as the substrate is left in an ambient atmosphere. In addition, Tomozeiu44 has shown that the g-factor of E cen ters is slightly dependant of th e thickness of the silicon oxide layer. In our case, the thickness corresponds to the natural oxide formed at the surface.

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119 The ion implanted silicon samples which we characterized have similar magnetic characteristic as sp-Si, that is, a magnetic hysteresis loop at room temperature and paramagnetic centers. Once again, these samples do not contai n elements with d or f shell electrons and therefore fits well within the quasiferromagnetic materials point of view Overall, we suggest that ion-implanted silicon materials seem to have the same magnetic behavior as sp-Si and therefore can be explained by th e same quasiferromagnetic model. 5.3 Neutron Irradiated Silicon Neutron irradiated silicon samp les were prepared following the same general ideas as ion implanted silicon. We tried to manufacture the material with the largest possible density of paramagnetic defects hoping that they would form in teracting clusters. In this section we present magnetization curve of neutron irradiat ed silicon. I have already published4 this work in 2006. Thus, only a brief summary will be given here. A piece of silicon wafer was exposed to therma l neutrons in the University of Florida nuclear reactor for 12 hours. A 12-hour exposure equate to a dose of 416 cm-2. The magnetization curve was measured at 10K, to reduce large noise, see Figure 5-7. According to Jung and Newell56 weak magnetic interaction are observed between closely spaced dangling bonds in neutron irradiated silicon. Jung measured a distance of 0.5 nm between two particular types of dangling bonds in ne utron irradiated sili con using an electron paramagnetic resonance technique. Magnetic hysteresis and weak magnetic in teraction between paramagnetic centers contribute to classify neutron irra diated silicon as a quasiferroma gnet. Similarly to ion implanted silicon, neutron irradiated silicon has the same magnetic characteristic as sp-Si and therefore should be in the same magnetic class.

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120 -5.E-06 -4.E-06 -3.E-06 -2.E-06 -1.E-06 0.E+00 1.E-06 2.E-06 3.E-06 4.E-06 5.E-06 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) Figure 5-7. Magnetization versus ma gnetic field strength of neutron irradiated silicon at a dose of 416 cm-2. The magnetization is adjusted for the diamagnetism of the substrate. The measurement temperature was 10 K. Once again, SIMS spectra were taken on a neutron irradiated sample and no magnetic elements (such as Fe, Ni, Co) were found. 5.4 Highly Oriented Pyrolitic Graphite In this section we present another material which we classify as quasiferromagnet. This material is not based on silicon. Highly oriented pyrolitic graphite (HOPG) an allotrope form of carbon, was purchased from Mikromash57. This material is processed from pure graphite at temperatures of 3,000C under pressure. This ma terial was previously known for its unusual magnetic properties which triggered our interest. In this respect, we present the magnetization measurements as well as electron paramagnetic resonance data which relate this material to quasiferromagnetism.

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121 -8.E-05 -6.E-05 -4.E-05 -2.E-05 0.E+00 2.E-05 4.E-05 6.E-05 8.E-05 -1500-1250-1000-750-500-2500250500750100012501500Field (Oe)Magnetization (emu) Figure 5-8. Magnetization as a function of magnetic field stre ngth of HOPG graphite. The magnetization is adjusted for the diamagnetism of the sample. The measurement temperature was 300 K. 5.4.1 Magnetization Response of High ly Oriented Pyrolitic Graphite The as-purchased material was measured with our SQUID magnetometer at room temperature. A wide hysteresis is observed. Sin ce the sample also exhibits strong diamagnetism, its contribution was subtracted, see Figure 5-8. The coercive field is about 200 Oe, which is much larger than in the case of silicon ba sed quasiferromagnets. For example, sp-Si has a coercive field of about 50 Oe and ion implanted silicon one of about 100 Oe. 5.4.2 Electron Paramagnetic Response of Highly Oriented Pyrolitic Graphite The electron paramagnetic resonance of HOPG graphite is more involved than in the case of silicon-based materials. HOPG is a conductor and therefore the EPR line do follow a rather complex model call Dysonian lines named after Dyson58,59 who theoretically studied the EPR of

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122 conductors and in particular of metals back in 1955. However, in the case of HOPG the EPR intensity line can be reduced to an asymmetric Lorentzian line (only the first term of the Dysonian line) with the following equation: 2 2 00 2 2 2 021 1 HHHH dP A dH HH where dP dH is the EPR intensity, A the amplitude, H the field, H0 the center field and the full width. Figure 5-9 displays the compar ison between the EPR data and Dysonian line model for HOPG graphite at room temperature. -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 33203322.533253327.533303332.533353337.533403342.533453347.53350Field (Oe)Intensity (a.u.) Data Dyson Model Figure 5-9. Electron paramagnetic resonance spectra of HOPG gra phite (blue squares) and its Dysonian line model (solid red). The coeffi cient of correlation is 0.99. Experimental parameters, power = 0.6315 mW, power attenuation = 25 dB, modulation field = 1 G, time constant = 5 ms, detector ga in = 60 dB, temperature = 300 K. A correlation coefficient of 0.98 is found between the data and model. This is a quite reasonable match considering that we approximated the Dysonian line using only one term. (The g-factor = 2.0086

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123 reader is referred to the original paper written by Dyson58 to see the complete equation). In addition, according to Feher59 who confirmed the work of Dyson on different conductive materials, any materials modeled with the equa tion used to model HOPG contains paramagnetic impurities distributed throughout the volume of the metal. Once again, we found a material with paramagne tic impurities and a magnetic hysteresis at room temperature. These characteristics are similar to the ones of sp-Si and to ion and neutron irradiated silicon. Even if HOPG graphite is different from silicon-based material due to its conductive nature, we suggest that it should also be classified as a quasiferromagnetic material. 5.5 Summary In this chapter we looked at several different materials from the quasiferromagnetism point of view. In brief: The original work started by Jonathan Hack is in line with our suggested quasiferromagnetic model, that is, the parama gnetic centers observed by EPR are at the origin of the observed magnetic hys teresis at room temperature. Ion-implanted silicon with either argon or si licon and neutron irradi ated silicon contains paramagnetic centers and display magnetic hysteres is at room temperature. Similarly to spSi, we suggest that the macroscopic behavior is explained by th e interaction of the paramagnetic centers. HOPG graphite exhibits a magnetic hysteresi s at room temperature in addition to a Dysonian shaped EPR spectrum, characteris tic of paramagnetic centers in conducting materials. When compared with sp-Si, strong similarities suggest a quasiferromagnetic behavior.

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124 CHAPTER 6 CONCLUSION The present investigations have been conducted to study in detail unknown m agnetic properties of non-magnetic materials. Becau se of their uniqueness we term them quasiferromagnetics. The experi mental results and interpretati ons which have been observed during this study are summarized below. 6.1 Macroscopic Magnetic Behavior of Spark-Processed Silicon It has been confirmed that spark-processed silicon displays a ma gnetic hysteresis quite analogous as Fe, Co, Ni and rare-earth metals Once again, sp-Si does not contain magnetic impurities at levels which would explain the ma gnetic hysteresis at room temperature. The magnetization (remanent and at 1000 Oe) of sp-Si decreases as the temperature increase. Applying the Weiss equation to th e magnetization data, we evaluated a Curie temperature of 765 K for sp-Si. It should be not ed in passing that at such temperatures the annealing effect is quite sma ll but still noticeable. A new technique was developed to measure the magnetization at such high temperatures. On the other hand, at low temperatures (bel ow 100 K), the magnetization at 1000 Oe of spSi follows the Curie-Weiss law, characteristic of paramagnetic materials. 6.2 Electron Paramagnetic Resonance of Spark-Processed Silicon The electron paramagnetic resonance of sp-Si allowed the identification and characterization of paramagnetic centers within th e material. Two type of centers were identified namely, the D centers, (silicon dangling bond back-boned by three other silicon atom) and the E centers, (silicon dangling bond back-boned by three oxygen atoms.) The D centers amplitude decrease as function of the temperature in a si milar manner as the magnetization measured with the SQUID magnetometer. Applying the Weiss e quation to the EPR data, we evaluated a Curie

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125 temperature of 710 K for the sp-Si D centers. In c ontrast, the E centers amplitude is essentially independent of temperature in the range 300 to 800 K. A new heating system was built for the EPR system in the process leadi ng to these results (Appendix E). At low temperatures, both the D and E center amplitudes follow the Curie-Weiss law, characteristic of paramagnetic materials. This is a similar behavior as the magnetization measured with the SQUID magnetometer. In addition, the pulse EPR t echnique allowed the measuremen t of the local average spin concentration. We measured a concentration of 1.419 cm-3 for the D centers and 0.519 cm-3 for the E centers. This translates into a maximum spin to spin distance of 3.7 nm. 6.3 Quasiferromagnetic Model for Spark-Processed Silicon In order to explain the origin of the magnetic hysteresis loop observed at room temperature in sp-Si we have developed a model based on our experimental results. Fi gure 4-1 illustrates the most important assumption, that is, the distribu tion of paramagnetic centers (D and E) is not homogeneous. Using this assumption leads to the possibility of having spin-spin distances of less than 2 nm which is the commonly accepted uppe r limit for exchange interaction to occur between spins. It has been shown from previously published50,51 work from our group that sp-Si does not have a homogeneous structure. Furthermore, sp -Si was also shown to have nanocrystals of silicon embedded into an amorphous SiO2 matrix. Due to the physical nature of the D centers (that is, containing only silicon at oms) they can only be located in silicon rich domains while the physical nature of the E centers (that is, containing both silicon and oxygen atoms) they can only be located in the SiO2 matrix. Therefore, we suggests that D centers are forming clusters in or around silicon nanocrystals lead ing to a high local density of spins and subsequently leading to possible exchange inte ractions between them.

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126 In addition to the distribution model, our e xperimental data suggest that D centers are responsible for the observed magnetic hysteresi s. Using two different techniques (SQUID magnetometry and EPR) we found that the magnetization of the D centers (i.e. amplitude) and the macroscopic magnetization have close Curie temperatures (765 K and 710 K respectively) in addition to a similar temperature response. At low temperatures, they both follow the CurieWeiss law and at higher temperatures they both follow the Weiss equation. 6.4 Other Quasiferromagnetic Materials In addition to sp-Si, we have found severa l other materials which we classified as quasiferromagnetic materials. We classified them as such because similarly to sp-Si they display a magnetic hysteresis at room temperature and contain paramagnetic defects. These materials are: Ion implanted silicon with silicon at a dose of 516cm-3, Ion implanted silicon with argon at a dose of 216cm-3, Neutron irradiated sili con at a dose of 416cm-3, HOPG graphite. Similarly to sp-Si, we suggest that the macr oscopic magnetic behavior is explained by the interaction of the paramagnetic centers. 6.5 Future Work We presented experimental work done on ion-im planted silicon; neutron irradiated silicon and highly oriented pyrolitic graphite and how they are related to sp-Si and quasiferromagnets. We suggest that all material with a high dens ity of interacting para magnetic centers with a magnetic hysteresis and no magnetic elements (atoms containing d-shell and/or f-shell electrons) should be called a quasiferromagnet. First, we believe that there are many othe r techniques (such as plasma processing, evaporation, sputtering) whic h under specific condition could create materials with unpaired

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127 bonds, which could contain magnetically interacti ng paramagnetic centers. This present a great area of engineering research wh ere new material could be discovered and where such materials could lead to application such as spintronics transistors. In addition, the materials presented in this study should be investigated further. For example a more complete EPR study could be done and in particular pulse-EPR studies. Such a study would allow the confirmation or distinction between these materials and sp-Si. We think that conductors such as HOPG and semiconductor-b ased quasiferromagnets are slight variation of one another and we should qualify them type 1 and type 2 quasiferromagnets according to their conductivity. More research should be done toward understandi ng the link between the conductivity and the magnetic properties as there are the bases for buildin g future spintronics devices. Finally, even if the materials which we presented in this dissertation could not be used directly for the manufacturing of devices it should be noted th at the fundamental understanding of local magnetism (cluster of spins) is necessa ry to further the engineering of new spintronic devices. Magnetism is an exciting research topic as evidenced by the recent Nobel Prize. This dissertation has led me to grow and learn basi c research principles which I will use throughout my life. In the mean-time, working on this topic has allowed us to advance it through the discovery of quasiferromagnetism. Before we invented the concept of quasif erromagnetism and before we start to study consistently the magnetic properties of spark-processed silico n very little was known on the magnetization of materials containing large amo unt of paramagnetic centers. In addition, only a

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128 restricted amount of information was known about the characteristic of such materials at the electron level. I believe that this work is the first step in the direction of understanding magnetism not stemming from d or f-shell magnetism. It should be pursued further.

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129 APPENDIX A SPARK PROCESS POWER SUPPLY I designed and fabricated a power supply whic h was used for the fabrication of sparkprocessed silicon. In this Appe ndix, I describe how the power supply works and needs to be operated. A.1 Power Supply Principles of Operation First, we describe how the power supply circui t works. Its schematic is plotted in Figure A1. The 110V AC coming from the wall outlet is transformed into 24V DC. Then the voltage is again decreased to 12V DC corresponding to th e pink subsection of the circuit only. This subcircuit creates a pulsed DC wave form with a low current (typica lly 2 mA). The pulsed signal is obtained by charging a capacitor (C1, C2, C3 or C4) through a resistor (R1+F) for the high state (V = 12V) and discharging the same capacitor through another resistor (R2+G) for the low state (V = 0V). A NAND gate is used to square the sign al. Then, the output of this gate is inversed and amplified (3 times) by feeding the signal through three other NAND gates. The output of the pink subcircuit can be visualized on an oscillo scope using the outlet labeled E. Figure A-2 displays schematically what is seen on the osci lloscope. The length of the low and high states can be calculated from the product of the capacitor by each of the respective resistors. Since we use variable resistors (F and G) we can vary the duty cycle and the frequency. The frequency is equal to the inverse of the su m of the low and high state ( 1ifrequency GFC ). The duty cycle is equal to: 11 22PRF PRG The frequency and duty cycle range which are limited by the capacitor Ci can be expanded by using a se lection of four capacitors (C1, C2, C3 and C4). The second subcircuit, in green on the schematic, uses a BJT transistor (T1) to pre-amplify the pulsed DC signal from a 2 mA to 200mA.

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130 Figure A-1. Power supply schematic. C1 C2 C3 C4 Voltage regulator 7812 0V 24V 12V G F D D2 D1 R1 R2 R3 R4 CMOS 4093 T1 T2 E To sample stage To spark electrode C Flyback Transformer 1 2 3 4 110V AC to 24V DC Transformer A B Top Fan Back Fan T2 Fan

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131 Then, the signal is amplified even mo re using a power MOSFET transistor (T2). The current flowing through the orange subcircuit is about 2 Amps. Finally, the high current (2 Amps) low voltage (24V) pulsed DC signal is tran sformed into a high voltage (several kV) low current (few mA) pulsed signal thro ugh the flyback transformer. The spark tip is connected to the high voltage output of the flyback transformer wh ile the stage is connect ed to the ground. In addition, a variable resistor is placed in series with the flyback transformer to increase or decrease the output high voltage. Figure A-2. Typical waveform observed at the read out (E) on the screen of an oscilloscope. A.2 Power Supply Inner Components Practically, several cooling devices were adde d. Heat sinks were us ed to cool down the voltage regulator and the high power transistor (T2). In addition to the heat sink, the high power transistor (T2) was cooled by a large fan. Two other fa ns were positioned at the back of the power supply to cool down the flyback transfor mer and one on the top of the box to cool down the entire circuit. A previous bad experience with an uncooled circu it taught me to be on the safe side by adding more fans than probably needed. Fi gure A-3 displays a picture of the built circuit as described. P2 = (R2+G)Ci P1 = (R1+F)Ci P = P1 + P2 Time 0 V 12

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132 Figure A-3. Power supply without its top cover. To complete the description of the power supply, a picture of the front panel is included in Figure A-4. The front panel allows the variation of the controls A G. Below is the list of the controls with their meaning and labels: A, main switch B, high voltage switch C, high voltage power control (variable resistance 0 to 300) D, frequency range selector E, waveform read out F and G, frequency and duty cycle fine ad justment (variable resistance 0 to 75k). A list of component is incl uded for a full description: C1 = 10 nF (1.6 12kHz) C2 = 3.5 nF (5 40kHz) C3 = 1 nF (12 100kHz) C4 = 0.6 nF (25 125Hz) D1, 1N4148 diode T2 with cooling fan 110V AC to 24V DC Flyback transformer Voltage regulator CMOS 4093 T1 under board B A C D 110V AC input Back Fan

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133 D2, 1N4148 diode R1 = 10k R2 = 10k R3 = 1k R4 = 1k CMOS 4093, quad 2 input NAND Voltage regulator 7812, Vout = 12V DC T1, 2N2222 NPN BJT transistor T2, IRFPS43N50K HEXFET power MOSFET transistor Flyback transformer from high vo ltage circuit of television set Fuse 110V, 0.75Amp. Figure A-4. Front side of the spark machine. The labels A G designate the same control as in the schematic (Figure A-1). Finally, it is to be noted that the sparks do not occur under all conditions. The power supply will only creates a spark when specific conditions of frequency, power, duty cycle and sparking gap are met. A B C D E F G

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134 APPENDIX B HgCo(SCN)4 MAGNETIC REFERENCE B.1 SQUID Magnetometer Verification This reference material is used to verify that the SQUID magnetometer is properly functioning. Several references can be used to validate magnetization measurements with the SQUID magnetometer at very low temperature (2-100K). The cobalt mercury cyanide is a widely used reference for this range and was readily available to us. This material comes in a powder form and special handling is required due to its toxicity and potential to contaminate the magnetometer. A special sample holder was designed to prevent loss or scattering of the material during the measurement process. We are desc ribing the sample holder here at first. The measurement process in the SQUID magnetometer is done in a helium atmosphere, thus requiring pumping the chamber to a vacuum and then backfilling with helium. Since pumping down could move HgCo(SNC)4 particles outside the holder, into the pump system and onto the detector, we prepared a quartz ampoul e under argon gas. The quartz ampoule is made of a 5 mm outside diameter (4 mm inside diamete r) quartz tube closed on each end. The ampoule was back filled with argon just below one atmo sphere before it was closed. In order for the reference material to be positioned in the center of a symmetric holder, it was placed inside a plastic straw, normally used as a sample holder, but seating on another pi ece of quartz tube such that the ampoule seats in the middle of the stra w. This not only places the sample properly but also virtually eliminates the magnetization fr om the quartz ampoule. The SQUID magnetometer is a differential technique and as such, makes differential measurements between the area above the sample, the sample itself, and the area belo w the sample. The design of our holder, placing quartz above, at the sample and below by adding a support tu be underneath, creates a net

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135 difference of zero. Therefore the quartz holder does not appear as a component of the observed magnetization. Only the magnetization from the sample is observed. R2 = 0.999997 -0.004 -0.003 -0.002 -0.001 0.000 0.001 0.002 0.003 0.004 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) Figure B-1. Magnetization ve rsus field at room te mperature for HgCo(SNC)4 (square). A linear curve has been fitted to the data points (solid line). The magnetization as a function of magnetic field at room temperature for HgCo(SNC)4 prepared as described is displayed in Figure B1. The typical positive linear trend is observed between the magnetization and the field as it is expected for a paramagnetic material. A very good correlation is found between the data and the linear fit (R2 = 0.999997). The sample mass is calculated from the accepted magnetic susceptibility31 measured at 20C. A magnetization of 0.003162 emu at 1000 Oe and 20C (293K) leads to a calculated mass of 191 mg. This calculated mass is useful for comparing the suscep tibility constants in the gram unit system. The magnetization versus temperature of HgCo(SNC)4 is plotted in figure B-2.

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136 0.00 0.03 0.05 0.08 0.10 0.13 0.15 0.18 0.20 0.23 0.25 0.28 020406080100120140160180200220240260280300Temperature (K)Magnetization (emu) Figure B-2. Magnetization versus temperature at 1000Oe for HgCo(SNC)4. The magnetization increase as the temperature is decreased. The magnetization is modeled using the sum of three terms define as: 0() ()diaparaparaTT where () M agnetization T Field dia is the diamagnetic susceptibility independent of temperature, 0para is the temperature independent pa ramagnetic susceptibility and ()paraT is the temperature dependent paramagnetic susceptibility, whic h is also called the Langevin paramagnetic susceptibility and is a function of the temperature as follows: ()paraC T T where C is the Curie constant, and is temperature constant. We apply the Curie-Weiss law to our data set; the fitting constants are presented in Table B 1. To visualize the good correlation between our meas ured data and the Curie-Weiss law, we plot

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137 the temperature dependent part of the magnetizat ion as function of inverse temperature minus theta. The temperature dependent part of the magnetization is proportional C/(T) and is presented Figure B-3. R2 = 0.9998 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.00 0.05 0.10 0.15 0.20 0.25 0.301/(T+1.95K)Magnetization adjusted for diamagnetism Figure B-3. Magnetization adjusted for diamagnetism as a function of the inverse temperature (squares). The temperature is shifted by 1.95K A linear trend is fitted to the data (solid line). Using these equations I modeled my m easurements and the one of OConnor32 using their published data. The values are presented in Table B-1. The analysis of O Connor contains errors and a detailed treatment of the magn etic susceptibility of HgCo(SNC)4 is the following sections. Nevertheless, the measurement of the data by OConnor is consider ed to be excellent33. Table B-1. Constants from susceptibility model. 0diapara [10-6 g-1] C [10-6 g-1] [K] This work -3.05 5056 1.95 OConnor32 -7.82 5433 1.98

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138 A good agreement between our measurements and the one from OConnor is observed. If we compare directly our modele d constants to the ones of OC onnor, it does not seem that we have a very good match. But if we look at the co rrelation between the susceptibility as function of temperature, which we are ultimately intere sted in, we find an excellent match with a correlation coefficient of 0.9999. This coefficient was calculated using the data of Table B-2, which displays the susceptibility values calcula ted from our measurement and the susceptibility values from OConnor. We conclude that HgCo(SNC)4 is a good reference for very low temperature magnetic measurements and that our SQUID magnetometer is working properly in the 2 to 100K range since we had a very good corre lation between our data and previously published ones. HgCo(SCN)4 is commonly used as a magnetic refere nce thanks to its ease of preparation and stability31-34. In the following sections, we present several issues encountered during the magnetic properties review of HgCo(SCN)4. First, we take a look at why some discrepancies can be found between a proposed model (for exampl e Curie-Weiss law) and measured data. Then, we will review the models proposed to explain the magnetic properties of this standard and discuss their validity. B.2 Model Weighting The Curie-Weiss model is widely used to model paramagnets. But as computer modeling evolved the method employed to comp are a set of data to a model changed. We show here that using a classical technique leads to slightly different fitting parame ters than using a more direct approach. Lets use the Curie-Weiss law as an example for our purpose of showing these differences. We will use the following e quation to represent the Curie-Weiss law: C M T where T is the temperature and M the magnetic susceptibility, C and are fitting parameters.

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139 Table B-2. Magnetic susceptibility [10-6 g-1] as function of temperature of HgCo(SNC)4 of our data set and OConnors data set. T[K] OConnor32This work 102.6 46.4 45.4 96.85 49.9 48.1 91 53.5 51.2 82.85 57.9 56.3 75.72 62.8 62.0 68.88 69.7 68.5 61.66 78.0 76 53.76 89.8 88 45.64 105 103 37.58 128 124 31.43 153 148 27.87 170 166 25.77 185 179 24.72 193 187 23.66 202 195 22.83 209 201 22.21 214 207 21.56 220 213 20.91 227 219 20.27 235 225 19.62 241 232 18.89 251 241 18.06 262 251 17.26 273 262 16.5 285 273 15.64 300 287 14.2 329 314 13.15 353 336 11.92 386 367 10.56 430 408 9.23 484 456 8.02 544 511 6.91 613 573 5.91 691 642 5.21 758 702 4.5 838 775 4.202 862 815 3.911 904 853 3.611 954 898 3.226 1025 966 2.9 1093 1033 2.39 1232 1165 1.99 1379 1299

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140 The classical fitting method would be to plot 1 M as function of T. The equation is rewritten as: 11 T M CC In this case we expect the data to have a linear trend with a slope of 1 C and a y-intercept equal to C This classical method can be done qui ckly without computer help. On the other hand, the more direct method of fitting the equation requires a computers help. To illustrate our point we plot the data accord ing to each method in Figure B-4. The A graph illustrates the direct method while the B graph illu strates the classical one. In addition the data used for these two graphs are shown in table B-3. Table B-3. Data example. T M 1 M 0 8.131 0.123 0.5 2.544 0.393 1 1.352 0.739 Both models lead to excellent correlation coefficient of 0.999 with the direct method and 0.995 with the classic one. Even with very good correlation coefficient, the fitting parameters can have large discrepancies up to 18% in our case as show in table B-4. Table B-4. Fitting parameters. Constants Direct MethodCl assic MethodDiscrepancy C 1.780 1.620 9% 0.2180.17818% We use the same data, the same equation but the fitting parameters were evaluated differently leading to large discrepancies! Our quantification of large is due to the fact that we expected very small differences in our fitting para meters since the correlat ion coefficients are so high. Therefore, one must be careful when usi ng the coefficient correl ation alone as a judging factor for a good model fit.

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141 A 0 2 4 6 8 10 00.20.40.60.811.2TM M Model M B 0 0.2 0.4 0.6 0.8 1 00.20.40.60.811.2T1/M 1/M Model 1/M Figure B-4. Example of the Curie law model. A) M-T plot and its model. B) M-1/T plot and its model. The discrepancies in fitting parameters betw een the classic and direct method comes from the weighting of the data points. The direct me thod will weight each data point equally where the classic method will decrease the weight of the data point with high M values and increase the

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142 weight of the data poin t with low M values. In physics term s: the direct method considers each data point to have the same precision while th e classic method assumes that the large M data point have less precision and should account for less. In the case where we know which data point have more precision we can weight the model accordingly. But in the case of the classic method the weighting is, in most cases, unrelated to the precision of the data and therefore does not account properly for it. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0102030405060708090100110Temperature (K)Magnetic susceptibility (10-6 g-1) Measured data Direct Method R2 = 0.9998 Figure B-5. Magnetic suscep tibility of HgCo(SNC)4 and its model using the direct method. On the other hand the direct method (as presen ted here) does not account for the precision either but conceder the data poi nt to be equal. If no informa tion is known about the precision, one should use the direct method and not the classic one. If one knows the precision of each data point, it is possible to take th is information into account in th e direct method and obtain more

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143 trustworthy fitting parameters. Historically, the classical method has been used because computers were not available. When high resolu tion is not required the classical method can be used but since computers are so widely used no wadays we believe that the direct method should always be used. 0 0.003 0.006 0.009 0.012 0.015 0.018 0.021 0.024 0102030405060708090100110Temperature (K)1/(susceptibility+0.288) 1/(Measured susceptibility+0.288) Classic Method Figure B-6. Inverse magnetic susceptibility of HgCo(SNC)4 adjusted for diamagnetism versus temperature and its model using the classic method. Now we compare the direct and classic method on physical data. For our purpose we use the magnetic susceptibility data provided by OConnor32 and the model equation: 0C T for the direct method and 011 T C for the classic method. The data with its model using the direct method is plotted Figure B-5. In addition, the inverse susceptibility adjusted for diamagne tism (using a value proposed by OConnor32) and its model

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144 using the classical method is pl otted Figure B-6. In both cases the model and data match very well (correlation coefficien ts better than 0.999). But the fitting parameters do not mach that well as we discuss now. The diamagnetic susceptibility (0 ) must be set to use the classic method. First, we use the value found using the direct method. This allows observing only the effect of weighting on the model and not the effect of choosing a set value. The fitting parameters are presented in Table B5 for comparison. A large discrepancy is found fo r the value of theta between the methods and a moderate discrepancy is found for the Curie c onstant. Applying these two methods on physical data reveals that weighting the data can be an important issue. Once again, since we do not know the precision, we can only assume that all measurements have the same precision and therefore we must weight equally our data points when applying the model. Now lets see what happens to the fitting parameters when the diamagnetic susceptibility is changed. Table B-5. Comparison of the dire ct and classic method of OConnor data set. For both methods the diamagnetic constant is set and equal to the value found through the direct method. Constants Direct MethodCl assic MethodDiscrepancy 0 [10-6 g-1] -7.86-7.860% C [10-6 g-1] 5389 5621 4.3% [K] -1.82 -2.62 44% r2 0.9998 0.9991 N/A OConnor used an empirically calculated value32 for the diamagnetic susceptibility of HgCo(SNC)4. If we use that value we obtain the fitting parameters in Table B-6. When comparing the direct and classic method we obt ain large discrepancies. In particular the diamagnetic susceptibility is twen ty times larger when using the direct method than when we use the proposed value by OConnor. In addition the discrepancies for the other fitting parameters are larger than when we use the same diama gnetic constant. We conclude that setting the

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145 diamagnetic constant in the cla ssic method leads to additional vari ation in the fitting parameters. This is another reason why one should use the direct method rather than the classic one. Table B-6. Comparison of the dire ct and classic method with OC onnor data set. For the classic method the diamagnetic constant is set a nd equal to the value proposed by OConnor. Constants Direct MethodCl assic MethodDiscrepancy 0 [10-6 g-1] -7.86 -0.288 96% C [10-6 g-1] 5389 4902 9% [K] -1.82 -1.02 44% r2 0.9998 0.9997 N/A B.3 Temperature Independent Susceptibility The previous section led us to see that the di amagnetic constant is an important factor in the model of the magnetic susceptibility of HgCo(SNC)4. In this section we will discuss what has been previously done regardi ng temperature independent sus ceptibility. It includes the diamagnetic constant and the paramagnetic temp erature independent constant, also sometimes called Van Vleck magnetism38,60. The Van Vleck susceptibility is given by: 2 2 22 0 0 1 00() 2 6Z zz Bi ni neLgSn e N r VEEm where N V is the spin density, 2 2 00() 2zz B n nLgSn EE is the temperature independe nt paramagnetic term and 2 2 0 16Z i i ee r mis the diamagnetic term. In the first term, Lz is the orbital angular momentum operator projected on the z-axis, Sz is the total spin angular momentum projected on the z-axis, g is the Lande factor, E is the energy, n designates the electron number and B is the Bohr magneton. In the second term, e is the electrons electric charge, 0 is the vacuum magnetic permeability, me is the electron mass, r is the electr on radius and Z is the total number of electrons. In practice, the full calculation ha s only been performed on monoatomic gases and

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146 small molecules with high symmetry due to complexity of electron orbitals. In a large molecule like HgCo(SNC)4, the simplest approach is to use a linear combination of individually calculated temperature independent susceptibilities for an atom or small group of atoms. Selwood61 and Pascal62 proposed values presented in Table B-7 for the diamagnetic term. From the stoichiometric composition we found 06 1371243518910diamol according to Selwood and 0 614(33.264.8510.3)1232.3123810diamol according to Pascals method. It must be added in pa ssing that Selwood [61] recognized that these diamagnetic corrections are not to be taken as absolute values. Table B-7. Diamagnetic correction per mol. Species Selwood61 0 dia [10-6 mol-1]Pascal62 0 dia [10-6 mol-1] CNS-35 -33.26 C-N 0 -4.85 C-S 0 -10.3 Co2+ -12 -12* Hg2+ -37 -32.31 HgCo(SNC)4 -189 -238 Pascals value was not available therefor e it was taken to be equal to Selwoods. In addition to the diamagnetic correction a temperature independent paramagnetic correction may be requir ed. According to Nelson63 Co2+ has a non-zero paramagnetic susceptibility of 06 143010paramol. This value is similar to the calculation of Cotton64 based on optical measurements. But according to Selwood, Cobalt-cyanide salts, [Co(CN)x]-y, do not have a temperature independe nt paramagnetic susceptibility if they are coupled with a nonmagnetic element such as Hg. Therefore no temp erature independent su sceptibility should be added in our model. Nelsons method includes, first, measuring th e magnetic susceptibility from 40 to 300 K. This is done in order to avoid the low temperat ure effect which will be discussed in the next

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147 section. Then modeling th e data using the equation: 0C T where00 0 paradia In addition, Nelson calculates the temp erature independent susceptibility (0 para ) from the previous equation. Using this met hod on my data I obtained 06 127010paramol and 06 130210paramol using OConnors data. This is far from what Nelson found (06 143010paramol). -0.2 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Figure B-7. Three dimensional representation of HgCo(SNC)4. X,Y,Z are the fractional coordinates. Hg Co S N C X Y Z

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148 Finally, according to Selwood, the higher the symmetry of a molecule the better the correction agree with experime nt. In the case of HgCo(SNC)4 the molecule has a complex symmetry65 and therefore the temperature independe nt corrections are not accurate. A threedimensional plot of a section of HgCo(SNC)4 is presented in Figure B-7. In conclusion, the suggested values for the HgCo(SNC)4 temperature-independent susceptibility corrections need to be taken w ith a grain of salt. We found many publications on this topic but there were lots of inaccuracies or contradictory explanat ions and therefore we suggest that the full calculation of the temper ature independent susceptibility using electron orbitals be performed before an improved analysis is proposed. B.4 Zero Field Splitting and Exchange Interaction I would like to finish th is appendix with effects seen at ve ry low temperature in the case of this standard material, namely zero field splitting and exchange interaction. Nelson63, OConnor32 and Hatfield66 all agree that below 20 K both zero field splitting and exchange interaction must be taken into account to properly model the magnetic susceptibility of this cobalt salt. But none of them agree on the model. Hatfield66 seems to have the most accurate model for zero field splitting as he uses both meas urements as a function of temperature and field to validate his equation. He propos es the following set of equations: 02 3 23 sinhsinh 22 9 3 22 3 4 coshcosh 22x B x B y y e yy Ng y y kT e

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149 2sinh 33 cosh() 22 coshzzx B zx z By y eee Ng yxx kTeyee BD x kT B BgH y kT and 23 4 y z x The constants are defined as follows: D is the zero field splitting constant, kB the Boltzman constant, T the temperature, g the La nd factor, H the magnetic field and B the Bohr magneton. 0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 2.5E-04 3.0E-04 0 10000 20000 30000 40000 50000Field (Oe)Susceptibilty (a.u.) Figure B-8. Magnetic suscep tibility of HgCo(SNC)4 as function of magnetic field at 2 K (square) and its model (solid line). Using Hatfields equations applied to the sus ceptibility versus field measurements at 2 K we found a zero field splitting constant of 7 cm-1 (Figure B-8). This value is at the same order of

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150 magnitude to the one calculated by Hatfield (19 cm-1). In addition Hatfield66 recognize that he did not have a precise value for the zero-field splitting. The zero-field splitting effect has been show n before and we successfully reproduced the measurement and modeling technique used. This confirms that our SQUID magnetometer is properly calibrated. Finally the model proposed for the exchange in teraction occurring at very low temperature can be reviewed in the work by Nelson on HgCo(SNC)4 crystals. The measurement of the exchange interaction in this material is well beyond the scope of this work and a good presentation of this effect and model is presented63 on a HgCo(SNC)4 crystal. B.5 Conclusions This appendix was aimed at showing several issues which have occurred during the study of magnetism. First, it is a complicated topi c as shown by the contradictory experiments and models proposed by several leading authors in this field on a standard material. Secondly, we were able to reproduce accurately the results produced by others. It demonstrates that our methods and equipment are in good working conditions. Also, we wanted to raise awareness on the difficulty of modeling as different authors us e different techniques which add confusion to an already difficult topic. Finally, we suggest that this material be studied further using optical absorption measurements for example, to compare with zero field splitting value from magnetic measurements or that its temper ature independent susceptibility be fully modeled using quantum theoretical calculation.

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151 APPENDIX C ALUMINUM MAGNETIC REFERENCE FO R TEMPERATURE RANGE 50 300 K Aluminum has been well studied in the 50300K temperature range and is a well suited magnetic reference in that range due to its larg e temperature dependence. This Appendix details the results and conclusions presented in section 3.3.2. R2 = 0.9993 -4.E-05 -3.E-05 -2.E-05 -1.E-05 0.E+00 1.E-05 2.E-05 3.E-05 4.E-05 -1000-800-600-400-20002004006008001000Field (Oe)Magnetization (emu) Figure C-1. Magnetization versus field at room temperat ure of 99.999% pure aluminum (squares). A linear curve is fitted to the data (solid line). First, we measured the magnetization of an aluminum piece as function of magnetic field at room temperature to evaluate the magnetic su sceptibility. The data ar e plotted in Figure C-1. The magnetization is linearly proportional to the field as expected for a paramagnet. The measured magnetic susceptibility at room temperature is 3.377-8 emu for the aluminum sample. Using the measured weight of the samp le (53.4 .1 mg) we calculated a sample volume

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152 of 0.0198 .00004 cm-3 leading to a volume su sceptibility of 1.70.03-6 cm-3. This value is very close to the published2 value of 1.65-6 cm-3. 3.00E-05 3.15E-05 3.30E-05 3.45E-05 3.60E-05 3.75E-05 3.90E-05 4.05E-05 4.20E-05 4.35E-05 020406080100120140160180200220240260280300Temperature (K)Magnetization (emu) Figure C-2. Magnetization versus temperat ure at 1000 Oe for 99.999% pure aluminum. Next, we measured the magnetization as func tion of temperature at 1000 Oe. The data are plotted in Figure C-2. The magnetization decreases as the temperature increases but not like the Curie law. Rather, aluminum magnetization is lin early dependant on the square of temperature according to Hedgcock34. A linear trend is fitted through our magnetization measurement versus temperature square as seen in Figure C-3. Table C-1. Comparison of model constants for aluminum. 0 diapara [10-6 cm-3] B [10-12 K-2cm-3] This work 18.8 -3.96 Hedgcock34 19.2 -3.70

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153 Using the calculated volume of our sample we obtained fitting parameters displayed in Table C-1 in cm-3 units for direct comparison with Hedgcocks work34. For modeling our data we use the following equation: 02 diapara B T We found a correlati on coefficient of 0.997 between our data and the model. R2 = 0.997 3.0E-05 3.2E-05 3.4E-05 3.6E-05 3.8E-05 4.0E-05 4.2E-05 4.4E-05 0100002000030000400005000060000700008000090000100000Temperature2 (K2) Magnetization (emu) 100K 300K 200K 150K 50K Figure C-3. Magnetization as function of te mperature square at 1000Oe for 99.999% pure aluminum (diamonds). A linear trend is fitted to the data (solid line). The results from HgCo(SNC)4 and Aluminum reference lead us to conclude that our SQUID is properly calibrated from 50 to 300 K.

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154 APPENDIX D OXYGEN CONTAMINATION AT LOW TEMPERATURES This Appendix is aim ed at giving all the details necessary to visualize the oxygen contamination problem. As stated in section 3.3.3 oxygen is paramagne tic in its gas and liquid phases, becomes antiferromagnetic when solid below 54.3 K, and changes its crystal structure36 ( to at 43.8 K). The magnetic transitions of oxygen at 54.3 K and 43.8 K generate a noticeable change in the measured magnetic suscep tibility of a sample while some gaseous oxygen is left in the sample chamber. For example Figure D-1 displays the magnetization of a piece of plastic straw as a function of temperature at 500 Oe. A very large peak around 50 K is observe d above a broad flat magnetization (equal to the diamagnetic su sceptibility of th e piece of straw). -3.8E-05 -3.7E-05 -3.6E-05 -3.5E-05 -3.4E-05 -3.3E-05 -3.2E-05 -3.1E-05 -3.0E-05 -2.9E-05 -2.8E-05 0255075100125150175200225Temperature (K)Magnetization (emu) Figure D-1. Magnetization versus temperature for a piece of plastic straw at 500Oe.

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155 In our SQUID magnetometer, a sample is normally measured in a Helium gas atmosphere. Following the sample loading, the load lock (or the entire chamber) is purged with Helium gas. But due to pumping and Helium quality there is still oxygen left in the chamber. To find out what was the oxygen residual limit, we measured the magnetization versus temperature of another piece of straw for several different numbers of purges. The data is presented in Figure D2. -4.E-05 -3.E-05 -2.E-05 -1.E-05 0.E+00 1.E-05 2.E-05 303540455055606570Temperature (K)Magnetization (emu) 0 purge 1 purge x 7 2 purges x 30 3 purges x 50 Figure D-2. Magnetization at 1000 Oe of a piece of straw as a function of temperature for several different purges. The 0 purge magnetization has been shifted by -15K. The 1,2 and 3 purge magnetization has been multiplied by 7, 30 and 50 at 40, 45 and 50K. For better visibility the ma gnetization at and around the oxygen peak has been multiplied by a scalar listed in the Figure D-2 legend. When no purge is performed a large peak is observed as expected since we leave a large amount of ox ygen gas from air in the chamber. But, even when we purged 3 times the oxygen peak is still visible. Plotting the oxygen peak height as a

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156 function of the number of purges done during the loading of the samp le helps us better visualize the decrease of oxygen amount present in th e SQUID magnetometer chamber. Figure D-3 displays such a graph. 0 1 2 3 4 5 00 511 522 533 5Number of purgesMagnetization (10-5 emu) Figure D-3. Oxygen magnetization peak height versus number of purges (diamonds). An exponential decay model is fitted to the data in solid. An exponential decay model is used to mode l the decrease of oxygen amount as function of the number of purge. The model has the following form:0 0/ nnMMAe, where M0 is the residual magnetization due to oxygen, A is the exponential amplitude and n0 is the exponential decay constant. Applying this model to our data, we found M0 = 0.059-5 emu, A = 4.44-5 emu and n0 = 0.42. We found that a small but visible residual amount of oxygen is present and further purging would not decrease it. This small trace of oxygen could be explained by the

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157 limiting pumping capability of the mechanical pu mp and the presence of trace oxygen within the helium gas use to cool down the sample. It is to be noted that the magnetic oxygen p eak position depends on the rate at which the temperature is changed37. For example, this is observed on our zero purge experiment, and this is why we shifted our curve accordingly to better visualize the peak height as function of the number of purges. Finally, this oxygen effect is only visible in samples with magnetization in the 10-5 10-6 emu range. Therefore we recommend, in addition to multi-purging, using samples as large as possible to decrease the relative effe ct due to oxygen magnetic transition.

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158 APPENDIX E ELECTRON PARAMAGNETIC RESONAN CE SYS TEM OVEN APPARATUS The design and construction of an oven wa s required for above room temperature measurements of electron paramagnetic resonance. In this appendix we will describe how it is designed and how it works. To simplify the explanations, Figure E-1 is pres ented. In this figure, the left side is a picture of the oven apparatus including the resona nt cavity and the waveguide, while on the right side a schematic representation of the cross cut is plotted. First, at the bottom of the oven apparatus, room temperature nitrogen gas is introduced into the hot quartz ampoule. Nitrogen was used because of its wide availability, none corrosive nature and its zero background signal in the EPR cavity. The temperature range of the ampoule can be varied from 20C to 1000C by adjusting the curren t in the heating elemen t with a Variac. An Etype thermocouple is built in the outside of the ampoule to monitor the qu artz temperature. The nitrogen is slowed down in the ampoule due to the increase in cross se ction and small quartz piece making the molecular path length longer. Anot her thermocouple can also be inserted at the output to monitor the temperature of the nitr ogen. Typically high temperatures of near 600C have been utilized. Since we only want to heat the sample a nd not the cavity, we used an insulating double wall quartz tube to prevent heat from warming up the cavity and thus affect the measurements. The insulation in the quartz tube is obtained by pumping the space between the walls down to 105 torr with a turbo-pump. The stainless steel me tal casing was designed with an inner groove to accommodate two viton o-rings. These o-rings are very critical for high vacuum quality. To prevent fast degradation as the temperature ri se in the column, only viton o-rings, specially designed for high temperature were used.

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159 Figure E-1. Picture and schematic cross sect ion of the oven apparatus for the electron paramagnetic resonance system. Quartz sample holder Cap with Viton seal Hot N2 output Microwave cavity To vacuum pump Double wall quartz tube Sample Translation stage Heating element Ceramic insulation Cold N2 input Power from Variac Q uartz am p oule Broken quartz pieces Microwave wave-guide

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160 The hot nitrogen gas flows through the cavity warming up the quartz sample holder and is then released in the air through the exit port. Once in the air, the gas cools down very rapidly. The design of the top part allows the variation of the viton o-ring inner diameter by screwing in or out the cap (squeezing or releas ing the o-ring). Since the sample holder passes through the o-ring, simply screwing in the cap will lo ck the holder in place. The sample position can be adjusted by sliding the sample holder through the o-ring when the cap is unscrewed. To accommodate various sizes of quartz holder diameters, three inserts have been manufactured. This allows the use of 3, 4 and 5 mm quartz tubes. A thermocouple can be inserted in the quart z holder and positioned a few millimeters away from the sample without pertur bation of the spectrum acquisiti on. This method allows a very accurate samples temperature measurement. In addition, a translation stage is used to adjust the waveguide and cavity position in the center of the magnet. For practical reasons, the movi ng part of the stage is made of plastic. It will melt if the experiment is conducte d for too long (more than 2 hours). Finally, the sample temperature is controlled by varying the power to the heating element and the flow of nitrogen. At temperatures belo w 300C at the sample, the cavity stays at room temperature which allows a high quality resonanc e. But, when high temperatures are reached (500C) the cavity warms up just enough to m odify to resonance condition and affect the observed spectrum. To properly acquire EPR spectra at elevated temperature, a water cooling system would be necessary to maintain the cavity at room temperature. But, such modifications are beyond our capabilities. Bruker, the manufacture r of the EPR system which we use sell a high temperature (up to 1300 K) cavity for $50,000. I manufactured our system for less than $1,300.

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161 LIST OF REFERENCES 1B. D. Cullity, Introduction to Magnetic Materi als, Addison-Wesley Publishing Company, Reading, Massachusetts, USA, 1972. 2R. E. Hummel, Electronic Prope rties of Materials, third ed ition, Springer, New York, New York, USA, 2001. 3J. Hack, M.H. Ludwig, W. Geerts, and R. E. Hummel, Mat. Res. Soc. Symp. Proc. 452, 147 (1997). 4T. Dubroca, J. Hack, and R.E. Hummel, Appl. Phys. Let. 88, 182504 (2006). 5P. Esquinazi, A. Setzer, R. Hhne and C. Semmelhack, Phys. Rev. B 66, 024429 (2002). 6P. Esquinazi, and R. Hhne, J. Magn. Magn. Mater. 20, 290 (2005). 7D. Spemann, K. Schindler, P. Esquinazi, M. Diac onu, H. Schmidt, R. Hhne, A. Setzer, and T. Butz, Nucl. Intr. And Meth. B 250, 303 (2006). 8P. Reichart, D. Spemann, A. Hauptner, A. Bergma ier, V. Hable, R. Hertenberger, C. Greubel, A. Setzer, G. Dollinger, D.N. Jamieson, T. Bu tz, and P. Esquinazi, Nucl. Intr. And Meth. B 249, 286 (2006). 9Y. Kopelevich, P. Esquinazi, J. Torres, and S. Moehlecke, J. Low Temp. Phys. 119, 691 (2000). 10P. Esquinazi, A. Setzer, R. Hhne, C. Semm elhack, Y. Hhne, D. Spemann, T. Butz, B. Kohlstrunk, and M. Lsche, Phys. Rev. B 66, 024429 (2002). 11D. Spemann, K.-H. Han, P. Esquinazi, R. Hhne, and T. Butz, Nucl. Intr. And Meth. B 219, 886 (2004). 12P. Esquinazi, R. Hhne, K.-H. Han, A. Set zer, D. Spemann, and T. Butz, Adv. Mat. 15, 1719 (2003). 13A.V. Rode, E.G. Gamaly, A.G. Christy, J.G. Fitz Gerald, S.T. Hyde, R.G. Elliman, B. LutherDavies, A.I. Veinger, J. Androulakis and J. Giapintzakis, Phys. Rev. B 70, 054407 (2004). 14A.V. Rode, E.G. Gamaly, A.G. Christy, J.G. Fitz Gerald, S.T. Hyde, R.G. Elliman, B. LutherDavies, A.I. Veinger, J. Androulakis, a nd J. Giapintzakis, J. Magn. Magn. Mater. 290, 298 (2005). 15A.V. Rode, A.G. Christy, N.R. Madsen, E.G. Gamaly, S.T. Hyde, and B. Luther-Davies, Cur. Appl. Phys. 6, 549 (2006). 16W. Orellana, and P. Fuentealba, Surf. Science 600, 4305 (2006). 17N. Park, M. Yoon, S. Berber, J. Ihm, E. Osawa, and D. Tomanek, Phys. Rev. Lett. 91, 23 (2003).

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163 40W.L. Warren, E.H. Pointdexter, M. Offenberg, and W. Muller-Warmuth, J. Electrochem. Soc. 139, 870 part I (1992). 41W.L. Warren, J. Kanicki, F.C. Rong, and E.H. Pointdexter, J. Electrochem. Soc. 139, 880 part II (1992). 42C.J. Nicklaw, M.P. Pagey, S.T. Pantelides, D.M. Fleetwood, R.D. Schrimpf, K.F. Galloway, J.E. Wittig, B.M. Howard, E. Taw, W.H. McNeil, and J.F. Jr. Conley, IEEE Trans. Nucl. Sci., 47, No 6 (2000). 43V.Y. Bratus, M.Y. Valakh, I.P. Vorona, T.T. Petrenko, V.A. Yukhimchuk, P.L.F. Hemment, and T. Komoda, J. Lumin. 80, 269 (1999). 44N. Tomozeiu, E.E. Van Faassen, W.M. Arnoldbik, A.M. Vredenberg, and F.H.P.M. Habraken, Thin Sol. Films 420, 382 (2002). 45K.G. Shaw, and R.K. MacCrone, J. non-Cryst. Sol. 159, 253 (1993). 46B. Rakvin, and B. Pivac, J. Appl. Phys. 81, 3453 (1997). 47P.A. Thomas, M.H. Brodsky, D. Kaplan, and D. Lepine, Phys. Rev. B 18, 3059 (1978). 48L.J. Berliner, G.R. Eaton, and S.S. Eaton, Biological Magnetic Re sonance vol. 19, Plenum Publishers, New York, New York, USA, 2001. 49S.J. Hudgens, Phys. Rev. B 14, 1547 (1976). 50J.G. Polihronov, R.E. Hummel, and H.-P. Cheng, J. Lumin. 101, 55 (2003). 51Shepherd N.D., University of Florida dissertation, Visible electro -luminescence in sparkprocessed silicon, 2001. 52J.C. Gourdon, P. Fretier, and J. Pescia, J. Physique Lettres 42, L-21 (1981). 53A. Schweiger, and G. Jeschke, Principles of Pulse Electron Paramagnetic Resonance, Oxford University Press, Oxford, England, 2001. 54S.S. Eaton, and G.R. Eaton, J. Mag. Res. 102, 254 (1993). 55N.N. Gerasimenko, A.V. Dvurechenskii, A.I. Mashin, and A.F. Khokhlov, Fiz. Tekh. Poluprovodn. 11, 190 (1977). 56W. Jung, and G.S. Newell, Phys. Rev. 132, 648 (1963). 57MikroMash USA, 9755 SW Commerce Cir, Suite B-1 Wilsonville, OR 97070. 58F.J. Dyson, Phys. Rev. 98, 349 (1955). 59G. Feher, and A.F. Kip, Phys. Rev. 98, 337 (1955).

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164 60J.H. Van Vleck, The Theory of Electric a nd Magnetic Susceptibiliti es, Lowe and Brydone Printers Ltd, Oxford, England, 1932. 61P.W. Selwood, Magnetochemistry, Interscience P ublishers Inc., New York, New York, USA, 1956. 62L.N. Mulay, and E.A. Boudreaux, Theory and Applications of Molecular Diamagnetism, Wiley-Intersience Publication, New York, New York, USA, 1976. 63D. Nelson, and L.W. Haar, Inorg. Chem. 32, 182 (1993). 64F.A. Cotton, D.M.L. Goodgame, M. Goodgame, and A. Sacco, J. Am. Chem. Soc. 83, 4157 (1961). 65J.W. Jeffery, and K.M. Rose, Acta Cryst. B24, 653 (1968). 66D.B. Brown, V.H. Crawford, J.W. Hall, and W.E. Hatfield, J. Phys. Chem. 81, 1303 (1977)

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165 BIOGRAPHICAL SKETCH Thierry Dubroca was born in France in 1977. He attended Notre Da me high school at Fontenay-le-Compte where he graduated with honors in 1995. After attending competitive classes in mathematics and physics for three years at the preparatory scho ol St. Joseph in La Roche-sur-Yon, he was successfully admitted to the National School of Engineering Physics in Grenoble, France. He graduated with honors in Ju ne 2001 with an engineering degree in applied physics and a minor in entrepreneurship. Thierr y concurrently earned a masters degree in semiconductor physics from University Joseph Fo urier and the Grenoble National Polytechnic Institute in September 2001. In 2000, while completing his engineering degree in France, Thierry moved to Gainesville, FL where he was an exchange student at the Univ ersity of Florida. He continued on and earned a masters degree in material science and engineering in 2002. He started as a teaching a ssistant for Dr. John Ambrose and the Major Analytical Instrumentation Center. During the fall 2001, he joined Prof. Rolf Hummels group where he worked as a research assistant on infrared spectr ometry. Thereafter, while he began his doctoral research on magnetic properties of materials, he studied management, and, in 2004, received a Master of Science in management from the Warrington College of Business and Administration at the University of Florida. Thierry finishes his education earning a Ph.D in material science and engineering from the University of Flor ida while still being unde r the supervision of Professor Rolf Hummel. That same year, he won the Rugby South conference championship with the Gainesville Hogs.


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