Doping experiments on magnetic heavy fermion superconductors

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Doping experiments on magnetic heavy fermion superconductors
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Thesis (Ph. D.)--University of Florida, 1995.
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Includes bibliographical references (leaves 166-176).
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by Weonwoo Kim.
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Full Text










DOPING EXPERIMENTS ON MAGNETIC HEAVY FERMION
SUPERCONDUCTORS
















By


WEONWOO KIM


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















ACKNOWLEDGMENTS


I wish to express my sincere appreciation to Professor Gregory R.


Stewart not


only for his stimulating suggestions and valuable advice throughout the entire research of

this work, but also for his patient encouragement when I had a hard time in my course


work and research.


In addition, I am very thankful not only to Professor P


Kumar for his


delightful


clear


discussions


comments


in physics,


to Professors


Takano,


Sullivan,


Ingersent,


and T.J.


Anderson for their valuable advice and


suggestions.


Special thanks go to Dr.


Dr. J.


B. Andraka for his


Kim for his help in experiments, R. Pietri, a


valuable discussions and cooperation,

nd S. Thomas for his proofreading of


the manuscript as well as pleasant relationship.

The faculty, postdoctoral fellows, administrative, and technical support from the

machine shop, cryogenics, and electronic shop have contributed a great deal to this work.

Finally, I dedicate my warm love and gratitude to my family including my wife

Hea-Kyung for her consistent trust and encouragement, two sons Dong-Hwa and Dong-

In, and relatives in Korea for their support and prayer.


HAPPY


THE


PERSON


WHO


REMAINS


FAITHFUL


UNDER


TRIALS,


BECA USE WHEN HE SUCCEEDS IN PASSING SUCH A


TEST,


HE WILL RECEIVE


AS HIS REWARD THE LIFE WHICH GOD HAS PROMISED TO THOSE WHO LOVE


HIM.


(James 1:1

















TABLE OF CONTENTS


pages

ACKKNOWLEDGMENTS......... ...............................................

LIST OF TABLES ...........................................................................................................v

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

ABSTRACT ...................................................................................................................ix

CHAPTERS

INTRODUCTION ..................................................................................................... 1


Overview of Heavy Fermion Systems..


1.1.1
1.1.2
1.1.3
1.1.4


Classification of Heavy Hermion Systems.......
M ass Enhancement ............... ................... .......
Superconductivity ............................................
M agnetism ............... ....................................


...... 1
......2
.....5


........6


M motivation ................... ................. ..........
Experimental Techniques ...........................


1.3.1
1.3.2


Sample Preparation...........
Measurement Techniques..


Fermi Liquid Theory.........
Non-Fermi Liquid Theory.


2.2.1
2.2.2


* *. *. *.. .. .... . . ... *. *..o 4 4 .4 *... .. ..


Multichannel Kondo Effect......


Phenomenological Theory of a Critical Point at T


= O K.................


.....38


NON-FERMI LIQUID BEHAVIOR OF MAGNETIC HEAVY FERMION


1T TPFPR rfNTT TTTTOR 5


An


I(ltl)lllt)((l(llltl11(111(1111111111111
)(11111)1)1)()11(111(111(1)1((1111111111


...................6


REVIEW OF THEORY. ................... ................... ................... .........


r










3.2.3 Non-Fermi Liquid Behavior of UxThl.xRu2Si2 for x < 0.07..................49


3.2.4 Non-Fermi Liquid Behavior of UxThl.xRu2Si2 for 0.07




3.3 Magnetism and Its Connection to Non-Fermi Liquid Behavior in
U i-.xM xNi2Al3 {M = Th, Pr, and Y } ............................................


3.3.1


UNi2Al3 ................


3.3.2 Non-Fermi Liquid Behavior in Ul-xMxNi2Al3 (M = Th, Pr, and Y}...


4.1.1


4.1.2 M magnetic Properties ............................................................................95
4.1.3 Concentration Determ nation ...............................................................96


4.1.4 Isotope Effects...........


4.1.5 Pressure-Composition Isotherms ................... ................... ................... 97


4.2 Overview of UPd2A3 ........


4..1 oma tae ......... ........... ........... .S..


4.3 Experimental Apparatus...........
4.4 Sample Preparation ..................


*4.**4* *4 *4**S. *4*** ** '........*4***. *4*. ** *4*44*4 .... *4*. *** *4*. *4** 99


S 4*'**~~* *4**t4~4 *44~ 4~~**~* *4* *4 *******~ .. . .. .. . .
4*4**44 *4~ ~ *4 *4*4**4* 4**~** *4**-** *. 4***~*~~ ~4***


4 e.4 1 c1'ry t lln Saii le. 494**4*4**..... 44 *9444*4**4 4.5* 4 44. *4 *4 4** 49**. 4..... ....... ***11

4.4.3 Pasvto c1 Samxpile. 44...#**.... ... *444*....*..4.. 4444*4**44* .**.. 4.***4..*.. 1 1 J.


4.5 Hydrogen Effects on UPd2A13 .............
4.5.1 Hydrogen Effects on Uranium.....


* *.. .... . .. 4. ..... ... .. . . .


4.5.2 Hydrogen Effects on UPd2A13Hx ..... ...................... .................... 1 22

SUMMARY AND CONCLUSION. .............. .................. ................................ .....148


UxThl-xRu2Si2 for x 0. 17........


5.2 U1-xMxNi2Al3 {M =
5.3 UPd2AI3Hx .............


APPENDIX


Th, Pr, and Y)


PRELIMINARY RESULTS OF UNi2AI3Hx, CeCu2.2Si2Hx, AND UPt3Hx


4* *494.4 15e


IR.IFEIR.J.N1I ES.. *4.4.**4_.. *4 .** 4* .*. *4*4*4** 4 *.4.4.*.4.. 9.***444**44*b. .. ... *4*94 4* 44.**4*4**. ** 6

fln~flCZDur An-i Al CVPTC'T- 177


........................................


HYDROGEN DOPING EF~CTS ON UPd2A13 ........................................

4. 1 Review of Hydrides. ................... ................... ................... .......


Electronic Properties ................... ................... ................... ..........


















LIST OF TABLES


Tables


The physical quantities of two channel spin 1/2 and electric quadrupolar
(pseudospin 1/2) K ondo effect ............. ....... ............ . ..... . . ....... . . .


Kondo temperature TK in UxThi.xRu2Si2 for 0.07


.... 38


x 0.17


.........................5 5


Physical parameters for Uo.9Mo.


1Ni2Al3 (M


= Ce, Th, La, Y


Physical relations between the U and the doped elements .............................. 73

Parameters for hydrogen doped UPd2A3Hx ................... ............... ......... . 127


Panes


and Pr)..............73
















LIST OF FIGURES


Pages


Classification of heavy fermion and intermediate valence compounds..............4

Diagram of heat flow in the system used for thermal relaxation method......... 13

The sample platform and copper-ring heat reservoir. ..................................... 14

Block diagram of experimental setup for the specific heat measurements....... 16


Specific heat as a function of T/TK in constant magnetic field and n


for S


1/2 and S


...........32


Magnetic susceptibility as a function of T/TK in constant magnetic field


and n


1 forS


................33


Entropy, specific heat, and specific heat divided by temperature as a function
of T/TK in constant magnetic field for S = 1/2 andn = 2................................ 34


Crystal and spin structure of antiferromagnetic superconductor URu2Si2.......46


Magnetic susceptibility of UxThi.xRuzSi2 for x


Low temperature resistance normalized to the room-temperature value R,


of Uo. 7Tho.g3Ru2Si2 ............


The anomaly TA in terms of concentration x. ................... ................... ........... 58

Csd/Tas a function of In Tin UxThi.xRu2Si2 for 0.07 < x < 0.17....................59


C/T vs. T2 for Uo.1Tho.9Ru2Si2 in two different magnetic fields.......................60

rlao;fot.;inn nfnlrnnn arrAtam h17 T.71 Q To.nA.. ^


9 99 9* *9 95 7~


FiguT~


3/2


3/2


~ 0.07...................................5















C/T vs. T for UNi2AI3 between 0


lc and 9 K.. ............,.,..............,....... ...*..'.7A0


x(7) between 1.8 K and 300 K for four samples of UNi2Al ..........................75

C/T vs. T2 for four samples of UNi2zA3 and Uo.9Ceoa.Ni2Al3........................... 76


C/T vs. T2 in Uo.9Mo.1Ni2A3 for M


3-16


= La, Th, Pr, and


C5sT vs. In Tfor Uo.9Mo.iNi2A13 (M


Cs'/T vs. In T for U.-xThxNi2A13 (x

C/T vs. T2 for UI-xThxNi2Al3 (x =


=0.01


0.015


,0.2,


and 0.3) .............. ......... 79


,0.2,


X vs. T72 for Uo.9Mo.0Ni2Al3 (M


3-20

3-21


X vs.


p as a function of temperature in U0.9Mo.iNi2A13 (M


= Pr, Th, and Y)............84


C/T vs. T


for Ui.xThxNi2Al3 (x


= 0.0, 0.0025,


0.005, and 0.015).................86


3-23


y(7) at low temperatures in Ul.xThxNi2Al3 (x


= 0.0025 and 0.005)...............87


3-24

4-1

4-2


C/Tvs. T for Uo.9Tho.Ni2Al3 in two different magnetic fields........................89

Two pressure-composition isotherms of a hydride .........................................98

Hexagonal PrNi2AI3 crystal structure observed in UPd2AI3.......................... 101


p(7) and x(7) in UPd2A13 below T


=25


K and up to T


vs. TofUPd2AI3 H


= 0 T and in several magnetic fields....................... 104


Y. ................... .............77


T dependence of Xde as measured for UNi2A13 ................... ................... .........68

p as a fUnction of temperature for UNi2A13.................................


Pr, Th, La, and Y) ................... ........._78


and 0.3)...........................80


Pr, Th, and Y) ................... ................... ....82


In T for U0.9Y0.1Ni2A13 -- 83


300 K. ..................1 02


--- --










X vs. T of UPd2Al3Hx for 0


Magnetization M vs.


magnetic field H for UPd2Al3Hx for


= 0 and 1.30.....128


4-10


Low-temperature C/T vs.


T of UPd2Al3Hx for 0


y(- C/T as T 0) vs. X in a In-In plot for a number of heavy systems.......... 132

Schematic model of XPS for UPd2Al3Hx .................................................... 133


4-11

4-12


4-13

4-14


Curie-Weiss


X(as T


temperature 0 c.w. vs.


concentration x for UPd2Al3Hx............136


4-15


4-16


C/TasT


X vs.


- 0) vs.


temperature T for UPd2Al3Ho.64 in magnetic field ................................ 141


4-17


Xvs.


4T of UPd2AI3Hx for x


1.09 and I


4-18


4-19


AC/Tvs. In T of UPd2A13Hx for


Specific heat of UPd2AI3Hx as C/Tvs. Tat the superconducting state.......... 145


C/T vs. T of UNi2Al3Hx (x


= 0.0, 0.23,


x(7) of UNi2Al3Ho.30 in different magnetic fields.......................................... 157


X(T) of CeCu2. Si2Hx for x


M(H) of CeCu2.2Si2Hx at T


= 0.0 and 0.07 ........... .... ....... .. ........... .......... 160


= 1.8 K for x


X of the polycrystalline sample of UPt3 as a function of temperature............ 162


x(7) of UPt3Hx for x


= 0.0 and 0.17 (both systems are pellets).................... 164


C/T vs.


T of UPt3Hx for x


= 0.0 and 0.17 (both systems are pellets)............165


- 0) vs.


x for UPd2AI3Hx ................... ................... ................... ....... 138


.30. ................... ..........__.__ ......


x<1.3 0. ........._.._._. ................... ..................1 26


x11.30. ................... .....129


x for UPd2AIJ)-Ix. ................... ................... .........., 139


1.09 and 1.30. ................... ................... 143


0.3 0, and 0.3 9), ................... ........._155


0.0 and 0.07.............................161














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


DOPING EXPERIMENTS ON MAGNETIC HEAVY FERMION
SUPERCONDUCTORS

By

Weonwoo Kim


August, 1995


Chairman:


Gregory R. Stewart


Major Department:


Physics


We present experimental results of non-Fermi liquid (NFL) behavior in UxTh~-x


Ru2Si2 and in Uo.9Mo.1Ni2Al3 (M


Y, Th, and Pr), and the hydrogen effects on UPd2Al3.


The objective of this work is to understand the origin of the NFL behavior and how

hydrogen changes the heavy fermion system.


In UxThi-xRu2Si2,


we have


observed


NFL


behavior


thermodynamic,


transport, and magnetic measurements for 0.07


x<0.17.


We report a temperature TA in


electrical resistivity p measurements which measures the onset of intersite correlations


between local magnetic moments.


The increase of p with T for 0.3 K


20K, the


approximately linear decrease of TA for 0.1


0.14, and the spin glass behavior in dec


Ixl









may be due to magnetic fluctuations at T


= 0 K or collective modes of excitations at low


temperatures rather than the single-site two channel Kondo effect (TCKE).


We have found another new system Uo.9Mo.0Ni2AI3 (M


= Th, Pr, and Y) which


exhibits the NFL behavior.


We observe a positive linear p with T forl.0 K


< 20 K in


Y-doped


samples


(less


wide


range


in T for


Pr-doped


sample).


susceptibility Xdc, T'l (Th and Pr doped) and In T (Y doped) dependence are observed as


a sign of NFL behavior.


The In T dependence of Cs/T as an NFL characteristic following


the destruction of the magnetic order as observed in C measurements, seemed to imply


NFL behavior may be due to


the proximity of magnetic


instability


where a


Kondo-compensated nonmagnetic state and


long range magnetic order are nearly


degenerate.

We have succeeded in doping UPd2Al3 with hydrogen by improving the activation


and poisoning of the parent samples.


In the normal state, the increase in both X(0) and


y(0) with hydrogen uptake can be interpreted as an enhancement of the effective mass


supported by the Sommerfeld free-electron behavior of these physical values


On the


other hand, magnetic correlations are proposed as a possible origin of the behavior in both


X(0) and y(0) based on the observed relations among 0 c.w.,


critical hydrogen concentration Cc.


X(0), and y(0) around the


The peak in X for UPd2Al3 seems to be due to the


short range magnetic correlations; we observe the shift of the peak to lower


T for more


hydrogen uptake and at higher magnetic fields for a given hydrogen concentration.


In the















CHAPTER 1
INTRODUCTION


In this chapter,


we will summarize heavy fermion systems based on not only a


coupling constant between local moment and conduction electron at each lattice site, but

also essential topics in this area while keeping in mind the magnetic and superconducting


ground states.


Our motivation to study non-Fermi liquid behavior by alloying experiments


and to perform hydrogen doping experiments on these HFS will be given below.


describe experimental techniques used to get our data in our laboratory.


We also


We are going to


explain


separately


experimental


techniques


apparatus


hydrogen


doping


experiments in chapter 4.


Overview of Heavy Fermion Systems


Heavy


fermion


systems


(HFS),


which


are usually


intermetallic


compounds


certain lanthanides or rare-earth elements (notably Ce 4f one-electron and Yb 4f one-hole)

and actinides (notably U, Pu, and Np), have attracted physicists for more than a decade


because of their fascinating physical properties [Stewart, 1984; Lee et al.,


1986; Ott and


Fisk,


1987;


Fulde


et al.,


1988;


Grewe


Steglich,


1991].


highly


correlated


electronic systems of HFS can be regarded as a lattice off-ions being embedded in a Fermi









Although both the Kondo effect


[Kondo,


1964]


occurnng at


each lattice site and the


strong low-lying magnetic fluctuations seem to play a central role, there is no accepted


microscopic


theory


either


mass


renormalization


or the


pairing


mechanism.


However, we are briefly going to describe the main topics in HFS so that we may reduce

any conceptual gap to understand following chapters.


1.1.1


Classification ofHeaw Fermion Systems


Each of these HFS can be characterized by a Kondo-lattice temperature, T (this

temperature corresponds to the Kondo temperature TK for an isolated Kondo impurity).


For T


, f-ions carry local f-electron-induced magnetic moments which are coupled


very weakly to the conduction electrons.


, however, this coupling becomes


strong enough to give rise to a nonmagnetic low temperature state [Grewe and Steglich,

1991].


ground


states


HFS


lanthanide


depend


heavily


on the


competition between the magnetic intersite interaction, i.e., the indirect Ruderman-Kittel-


Kasuya-Yoshida


(RKKY)


exchange


interaction,


on-site


Kondo


interaction


reducing


the local


magnetic moments


[Doniach,


1977].


If we use


the dimensionless


coupling constant, g = NF


we can express two energies (kI =-


1) as T*


~ exp{-1/g)


TpxxY ~g2


. NF is the conduction-band density of states at the Fermi energy EF, and J


is the exchange coupling constant between the local f-spin and the conduction-electron


S_1L


rr.f A


/lr f nArn ,*nn+ *ninrn ran*A n n4 j. 4k al ,1 1a a..j^ an at ap a1 1


~nin nnTn r nn Fniini~nn nnnn+nn,









the more localized 4f electrons.


Thus, two adjacent 5f configurations (5f2 and 5f ) may


be nearly degenerate, and one single parameter g may not be sufficient to classify the

various ground states of the HFS with 5f-ions.

In Figure 1-1, we show a schematic classification of HFS and intermediate valence


(IV) compounds with 4f-ions.


rare-earth magnetism, and for


1, there is a stable moment regime of an ordinary


g > 1 there is a charge fluctuation between the f-shell and


the conduction


band


exhibiting a nonmagnetic


Fermi-liquid


ground


state.


HFS


exist


between


above


regimes,


for 0


< 1.


4f heavy-fermion


compounds,


valence fluctuations are usually ignored so that local spin fluctuations,


which


have essentially the same origin as in dilute Kondo alloys,


exist for the weaker local


exchange


coupling.


Thus,


HFS


characterize


both


'magnetic


limit'


compounds and the


'concentrated limit'


of the Kondo alloys.


There also exists a critical value


where the on-site and the intersite interactions


have the same strength [Steglich et al.,


1994].


1, the strong hybridization


between 4f and conduction electrons fully compensates the local f-derived moments well


below T* resulting in Fermi liquid behavior.


However, these Fermi liquids appear to be


unstable against AFM and/or superconducting phase transitions at TN/Tc


<< T*


Also


there is a very interesting regime around


g=gc,


i.e., at the magnetic instability,


where it


seems that non-Fermi liquid (NFL) behavior takes place [Kim J.S. et al., 1992; Kim W.W.


et al., 1993; Andraka and Stewart,


1993; LOhneysen et al.,


1994; Steglich et al.,


1994].


g <<



















STABLE-
MOMENT
REGIME


<<1)


HEAVY


-FERMION


heavy fermior


'local


moment I
magnet'"


(LMM)


e.g,


Ce Al2!


metal
LA-


e.g.


I C


"band
e.g., Ce
supercc


e.g.


,Ce


"NFL


EGIME (g<1) INTERMEDIATE
1 metal VALENCE REGIME
(g >1)
Fermi liquid
eCu6 e.g., CePd3
magnet"
'(Cu,Ni)2 Ge2
,nductor
Cu2 Si2 "Kondo insulator"
e.g.,Ce3 Pt3Bi1


1 g=NFIJI


RE











1.1.2


Mass Enhancement


The origin of heavy quasiparticles may be due to either a single electron interaction

or a many body resonance (we already know that we can not simply apply the theory of a

single electron interaction, because we can not understand the development of the large


effective


mass


quasiparticles


at low


temperatures


simply


based


on the


single


electron

localized


theory). T

f-electrons


he single electron


light


interaction


conduction


(itinerant)


coupling

electrons.


between

This


initially well


coupling


hybridization makes the localized f-electrons delocalized, and the f-electrons contribute to


the Fermi level with a low


Fermi velocity.


A large part


of the mass enhancement is


obtained by local magnetic fluctuations reminiscent of the single impurity Kondo effect.

This large effective mass is observed by a large coefficient Yo of the electronic specific heat


forT


-> 0 K, a large 'Pauli-like'


spin susceptibility Xo, and a large coefficient


from the


Fermi liquid behavior in resistivity, i.e., p = CT2 (C


~ Yo2).


Despite these large physical


values, the Sommerfeld-Wilson ratio X/'Yo with proper normalization is of the same order

as in simple metals.


same


time,


there


exists


an intersite


magnetic


coupling


which


comparable in magnitude to the local Kondo temperature TK, between magnetic moments


induced by the partially filled f-electron shells.


One of the consequences of this interplay is


that heavy fermion compounds exist near magnetic instability, i.e., around the transition









1.1.3 Superconductivity


possible


origin


of the


superconducting


mechanism


HFS


can be


a large


magnetic


fluctuating


medium


which


furnishes


an attractive


potential


form


quasiparticle pairs.


Since the quasiparticles exist for


< TF/10O,


in the Fermi


liquid region, such a magnetic fluctuating medium observed in x(q, o) can be the origin of


the SC.


Here,


the parity


of the pairing depends on the nature of the magnetic spin


fluctuations, e.g.,


ferromagnetic spin fluctuations (for odd parity) and antiferromagnetic


spin fluctuations (for even parity).


Thus,


we can change the pairing strength by


changing the hydrostatic pressure.


For instance, the Grainesien parameter U is given by


(1.1)


where


V is a volume.


Under pressure,


TF increases causing a decrease of the pairing


strength which gives rise to a decrease of Tc (C


strength of the quasiparticles pairing).


'-~


, where is related to the


Another possibility is to apply a magnetic field to


change the pairing potential, e.g.,


UBel3 [Brison et al.


1988].


1.1.4


Magnetism


About the origin of magnetism in HFS, it seems to be basically similar to a general


magnetism which has been constructed on the Heisenberg model [Heisenberg,


1928] and


the Stoner model [Stoner,


1938].


The first model describes magnetism in terms of local


magnetic moments, and the other one describes magnetism in terms of itinerant electrons


"r12


-a~ogT, / dlog V






7


There has been a proposed picture [Doniach, 1977; Nozi&res, 1985] for a magnetic

state with well localized moments and only moderate enhancement of y, i.e., of order 0.1


J K-2mole'


as in CeAI2.


Starting from band electrons and ionic f-states, there is an end to


the quasiparticle renormalization when the spin order of renormalized moments occurs.


corresponding


RKKY


interactions


energy


scale


TpjcYy


are mediated


renormalized band electrons.


From then on, spin-flip scattering is frozen out and the band


electrons move in the fixed modulated exchange field provided by the magnetic moments.


For instance, TRKKY exceeds TM


by more than an order of magnitude for CeAI2 [Steglich


et al.,


1979b] (the long range magnetic ordering temperature,


TM, is usually responsible


for an antiferromagnetic ordering, but it can be a ferromagnetic ordering one, e.g., CeCu2


[Gratz


et al.,


1985]).


intermediate


y-values


above


point


moderate


renormalization for band electrons well above the Kondo lattice temperature T < TM


TRKKy.


Yo is usually lower due to the reduced density of excitations in the magnetically


ordered phase.


The ordered moments are correspondingly smaller than the free-ion values


in the proper CEF ground state.


Even though the density of states (DOS) near the Fermi


energy EF changes due to an exchange-split incipient Abrikosov-Suhl resonance (ASR)


[Abrikosov,

Fermi surface


1965; Suhl,


1965], no electronic excitation gap develops anywhere on the


In general, the specific heat well below TN follows C


= yT + 3T3 with a


cubic magnon contribution.


the other


hand,


the quasiparticle band


theory


can describe


heavy fermion









moments, have been transferred to the itinerant heavy quasiparticles.


Thus, this system


shows a strongly reduced magnetic moment and a large y-value in the electronic specific


heat.


In particular, a spin density wave (SDW) instability [Doniach,


1987] may open an


electronic excitation gap on parts of the Fermi surface, a situation strongly favored by the


nesting properties.


In that case, the density of quasiparticle excitations is reduced at low


temperatures and an exponential decrease of y(T) can take place below


for Ut-


xThxPt3 [Ramirez et al.


1986; Stewart et al.


1986].


However, most of HFS are typically in a crossover regime between the class of


local moment systems and of itinerant systems.


Also,


when both superconducting and


antiferromagnetic ground states coexist, there is a larger coupling between magnetic and

superconducting order parameters in the local moment system than in the itinerant system

because of the its larger ordered moment.


Before we close this section,


we would like to classify a large variety of ground


states in the HFS based on superconductivity (SC) and magnetism.


The first group has a


nonmagnetic ground state, i.e.,


paramagnetism without SC,


CeCu6 [Stewart et a.,


1984b].

1985].


The second group has a magnetic ground state without SC,

The third group has an SC ground state without magnetism,


e.g.,

e.g.,


UCu5 [Ott et al.,

UBel3 [Ott et al.,


1984].


The fourth group has SC and magnetism in its ground state, and we can divide the


fourth group into two subgroups:


UPd2Al3 [Geibel et al.,


One is the system where the two ground states coexist,


1991b], the other is the system where the two ground states










Motivation


We can change external physical parameters such as temperature and pressure to


study a system more thoroughly.


Alloying experiments with different elements (which


have different electronic configurations, atomic sizes, and local magnetic moments) are

also a very interesting and effective method in gaining more understanding and insight into


condensed matter physics.


In principle, alloying


can vary the band structure and the


chemical potential causing changes of DOS at EF.


understand HFS,


It is crucial to vary the DOS at EF to


because the DOS at EF in HFS (the DOS is proportional to y from


specific


measurements)


one of the


most


important


topics


to be


understood.


Alloying also changes the lattice constants inducing a variation in hybridization.


It causes


a change in the interaction mechanism, and sometimes even induces a phase transition.

Since NFL behavior studies have been a newly developing field [Seaman et al.,

1991; Andraka and Tsvelik, 1991], we have focused on the magnetic HF superconductors

(which would have a relatively small ordered moment below antiferromagnetic transition)

out of the family of HFS to find new NFL systems, because as we described briefly in


section 1.1.1, the magnetic instability can be the origin of NFL behavior.


We will discuss


this in detail in chapter 3.

As we all agree, one of the unavoidable results of alloying experiments is to disturb


the occupation of the sublattice.


Physicists have an idea to overcome such a disadvantage


iitnIrmr. no


rnfto+r +bo


1 1 l nii l


A~ .a..


''V tttIIII*It**rI IY;I *ns**uz; **tnl* **f **'.:n E1u\1tt **rnEIfl *lll IIRtI**tI u*IuI** II. r*.*III uI-r~nlt


(mn 44 4J


~~*1 ft


mnCC\nrl


I,,~tb


nl nm Anlr.






10

system unchanged, even at a relatively high doping concentration, (which is an essential

point for a systematic study) because hydrogen atoms can go into the lattice interstitially

as a proton (which is in size several orders smaller than the atom) by donating its electron


to the Fermi level.


Even though hydrogen atoms get extra electrons from the Fermi level


in some cases, the effect on the crystalline structure is still smaller than other usual doping

elements.

However, there are also very difficult problems, which we will describe in detail in

section 4.4, that we need to overcome in order to enjoy the advantages mentioned above.

After we studied several hydrided systems (usually for hydrogen storage), the hexagonal

crystalline structure of LaNi5 (one of most studied systems and a possible candidate for


hydrogen


storage)


stimulated


our research


on the


HFS


hydrides.


Hydrogen


doping


experiments can not only give more information about the parent system, but also induce a

new ground state in the hydrided system as will be discussed in chapter 4.


1.3 Experimental Techniques


We are going to describe in this section briefly how we made our samples and


what experimental techniques we used.


There is already a very detailed description about


this in J.S. Kim'


dissertation [1992].


However,


we will describe in detail how we made


our hydrided samples and what apparatus we used in the hydriding system in sections 4.3

and 4.4.









1.3.1


Sample Preparation


synthesized


each


polycrystalline


sample


stoichiometric


amounts


elements within 0.3


% accuracy using a Bihler arc melter.


Each sample was melted


several times followed by flipping each time to increase the homogeneity of the sample.


We especially have kept some air-sensitive elements, e.g


., some transition elements and all


lanthanides, in sealed Pyrex tubes to have the highest quality samples.


a pressure casting technique [Crow and Sweedler,


We sometimes used


1973] in the arc melter to make some


resistivity samples


If necessary,


we sealed the samples in evacuated quartz tubes and


annealed them in a temperature-controlled furnace for a few days or a few weeks.


we characterized the samples using a Philips X-ray diffractometer to


Then,


see if there is any


second phase and to determine the lattice constants.


Measurement Techniaues


Measurements of resistivity and specific heat down


performed in a


to about


4He cryostat by pumping the dewar or an inner


temperature measurements for resistivity,


specific heat,


K have been


4He pot.


Even lower


ac magnetic susceptibility


were done by using 3He cryostat with a movable charcoal rod, which absorbs and releases


3He depending on the temperature and pressure (boiling point of 3He is 3


.2 Kat


bar).


For the probe used, refer to J.S.


dissertation [1992] for a schematic drawing.


necessary,


magnetic


fields


T for


these


experiments


were


used


thermndvnamir meaRuhirementq


Kim's









1.3.2.1


Specific heat


Specific heat measurements can be classified into two groups, i.e., adiabatic and


diabetic


methods,


depending


on the


isolation


system


from


its surroundings.


Adiabatic methods attempt to isolate the sample system completely from heat sources or

heat leaks so that a sample with an internal heat source, e.g., radioactive material is not


suitable for this method.


On the other hand, diabetic methods in principle accept the fact


that no sample can be completely isolated from its environment.


The thermal conductance


of the main links between the sample system and its surroundings (or heat reservoir) is

measured and used to get the specific heat, and this is in contrast to a heat switch used in


adiabatic methods in order to stop heat flowing.


Thus,


we may regard adiabatic methods


as special cases of more general diabetic methods,


because we can regard the thermal


conductance in adiabatic methods as


becoming


zero.


Diabatic methods


improve


precision of specific heat measurements while they lose accuracy relative to the adiabatic

methods.


We used a thermal relaxation (or time constant) method [Bachmann et al.


Stewart, 1983] which is one of the diabetic methods.


small sample calorimetry in HFS.


1972;


This method is especially good for


In HFS, samples can be as small as 1 mg because of the


large specific heat at low temperatures resulting in a much smaller ratio of the addenda

contribution to the total specific heat than low y-value samples.

As we show in Figures 1-2 and 1-3, after we are in equilibrium temperature To, we
























1 +/11


K=-
AT







o


C Total


C Sample+ C Mdenda












Solder


u-Cu W

3/8" Sc

Sample


Copper


Ring


Epoxy
Pad


Evaporated
7% Ti-Cr Heater


H31LV


Silver


Epoxy


Au-Cu


Wires


Ge Chip


3/8" Sapphire


Thermormeter






15



the temperature of sample and platform decays exponentially with a time constant Ti (a

measure of the time for the sample and platform to reach thermal equilibrium) which is


inversely proportional to the conductance of the wire links.


We can express the relation as


follow:


+ ATexp(-t/ t,


(1.2)


The conductance K(T) of the wire links should be measured and calibrated


vs. temperature


for the later specific heat measurements using a relation K


= P/AT.


We use Ko, the K-


value at To + AT/2, to get the specific heat C


the addenda contributions.


= Ko-'i at To + AT/2 followed by subtracting


Here, the thermal conductance of sample and platform should


be much larger than that of the wire links.


Otherwise, there should be some corrections


due to the so-called x2 effect [Bachmann et al., 1972] to get a correct value of the specific

heat.


We would like to describe briefly how to measure specific heat using Figure


We set the frequency of an ac excitation


in the lock-in amplifier (LIA) around fo


= 2700


Hz such that it is not the multiple of 60 Hz to avoid any unwanted noise.


This frequency


setup in the LIA increases the signal-to-noise ratio by filtering out frequencies other than


fo with a width of frequencies.


We then set up the phase to get the maximum sensitivity of


the platform-thermometer resistance and thereby a best time-constant value.


We achieve


this by firstly finding a phase, where the LIA voltmeter shows no response for varying the


a C S -


n




































Wheatstone
Bridge 1


Platform Platform Block Block


thermometer


Heater


Heater


Thermometer











The block temperature is controlled by a block heater and measured by a block


thermometer at To.


We apply power P increasing the temperature of the platform-sample


assembly to


+ AT (AT/T,


The resistance of the platform thermometer is


measure by an ac


Wheatstone bridge, and the resistance value is used to get the new


platform


temperature


based


on the


precalibrated


data.


After


we are at


a stable


temperature, we turn off the platform heater.


We get the time constant tr by digitizing the


signal from the Wheatstone bridge using an analog-digital converter and subsequent signal


average.


With the K-value at this temperature, we have the specific heat after correcting


addenda


contribution.


Overall


absolute


accuracy


our measurements


approximately within


detailed


descriptions,


see the J.


Kim'


dissertation


[1992].


used


Ge-thermometer


block


thermometer,


a home


made


evaporated Ge-alloy was used for ac calorimetry to the platform thermometry (see J.


Kim's


dissertation [1992] for detailed process).


When we measured the specific heat in


magnetic fields up to 14 T (we can go up to 16 T if we lower the temperature of magnet


below


K by pumping the X-plate), we used Speer carbon-resistor thermometer for the


block-temperature measurements down to 0.3 K.


We calibrated it in zero magnetic field


with the block Ge-thermometer, then did a field correction according to Naughton et al.


[1983]


We also used a capacitive thermometer above 1 K as a thermometer in magnetic


'* 4 4I b


r -r rr+


---r r


L .I I II nnri in .t






18

the platform thermometer based on the precalibrated thermometers in magnetic field, and

subsequently corrections to the thermal conductance with the help of these two (block and

platform) field-calibrated thermometers in order to get the right specific heat were made.

1.3.2.2 Magnetic Measurements

For the ac magnetic susceptibility, we used a low frequency (around 86 Hz) mutual


inductance technique using home-made primary (superconducting wire) and


secondary


(Cu wire) coils [J.S. Kim,


1992].


After we put a specimen into the primary coil,


applied an ac voltage using a lock-in amplifier (EG & G Model 124 A) to the coil.


signal


detected by the secondary coil is amplified


by the lock-in and


gives a


voltage


difference due to the magnetic flux change in time, d

opposite


directions


there


electromagnetic


force


unintended


fluctuations of the applied voltage or field.).


This voltage difference is proportional to the


magnetization, and therefore the magnetic susceptibility [Signore,


1995].


We used this


technique to measure the superconducting transition temperatures of our HFS for 0.3 K


For dc magnetic susceptibility,


device (SQUID) from Quantum Design for 1.7 K


T in two opposite directions.


we used a superconducting quantum interference


400 K in magnetic fields up to


The basic idea of the dc measurement [Rose-innes and


Rhoderick, 1980] is similar to that of the ac method.


We move the specimen in the steady


magnetic field


applied


a dc


powered


solenoid


(corresponding to


the primary









the secondary coil detects the signal with a high sensitivity due to the SQUID.


We also


measured magnetization vs. magnetic field at a given temperature.


1.3.2.3


Electrical Resistivity


used


a standard


probe


technique


measure


resistance


specimen for 0.3 K


<70 K.


If necessary, we measured the dimension of the specimen


to get resistivity.


All measurements are automatically performed with computer controlled


equipment and data collection [J.S. Kim, 1992].















CHAPTER


REVIEW OF THEORY


We are going to review briefly the basic concepts and the physical quantities of the

Fermi liquid (FL) theory as a function of temperature, because it explains relatively well


the phenomena in heavy fermion systems.


However, unusual behavior,


which can not be


understood by the FL theory, has been observed in recent years.


There have been very


extensive theoretical developments both in a microscopic, e.g., the exact Bethe ansatz and

conformal field theory, and in a phenomenological theory to understand the origin of the


new behavior.


We will concentrate on the physical quantities for which unusual behavior


has been observed in, e.g., thermodynamics, transport, and magnetic susceptibility.


There


is no conclusive theory explaining all of the new phenomena.


2.1 Fermi Liquid Theory


The model of non-interacting fermions or a Fermi gas has worked relatively well in


a system of Fermi particles,


even though the interaction among the fermions is rather


strong.


Electrons in a metal serve as a classic example.


The reason why it does so well is


that the scattering rate of electrons is dramatically reduced because of the Pauli exclusion

' : 1,









assume


a non-interacting


quasiparticle


model


as a


good


approximation and


quasiparticles obey the exclusion principle.


He proposed a semiphenomenological method


[Landau,


1956].


He assumed firstly the interaction between the particles is adiabatically


turned on such that the Fermi gas gradually transits into the excited Fermi gas resulting in


a Fermi liquid.


Here, there is a one-to-one correspondence between the eigenstates of the


Fermi liquid and those of the non-interacting Fermi gas.


Secondly, he assumed that the


temperature is much lower than the Fermi energy, so excitations are confined to with an


energy of T (kB


= 1) near the Fermi surface, and those excitations have a sufficiently long


relaxation


to be


defined.


excitations


Fermi


are called


Like the bare particles, they obey Fermi statistics and have momentum


(or crystal momentum) as a good quantum number.


be considered as


However, since the quasiparticles can


particles in a self-consistent field, they have a renormalized effective


mass, and the energy of the whole system is no longer the same as the sum of the energy


of each particle in isolation.


Instead, the energy is a functional of the distribution function


n(k).


If the distribution function is changed by an infinitesimal quantity 6n(k),


Sn(k)


=n(k)


(2.1)


where no(k) is the distribution function of quasiparticles in the ground state, then the total

energy of the system changes by an amount


-x


ek6n(k),


(2.2)


quasiparticles.


- n,(k),


~









f(k, k' )n(k'),


(2.3)


where


jfk,k') is the interaction energy of the quasiparticles and of order 1/V,


of the system.


From Eqs.


the volume


(2.2) and (2.3), we have


-z


f(k,k'


)n(k )6n(k').


(2.4)


k k'


If the system is isotropic for k and k' on the Fermi surface, f"a)(k,k') depends only on the


angle


0 between


directions


k and


Here


f '(k,k')


f '(k,k')


are the


antisymmetric and symmetric parts of the quasiparticle interactions, respectively


They


can be expanded in a series of Legendre polynomials as follows:

00


f*'(k,k'


-z


f$(&)


P,(cosO)


where is completely determined by the set of coefficients /" and


a. It is convenient to


express f in reduced units by setting


N(EF) .f "'


Fi a)


, where N(EF) is the density of


states at the Fermi level.


After using


elementary thermodynamics,


we can relate the


physical quantities obtained from experiments to the Landau parameters Fi '(9) and F '(0)


as follows [Nozi&res, 1963; Pines and Nozieres,


989]:


Sx2k, N(EF)
3V


N(E,)


(2.6)


VK Fm


t2k2
= k (1+Fo


(2.8)


n=E; +


O~Mlb\l
E ,vrr~r~lT






23


where V is the volume of the system, C, is the specific heat, m is the bare mass of a Fermi


particle, m*


is the effective mass of


quasiparticle,


S is the sound


velocity.


electrical resistivity due to the impurity at low temperatures can be derived by applying a

Fermi liquid approach to the Anderson model for degenerate orbitals assuming electron-


hole symmetry near the Fermi level, and it is proportional to T

and Zawadowski, 1978].

Landau's theory was constructed for a neurtal Fermi

long range interactions. The only neutral Fermi liquid foun


[Yoshimori, 1976; Mihily


gas in which there are no

d in nature is the quantum


liquid


it becomes


degenerate


temperatures.


If there


interaction between the 3He atoms, the Fermi temperature or the degeneracy temperature

would be given by


Eo
k


ht2k'
2mk,


~5K.


(2.10)


with m


as a linear


x 1024g and, from the particle density c, kF


T dependence in specific heat and


Such quantum behavior


T independent magnetic susceptibility are


experimentally found at about 0.05 K. This reduct

comes from the interaction between the 3He atoms,


ion in TF by two orders of magnitude


the enhancement in the effective


mass of the quasiparticles.

Now let us consider the charged Fermi liquid rather than the neutral Fermi liquid.

Let us consider a system of noninteracting electrons which move in the periodic potential


was


= 3 X2 crln









where Uik has the periodicity of the lattice.


are good quantum numbers.


Both j, the band index, and k, a wave vector,


When we take account of the Coulomb interaction between


electrons, we can again establish a one-to-one correspondence between the eigenstates of

the real system and those of the noninteracting system by using the adiabatic switching

procedure as discussed in the neutral Fermi liquid.

A Bloch wave possesses an energy esO, and a velocity on the Fermi surface is given


by vk


= V(eoj) which is different from the velocity of a free electron k/m.


After we turn


on the interaction adiabatically, the quasiparticles have an energy Ekj = dE/Sn(k). Ekj is

constant over the Fermi surface, and is equal to the chemical potential p. We can again


define at every point of the Fermi surface a velocity vk,


Now,


which will be different from v k.


we know that the difference between vk of interacting electrons and k/m of a free


electron


is due


to firstly,


influence


of the


periodic


lattice


on each


electron


secondly, the "many body"


effect arising from the Coulomb interaction.


Thus, Landau's


theory of a Fermi liquid as applied to a spatially homogeneous state is suitable in the case

of the Coulomb interaction between electrons [Silin, 1958].


Just as for the neutral Fermi liquid,


we can now


define an interaction energy


between quasiparticles Ak,k') as the second derivative of the energy with respect to n(k).

Since the Fermi surface of a metal is generally not isotropic (e.g., due to the anisotropy of

the crystalline lattice), Ek depends on the direction of k and fAk,k') depends on both k and


Also, the divergence offlk,k') due to, e.g.,


the inhomogeneity of the system or the









mteraction


between screened


quasiparticles,


quasiparticle


its associated


screening cloud [Pines and Nozieres, 1989].

However, the Fermi surface is almost spherical, as in the alkali metals for example,


if the system'


behavior is nearly isotropic.


Thus, we can introduce a crystalline mass or a


band mass me such that


where jk is the current carried by a quasiparticle with wave vector k, and me is different


from the bare electron mass m because of the periodic potential acting on the electron


The real quasiparticle effective


mass m* due to the quasiparticle interaction is


defined by


where vk is the velocity of a quasiparticle on the Fermi surface.


The relation between m*


and me is given by


(2.14)


= m(l +F I/3).


We can also express the spin susceptibility X, in terms of the paramagnetic susceptibility X,

due to the noninteracting free electron gas as follows:


m(1 + Fo


-. (2.1
)


Equation (2.15) is meaningful only when








Otherwise,


the long wavelength fluctuations of the magnetic moment become unstable


giving rise to a ferromagnetic correlation.

Phenomena that are not influenced by quasiparticle interactions can be described in


terms of a one electron model with renormalized energies.


The de Haas-Van Alphen


effect and the low frequency Hall-constant in a high magnetic field are examples.


On the


other hand, phenomena affected by the quasiparticle interaction f(k,k') can not be exactly


described by the one electron model.


Instead


, they can be expressed in terms of the


Landau parameters above.


Some properties of heavy electron systems (HFS),


the Pauli-like magnetic


susceptibility


linear


temperature


dependence


specific


temperatures can be explained by the Landau FL theory even if there are strong on-site


correlations at low temperatures for T


An analogy has been drawn between liquid


He and the HFS, and it seems that there is relatively good agreement with experiments.

The Landau Fermi liquid theory is likely to work well in metals as long as there is no

critical behavior such as a phase transition.


Before we finish this Section,


let us mention that there are some problems in


translating the 3He results directly to the HFS.


One of those [Lee et al.,


1986] is the lack


of Galilean invariance in the HFS


, so that the effective mass is not simply related to the


Landau parameter F,


s as shown in Eq.(2.


Furthermore, the Fermi liquid theory does


not consider the effects of spin-orbital coupling, crystal symmetry, and band structure.






27


2.2 Non-Fermi Liquid Theory


We define non-Fermi liquid (NFL) behavior as that deviating from Fermi liquid


results, e.g., a logarithmic divergence of C/T


at low temperatures instead of saturation.


One possible theory to explain the NFL behavior is the multichannel Kondo effect.


will discuss the multichannel Kondo effect mostly based on the exact Bethe ansatz solution


[Schlottmann and Sacramento, 1993].


Subsequently, we will summarize another proposed


phenomenological


theory,


which is


based


on the scenario


of magnetic


quantum fluc-


tuations at


0 K, to explain the NFL behavior.


Multichannel Kondo Effect


The n-channel Kondo model for an impurity spin S and an integer n-number of

orbital conduction electron channels is given by Nozi&res and Blandin [1980]


-z


Ea +
kkmkina


S .mak ,o ac'mo',.


(2.17)


k,k ,m,o,o


where S is the spin operator describing the magnetic impurity, J is the antiferromagnetic

coupling constant, a are the Pauli matrices, and m labels the orbital channels.

The different orbital channels are strongly correlated close to the impurity and

form an orbital singlet; i.e., the spins of the conduction electrons at the impurity site are


glued together to form a total spin n/2 [Nozieres and Blandin,


1980; Andrei and Destri,


1984;


Tsvelik and Wiegmann,


1984].


In general, three qualitatively different situations


/%lM Ori ouh twn 4Kif* +10 f0 ontn nl ,lmnllno tn an k*mn .i o ntnn









Ifn =


the number of conduction electron channels is exactly sufficient to


compensate


impurity


a singlet


giving rise to


Fermi


liquid


behavior.


Classic examples are FeCu, FeAg, and CrCu.


< 2S, the impurity spin is only partially compensated (undercompensated


spin), because there are not enough conduction electron channels to yield a singlet ground


state.


An effective degeneracy of {(2S+1-n)


remains at low temperatures (and in zero


field).


This case may describe the integer valent limit of impurities with two magnetic


configurations like Tm.


>2S,


the impurity is said to be overcompensated. A critical behavior is


obtained as the temperature and the external field tend to zero.


The quadrupolar Kondo


effect [Cox, 1987a] is one possible realization of this case.

2.2.1.1 Compensated Impurity Spin


The basic model


describing the interaction


of a transition metal


(or magnetic)


impurity with a metallic host is the orbitally degenerate Anderson model:


where


++ d
k kma kma +d


mcid,


(2.18)


SrVk (dockmo + ckd. )
kma


cbna (CkAo) creates (annihilates) a conduction electron with momentum k=lkl in the


partial wave 1 =


2 with z-component m (Iml


< 1) and spin -,


and d


m, (dm,,) creates


(annihilates) an d-electron with quantum numbers m and


a, Ek is the conduction-state


-z
king


Smnc' m+o'
ma~aToa,,o









crystalline electric field (CEF) quenches the orbital angular momentum.


Third, the rather


large hybridization width of the 3d levels smears out the energy splitting of the ionic term.


Lastly, the direct orbital exchange,


which leads to an orbital singlet, is expected to occur


TK [Okada and Yosida, 1973].


This model can also be applied to rare earth (4f) or actinide (5f) impurities.


spatial extension of the wave function is reduced in such cases:


decreases the magnitude of the hybridization Vk.


low temperatures


Fermi


liquid


properties can


extracted


resulting in the singlet ground state,


where the coefficient y of the linear


T term in the


specific heat can be obtained via the Sommerfeld expansion as follows:


(2.19)


(n+ 2)TK


and the zero magnetic field susceptibility is given by


(2.20)


The Wilson ratio for the impurity is given by


432)
3


X,=


2(n+


-), (2.21)


which is same as (Ax/x)/(AC/C) [Nozieres and Blandin, 1980],


where AX and AC are the


contribution of impurities in the susceptibility and specific heat, respectively.


As we


Eq. (2.21) reduces to the Wilson ratio of the ordinary Kondo problem for n = 1. The


< 5f


2n:T,









liquid approach assuming electron-hole symmetry near the Fermi level [Yoshimori,

Mihaly and Zawadowski, 1978] as follows:


1976;


Pimp


-Poll


1 5;
8 (n+


itT


2)TK


Thus,


we see the T independent specific heat divided by temperature and susceptibility


along with T


2 dependence of resistivity at low Tin the compensated impurity spin.


2.2.1.2 Undercompensated Impurity Spin


Let us compare the compensated case, n


= 1 and S


1/2, with the case n


1 and


= 3/2 (all cases with S


> n/2 are qualitatively the same).


The specific heat as a function


of temperature is shown in Figure


. For spin S


= 1/2


and n


see Figure


2-la, the


height of the peak grows with field and asymptotically approaches the value of a free spin


Schottky anomaly.


For S


<< TK, e.g.,


= 0.01


TK in Figure


-1 b, the specific


heat has two independent peaks; the peak at lower T corresponds to the Zeeman splitting

of the ground multiple and the one at higher Tto the Kondo screening.


For S


= 1/2 and n


, the susceptibility has a maximum at low T due to the singlet


ground state in H

free spin behavior.


<< TK.

For 8


On the other hand, its maximum at about H


*1
I


and H


- T is reminiscent of


= 0, the Curie law as a straight line is shown in


Figure


However there is a smooth change in the Curie constant due to the change of


the effective spin from S at high


at low


The magnetic field lifts the


degeneracy at low


T and reduce the susceptibility to a finite value resulting from the









2.2.1.3 Overcompensated Impurity Spin

Since there are more conduction electron channels to compensate the impurity


spin,


the remaining conduction electron spin of (n-2S)


is delocalized giving rise to a


critical behavior.


The magnetic susceptibility in small field, H


<~c 1k,


diverges with a


power law given by


Wiegmann and


Tsvelik


[1983] and


Sacramento and


Schlottmann


[1991a]


-1+2/n)


n>2,




(2.23)


For n


and S


the susceptibility diverges with a logarithmic dependence on the


field [Desgranges,


1985].


Note that the critical exponent in Eq.


) only depends on


the number of channels, but not on the spin.


The entropy,


s, of the impurity in H


= 0and


= 0 is given by Tsvelik [1985], Desgranges [1985],


and Sacramento and Schlottmann


[1991b]


= 0,H


sin[7t(2S+1) / (n + 2)1


(2.24)


sinrx t/ + 2)]


In the presence of a magnetic field, the ground state is a singlet giving the corresponding


entropy equal to zero.


At high temperature the impurity spin behaves like a free spin in a


magnetic field.

At low temperatures, the zero field susceptibility X(7) and the specific heat divided


temperature C(T)/T


diverge


critical


behavior


given


Schlottmann


[1991c],


Ii'



















0.35
0.30
0.25
0.20


0.10


0.jQ 3


ojIT


10-2 10-1 100 101 102


/ TK


10'2 10-I 100 101












































0"3 10.2 10 "' 10 10 t 102


T/TK



























1500



1000
H


0.15 0.30 0.45
X (T=O)


I0~2 UN 1


o10t 10o 101 102


Figure 2-3


(a) Entropy, (b) specific heat, and (c) specific heat divided by temperature as


n fi r,.*;, fa TrIT.. ; rannctant mr nnansth fiGAd fCnr .V


= 1/9 and n = 7


The. ntrnnv ij ningiilar









For n


and S


(two channel Kondo model, see Figure 2-3), the critical exponent


vanishes and again a logarithmic dependence on the temperature arises [Tsvelik,


1985;


Desgranges, 1985; Sacramento and Schlottmann, 1989b, 1990, 1991a].


In Figure 2-3a, we


see that in zero field the entropy changes smoothly between the


value {In


}/2 given by Eq.


(2.24) for low T and the asymptotic free spin entropy,


high T. The results for the entropy for n


_ 2 is qualitatively different from the traditional


Kondo problem (n


= 1), where there is only one energy scale TK,


because as n increases


Kondo


screening


is less


pronounced


another


dependent


energy


scale


TK(HITK)' +2


exists.


The specific heat as a function of T/TK in constant field for n


= 2 and S


= 1/2


shown in Figure 2-3b, and these curves


just correspond to the slope, C,


= T(asl/T),, of


those in Figure 2-3a.


The H


= 0 specific heat curve shows the Kondo resonance.


small magnetic field and at low T, another peak develops due to the second energy scale

and the two peaks merge into one characterized by a Schottky anomaly at intermediate


fields H


-1k.


For H


0 the specific heat at low


T is proportional to


T and can be


characterized by a coefficient y.


In Figure 2-3c, we see that the value y for H


= 0 does not


saturate as T


-+ 0 K, but it becomes finite for H


Also a maximum in C/T


arises for


larger fields as a consequence of the developing


Schottky anomaly.


In Figure


2-3e,


we see


the logarithmic divergence of X in T for H


= 0 and n


and X decreases with field but


has a maximum which correlates with the low T peak of the specific heat.









of freedom of the U 5f-shell in the heavy fermion compound UBet3.


It can explain the


a magnetic


dependence


electronic


specific


magnetic


susceptibility, but cannot explain the strong negative magnetoresistivity.


The main assumptions of the model are the following:


configuration of the U ions is 5f


Firstly, the stable 5f-shell


and this leads to a ground multiple with total angular


momentum J


= 4 according to Hund's


Secondly, the CEF splits the J


= 4 multiple


into a F


1 singlet, 3 doublet,


and f4 and F


triplets.


The 13 non-Kramers doublet is


assumed


to be the ground


state.


Thirdly,


the excited


4 triplet


explains a


Schottky


anomaly in the specific heat, and the coupling to the F3 via the magnetic field gives rise to

the van Vleck susceptibility.


Kondo


effect


is incorporated


hybridizing


electrons


conduction states and by considering virtual excitations into the 5f


configuration with a


= 5/2 ground multiple,


cubic symmetry.


which is split into a ground state F


7 double and Fs quartet in


A nonvanishing matrix element between the F3 states of 5f


and the F


states of the 5f


can be obtained via the J


= 5/2 partial wave,


in particular with the


conduction electron states having Fs symmetry


. By projecting the 5f


states out


obtains the following exchange interaction,


'(0)1,


(2.26)


where J


>0,


S are the pseudospin operators for S


/2 of the electric quadrupole


JS 10,(0)+0,









magnetic


Kondo


Hamiltonian


corresponds


tetragonal


(quadrupolar) splitting related to a deformation of the cubic symmetry.


The magnetization


is the electric quadrupolar moment, thus the magnetic susceptibility represents actually the


electric quadrupolar susceptibility [Cox, 1987a, 1988a, and 1988b].


Also we should keep


in mind that even if the concentration of U ions is very small, they are going to interfere


with each other at low


behavior.


T due to a divergent correlation length associated with a critical


This interference competes with the local lattice distortion induced by a single


quadrupolar Kondo ion.


At low T(T


TK), the resistance is given by Ludwig and Affleck [1991]


R(T) /R(O)


-(T/ TKT)"2


(2.27)


The specific heat divided by temperature, C/T, and the electric quadrupolar susceptibility


Xq are proportional to -In T.


However, the proportionality coefficient of Xq is usually very


small so that we do not see the effect.


Instead,


we do see the van


Vleck magnetic


susceptibility which is not due to the ground state, but due to the coupling between the


ground state and the excited CEF level via the magnetic field.


=Xvv


It is given by


(2.28)


where Xvv


is the


T-independent van


Vleck magnetic susceptibility.


The coefficient r is


inversely


proportional


to the


CEF


splitting.


now


summanze


basic


physical


quantities in Table


2.1 as a function of temperature between the two channel spin 1/2 (or


magnetic dipole) Kondo effect and the two channel electric quadrupole (pseudospin 1


- rl(Tl T,)"2]









Possible examples of quadrupolar Kondo effect systems are UxY


.-xPd3 for


= 0.2


[Seaman et al.


1991], UxThl-xRu2Si2 for x


< 0.07 [Amitsuka et al.


1993


Amitsuka and


Sakakibara, 1994], and Ceo.lLao.CCu2.2Si2 [Andraka, 1994c].


Table


. The physical quantities as a function of temperature of the two channel spin


1/2 Kondo effect and the two channel electric quadrupole (pseudospin 1/2) Kondo effect.
Two Channel Spin Two Channel Electric
1/2 Kondo Effect Quadrupole Kondo Effect
p -TT -T
C/T In T In T

Xq a ln T ,a << 1
Xn, In T 1 T 2n 11 ~ Xvv ; for nonmagnetic ground state.
In T ; for a magnetic ground state.


2.2.2 Phenomenological Theory of a Critical Point at T


= 0 K with a Scaling Analysis


Even though there are several experimental results [Andraka and Stewart,


Lohneysen et al.


1994] which reveal a magnetic nature in the vicinity of a critical point at


= 0 K as an origin of the NFL behavior, there is no microscopic theory explaining the


NFL behavior.


However, recently there was a report [Tsvelik and Reizer,


1993] of a


possible explanation for the NFL behavior not based on a microscopic theory but on a

phenomenological theory.


Tsvelik


Reizer


proposed


phenomenological


theory


to explain


NFL


behavior,


which exhibits strong deviations from the Fermi liquid theory, observed in the


heavy fermion metallic alloys U0.2Yo.sPd3.


Their theoretical development is based on the









the resistivity are observed.


Secondly


there is a scaling in the magnetization M in the


following form,


H f(H
= -f( )
~TP '"


(2.29)


where y


- 0.3


,I3+.


~ 1.3


, and f(x) is a nonsingular function.


Thirdly


same scaling of H holds for the specific heat,


C,(H, T)


S(o, T)


H


(2.30)


Lastly,


the behavior


of the thermodynamic quantities becomes even more


singular


UCu4Pd,


which is closer to the antiferromagnetic (AFM) part of the phase diagram.


these properties hold below T


-10K.


The materials behave like Kondo alloys well above


temperature


T dependence


p [Seaman


et al


., 1991]


originating from the scattering of conduction electrons off U ions.


The Fermi liquid (FL) theory is based


on the assumption that the


low energy


excitations are dominated by fermionic excitations.


This assumption via the Pauli principle


implies a natural


energy


scale exists


in the theory,


chemical


potential


EF and


thermodynamic properties depend on T/sF and H/SF.


The dependence of C and M to the


magnetic field and temperature behave as described in Eqs.


(2.29) and (2.30).


Their


scaling clearly demonstrates the absence of a natural energy scale and thus the irrelevance

of NFL behavior with fermionic excitations.


Therefore,


Tsvelik and Reizer suggested that the low


T thermodynamics in the









transition occurs at a finite critical temperature T7, the notation T in Eqs.


(2.29) and (2.30)


should be changed T


- T1.


Although the nature of the T


= 0 K instability remains obscure,


glass


fluctuations


are suggested


as an essential


origin


based


on the


observed


experimental results in the alloys.

The free energy is given by


T
- Tf (
T
^J K


(2.31)


-S'


where h,


are external


fields


are dimensions.


fields


are relevant


if their


dimensions are positive 6,


In the scaling region, one must consider only the leading


singularity of the free energy F and then perform the limit

excitation spectrum o at the critical point is given by w q,


. Suppose that the


then the dimensional analysis


gives F


~ Tl+d/z
-~ 1


In the limit TK


oo and h,


, the indices of the singular X are given


+I+d (2.3


'T-T


If ,(0) are related to the thermodynamic correlation functions of the operators c,(t,x) as a


function of time and real space and the concept that the correlation must decay at t


oo is applied at finite temperature to restrict y's


(see the paper by


Tsvelik and


Reizer [1993]), the following relation is obtained:




The comparison of the specific heat result, C


- T n T, with the specific heat from the free


T-2S,


xi (O)









do not


control logarithms),


and the excitation spectrum at the critical


point


scales as


This result along with Eq.


(2.33) means that 6,


< 2 and this simple inequality is


very important, because in both a spin glass transition and a quadrupolar fluctuation a


magnetic field couples to a relevant field quadratically, i.e.,


2. The data from the


alloys show that the magnetic field scales as T


with 6


= 1.3 +0.1


which means that H2


has the scaling dimension 6(H 2)


requirement 6,


= 26


so that it rules out not


.6 +0 .


This estimate contradicts the


only the scenario related


to a spin glass


transition but also the one of an impurity quadrupolar fluctuations.


Recently, there was a


study of two channel Kondo effect with two impurities to consider a more realistic system


where intersite and on-site interactions compete all the time [Ingersent et al.,


1992].














CHAPTER 3
NON-FERMI LIQUID BEHAVIOR OF MAGNETIC HEAVY FERMION
SUPERCONDUCTORS


There has been a lot of interest in a non-Fermi liquid (NFL) behavior in f-electron


(Ce and U) heavy fermion materials for the past few years.


The physical properties of the


NFL usually exhibit a weak power law or logarithmic divergence at low temperatures.


critical point at T


= 0 K has been suggested as an origin.


The possible origins of a 0 K


critical


point


are an unconventional


single


effect


fluctuations


order


parameter near 0 K resulting in a second order phase transition.


Our attention will be


given to the NFL systems whose parent systems have the antiferromagnetic (AFM) state


and superconductivity (SC) at low


UxMi-xNi2Al3 (M


. A more thorough emphasis will be given to the


Th, Pr, and Y) and UxTh.-xRu2Si2 systems with experimental data to


suggest a possible ground state of these systems.


3.1 Overview of Non-Fermi Liquid Systems


Almost a dozen NFL systems have been discovered in recent years (see the review


papers,


e.g., Maple et al.


[199


Andraka [1994], and Steglich et al.


[1994a]).


These


systems


are Ce


or U


intermetallics


doped


a nonmagnetic


element


with


a few









conduction electrons resulting in


magnetic order, the nonmagnetic quadrupolar moments


interact with the charges of the conduction electrons participating in a quadrupole ordering


at low


The NFL materials exhibit several unusual physical properties in, e.g.,


specific


heat C, electrical resistivity p, and magnetic susceptibility Xm in contrast to the local Fermi


liquid theory with which we can describe some of the heavy fermion systems.

For instance, C/T is expressed in terms of In T dependence rather than constant in


temperature, p is linear in T"' or T or In T rather than in TP


, and Xm is linear in In T or T'n


rather than constant at low temperatures.


Thus, the existence of a critical point at T


=OK


has been suggested.


One of the possible origins comes from an unconventional moment


screening process such as multichannel Kondo effect [Schlottmann and Sacramento, 1993].


Another possibility is a


= 0 K second-order phase transition such as


a long


range


magnetic


order


[Andraka


Tsvelik,


Tsvelick


Reizer,


1993]


(another


possibility is due to dilute magnetic impurities in a disordered metal where a singularity


comes from the probability distribution for Kondo


temperatures [Dobrosavljevic et al.,


1992]).


There


have


been


extensive


experimental


studies


to confirm


above


theoretical suggestions


NFL behavior,


The parent heavy fermion materials, of which doped ones exhibit


vary from the nonmagnetic (CeCu6) to the magnetic system (UCus), from


the superconductor (UBe13) to Kondo insulator (CeRhSb), and even systems in which


and antiferromagnetic states coexist (URu2Si2).


We can roughly divide these systems into






44


1994], CeCus.7Auo.3 at pressure [Bogenberger and LOhneysen, 1995], UCu3.,Pd.s5 [Andraka


and Stewart, 1993], CexThi.xRhSb (may be disorder) [Andraka, 1994b],


and CePtSio.9Geo.i


and UCus.6Al.4 [Steglich et al.,


1994].


The second group members, being described to


exhibit


single


ion two


channel


Kondo


effect


(TCKE),


are Uo.9Tho.1Be13


[Aliev


al.,1995] and maybe UxThi.xPd2Al3 [Maple et al., 1995].


The last group members may be


described by either the first collective modes or the second single particle excitation, e.g.,


Ceo.1Lao.9Cu2Si2 [Andraka, 1994c], UxMi.xPd3 (M


and Tsvelick,


Y, Sc) [Seaman et al., 1991; Andraka


1991; Gajewiski et al., 1994], PrxYi.xCuzSi2 [Sampathkumaran, 1993], and


UxTht~xRu2Si2 [Amitsuka and Sakakibara, 1994].


So we present here some experimental results for UxThi.xRu2Si2.


It seems to us


that possible collective modes at low temperatures dominate over the single ion excitations


in the system.


Furthermore, we will present another new NFL materials Uo.9Mo.INi2A13 (M


= Th, Pr, and Y) and in the end we hope to convince that our new systems are more related


toa T


= 0 K long range phase transition than other possible origins.


Investigation of the Ground State in UxThl.xRu2Si2 for x


< 0.20


There has been a very interesting report [Amitsuka et al.,


1993] such that they


have found non-Fermi liquid behavior in UxThi.xRu2Si2 for


x < 0.07


The experimental


results of


C/T, p, and X due to U-ion exhibit a In T dependence for one or two decades of


temperatures.


They have attempted to explain the results of x and C/T


in terms of the






45


predict [Tsvelick, 1990; Ludwig and Affleck, 1991] that the resistivity subtracted from the


residual one, p(7)


- p(O), increases as -T-a with a positive a for T


->0.


We firstly summarize briefly the parent system URu2Si2 and its doping experiments


on the U-site with Th,


, La, and Ce.


We then


describe the main points of UxTht-xRu2Si2


experiments for x 0.07 by Amitsuka et al., [1993] with their recent new interpretation


[Amitsuka and Sakakibara,


1994].


Our emphasis will be given to the possibility of a


magnetic transition at low T with the resistance, specific heat, and magnetic susceptibility


measurements in UxThi-xRu2Si2 for 0.07


x <0.17


3.2.1 URu2Si,


The physical properties of the superconductivity (Tc =


netism (TN


1.5 K) and antiferromag-


17.5 K) in URu2Si2 [Palstra et al., 1985; Schlabitz et al., 1986; Maple et al.,


1986]


have


attracted


condensed


matter


physicists.


structure


is body-centered


tetragonal ThCr2Si2 with lattice parameters a = 4.219


A and


C =


9.575


A as shown in


Figure 3-1.


The spins on the U-sites are aligned antiferromagnetically to the c-direction


with alternate ferromagnetic sheets in a/2 apart.


It is a semi-heavy electron system with y,


the coefficient of electronic specific heat, being 64 mJ KI mole"' [Palstra et al.,


1985].


also shows a large slope of the upper critical magnetic field Hc2 at the superconducting


critical temperature


(-dHcJdT)Tc,


which is about


[Rauchschwalbe,


1987].


ThRu2Si2 has the same crystalline structure as URu2Si2, and y is about 10 mJ K'2mole"'























Ou


Ru


oS









For the AFM ordering there are several possibilities.


Firstly, it may be due to the


development of a charge density wave (CDW) or spin density wave (SDW) with a gap of


meV


from specific heat measurements [Maple et al.,


1986] or a gap of 7


meV


produced by the hybridization of U-5f states with conduction-electron states from the


inelastic neutron scattering [Walter et al.,


1986].


In this case, the nonmagnetic singlet


ground state is responsible for the transition.


However, there is a maximum around 30 K


in the electronic specific heat vs.


temperature in addition to the anomaly at TN.


The total


entropy


connected


both


peaks


is close


to R


implying


magnetic


temperature state of URu2Si2 is formed by localized 5f electrons in a CEF doublet ground


state [Schlabitz et al.


, 1986].


Secondly, it may be due to the long range Ruderman-Kittel-


Kasuya-Yoshida (RKKY) interaction of the localized U-5f magnetic moments supported


X-ray


resonance


magnetic


scattenng


[Isaacs


et al


, 1990]


magnetic


neutron


scattering [Mason et al.,


1990].


But, there is no indication of a Schottky anomaly in


specific heat up to 350 K even if most of the CEF levels should be populated at 200 K.


The entropy released below TN is about 0. 17R ln2 although the ordered moment is as

small as 0.03 Pa [Broholm et al., 1987].


In the magnetic susceptibility ym,


there is a broad peak around


55K,


which is


interpreted as being due to a short range magnetic correlation [Schlabitz et al.


the coherence effect in the Kondo lattice [Mydosh, 1987],


1986], or


or AFM fluctuations of 5f state


[Amitsuka et


., 1992].


High


magnetization


experiments


reveal


several


sharp









[Palstra et aL


1985; Schlabitz et al.,


1986; Broholm et al.


1987].


This invokes the


possibility of elucidating the interplay between the two ground states.


Doing Effects of URuSi,


There have been several doping experiments of Ut-xMxRu2Si2 (M


, La, and


Ce) into U-site to understand the fascinating properties of the parent system mentioned


above [Torre et al.,


992; Park, 1994; Park et al.,


994; Amitsuka et al.,


1992


Mihalik et


, 1993].


In U,-xLaxRu2Si2 for 0


x < 0.3 [Amitsuka et al.,


1992],


TN decreases for


0.07 and starts to increase for 0.07


x < 0.3 as the lattice parameters gradually expand.


Their argument is that 5f character continuously changes from an itinerant to a localized


nature with doping based on YX experiments.


There is a linear correlation between Tmn,


where Xm shows a maximum peak, and TN for 0.07


x<0.3


, indicating the same nature of


both


TN and Tm,.


So they concluded the maximum peak in Xm around


5K is related to the


AFM fluctuations of the 5f state.


In the U-rich case of Ui-xThxRu2Si2 for 0.0


x < 0.05 [Torre et al.,


1992],


small


doping of Th suppresses both TN


and Tc, and it can be explained in terms of the decreased


coupling


constant J between


conduction


electrons.


other words,


expanding of the lattice parameters causes a suppression of hybridization as shown in Eq.


) assuming the energy difference between the Fermi level and 5f level is unchanged


based on tetravalent character of U and Th.


Thus, both decrease of J and increase of Ri









- [JN(E,)12 I


where


(3.2)


VFf is the hybridization matrix, Er the Fermi level, Ef the energy of the 5f-level,


N(EF) the density of states at the Fermi level, and R0 the distance between lattice sites i


andj.


Torre et al. [1992] use the concept of "Kondo hole" to explain the minimum in the


resistivity.


However, it might be ruled out as shown by


Y-doping experiments [Park,


1994], specifically, the minimum in p at low temperatures exists up to 50 % doping.


the other hand, there have been a lot of interesting phenomena in the U-dilute case, namely

"non-Fermi liquid" behavior which we will describe in more detail in the following section.


Non-Fermi Liquid Behavior of UxTht.xRuSi, for x


< 0.07


A Japanese group has reported [Amitsuka et al.,


1993; Amitsuka and Sakakibara,


1994] that they have found non-Fermi liquid behavior in a single crystal of UxThi-xRuzSi2


for x


0.07, i.e.,


U-dilute case, such that C/T, p, and X due to the U-ions show a In T


dependence.


They have attempted to explain the experimental results in terms of the two


channel Kondo effect (TCKE) [Nozieres and Blandin,


1985; Sacramento and Schlottmann,


1980;


1991a; Seaman et al.,


Tsvelick and


1991] with a single impurity


based on the tetragonal 5f 2


configuration even though the resistivity data is totally in


disagreement with the model, which predicts the -T'" dependence of electrical resistivity.

They have claimed that the T independence of X'm, magnetic susceptibility along


the basal


plane


or a-axis,


originates


from


van Vleck


paramagnetism


due to


3.2.3


TRKKY


Wiegmann,









state was a magnetic doublet Fs5 (3H4, U4


, 5f2) rather than a nonmagnetic doublet.


Thus,


TCKE


in this


U-dilute system


UxThl-xRu2Si2


x < 0.07


is caused


dipolar


fluctuations in the ground state.


This ruled out the possibility of the


TCKE caused by


quadrupolar fluctuation in the ground state of 3 nonmagnetic doublet for the cubic and

tetragonal U-compounds [Cox, 1988b].


For instance,


there is no such magnetic ground state phenomena in


the cubic


symmetric systems such as


U0.9Th0oBe13


[Aliev


et al.,


1993;


Aliev


et al.,


1995]


[Seaman et al.,


1991] which are also believed to exhibit non-Fermi


liquid


behavior (there has been polarized inelastic neutron scattering in which they observed the

critical fluctuations around the antiferromagnetic position in the U0.2Yo.,Pd3 similar to that


of the Uo.45Y0.55Pd3 whose ground state is a magnetic F


s triplet).


In cubic symmetry, e.g.


Uo.2Yo.8Pd3, the selection rules used [Cox,


1993] restrict the lowest CEF state to the F


doublet that couples to the F


excited doublet via the F


8 symmetry conduction states.


this case the degeneracy of 13 comes only from the quadrupolar degrees of freedom.


the other hand, in the tetragonal symmetry, e.g. UxThi-xRu2Si2 for


x < 0.2, the


TCKE is


expected only when the Fst (5f ) lowest doublet couples to the frt (5f ') excited doublet


via the hybridization effects with the F6t+ F7t symmetry conduction states at the U-site.


the In T


dependence of Xem of UxThi-xRu2Si2 for


x < 0.07 is the very case not in the


electric quadrupolar field but in the magnetic field [Amitsuka and Sakakibara,


1994].


Thi nharht rclu ll ;e trnl anl, uhian the rulMhlt r..

U0.2Y0.8Pd3






51


Xq, to show In T divergence at low temperatures because Fst is doubly degenerate with the


quadrupolar


moment


c-plane.


investigate


possibility


ultrasound


measurements, from which the quadrupolar (or strain) susceptibility can be extracted, are

desired.


3.2.4 Non-Fermi Liquid Behavior of UxTh..xRu2Si2 for 0.07


x 0.17


A purely logarithmic temperature dependence of Xm (Xc'" in Figure 3-2) in the


c-direction breaks down at low temperatures (T


100 inK) for


x > 0.03 resulting in a


peak anomaly at temperature


Tm of the order of 0.1


K as shown in Figure


anomaly may come from an intersite magnetic correlation between U-ions, e.g., spin glass


ordering.


While we were doing the doping experiments in UxThi.xRu2Si2 for 0.07


we found a kink below


2 K in the resistance data.


This fact allowed us to speculate


T dependence of Xm


about


decades of temperature


observed


Uo.olTho.99Ru2Si2


might


correspond


to magnetic fluctuations


near


= 0 critical


point


[Andraka and Tsvelik, 1991], proposed already for other U-based alloys displaying similar


low temperature properties.


Since the temperature of the anomaly increases with


concentration x,


we have focused our investigation [Kim W.W. et al.,


1994] on the less


dilute systems corresponding to


laboratory, but we limited


x > 0.07 to operate at more accessible temperatures in our


x < 0.17 to avoid the problem of a miscibility gap for 0.2


0.9 [Torre et al., 1992].









































1 1 10


100


1000










Johnson Matthey Inc. (JMI), and 99.999 3


in detail.


Al from JMI as we described in section 1.3.1


Some resistivity samples were cast into a particular shape in a water-cooled


crucible


using


a pressure


casting


technique


inside


an arc furnace


[Crow


Sweedler


, 1973].


After we took the sample out of the arc furnace,


we subsequently


annealed it at 900 C for one week.


All samples showed single phase according to X-ray


powder diffraction data taken on a Philips diffractometer with a scan of 6 o per minute in

20.


Resistance.


These measurements were performed via a standard dc four-probe


method to temperature as low as 0.3 K.


If we look at the resistance data shown in Figure


3-3 in terms of T.


we see a kink below


2 K for all our concentrations.


The position of the


kink anomaly decreases as we dilute U-concentrations for


x < 0.14 as shown in Figure


3-4, and decreases abruptly for


x> 0.14.


crystalline sample [Amitsuka et al.,


1993


We think the peak at 250 mK in Xm from single

Amitsuka and Sakakibara, 1994] corresponds to


an anomaly TA in the resistance for


=0.07


Although the TA for


= 0.07 was not clear in


our polycrystalline sample, it is interesting to note that the TA approaches zero for


x -0if


we assume the linear decrease of TA for


x < 0.1-we can


see such a possibility for 0.1


<0.14.


Thus, it is desirable to check this behavior with single crystalline samples for


. This possibility allows us to speculate that the In T dependence of X'm observed in


Uo.oiTho.99Ru2Si2 may correspond to magnetic fluctuations near T


= 0 critical point.









[Amitsuka


Sakakibara,


1994])


in contradiction


to the


TCKE,


which


predicts


decrease in p with temperature caused by Kondo scattering.


Thus, it seems that the


behavior of p is closely related to the onset of coherence and correlated scattering.


other words, the NFL behavior of the resistivity in the UxThl.xRu2Si2 for U-dilute region

(x < 0.14) seems to be related to the intersite interaction of U (short range correlation or


even long range one as T

Specific heat. Sp


-> 0) rather than the single site two channel Kondo effect.


,ecific heat measurements did not reveal any signature consistent


with a phase transition at TA.


Only the specific heat for the 'most magnetic'


alloy of


0.14 showed a change of slope or a peak in C/Tat about 0.45 K shown in Figure 3-5; this


temperature is roughly three times smaller than the corresponding TA.


NFL behavior in p measurements at low temperatures,


Since we saw the


we can expect an unusual Fermi


liquid behavior in specific heat rather than Fermi liquid behavior,


observe a saturation of C/T at low temperatures.


in which we usually


We show specific heat due to the U-5f


contribution divided by temperature CsfT


vs. In Tfor 0.07


x 0.17 in Figure 3-5.


CwjT


for a given concentration is fairly linear in In T

again NFL behavior (the In T dependence of Cs


of Tdeviating for T


scale over more than one decade implying


= 0.07 holds for only one decade


3 K and this is also observed by Amitsuka et al. [1994]).


When we applied a magnetic field, CIT


monotonically decreased as we increased


the field up to 14 T


. For instance, C/T


at 1 K is decreased by about 42 % at H =


14 T


compared to the value in the H = 0 for x = 0.1, and it follows surprisingly well Fermi







[Steglich et al.


1994] as we apply magnetic fields, because a single-site interaction is


induced by the magnetic fields which destroy the weak long range correlations between


local magnetic moments.


A similar behavior of the magnetic field dependence has been


reported [LBhneysen et al.,

antiferromagnetic transition


1994] in system CeCus~.Auo.i,


= 0 Kin H


which is believed to have an


= 0, and comes back to the Fermi liquid


behavior


magnetic


According


to TCKE


[Schlottmann


Sacramento, 1993] as we described in Figure 2-3c, however, CIT should increase from the


zero field value for the magnetic field roughly comparable to TK.


For instance, C/T for x


0.1 should increase at least by a factor of five at H


= 10 T and T


Kfor TK


10K,


T/TK


= 0.1 and H/TK


= 1 (see


Table 3-1).


TK listed in Table 3-


1 has been obtained from


the slope of the linear fit of Figure 3


using the formula (3.3) from


TCKE model and


assuming TK is independent of magnetic field:


C5f/T


1R T
In(.41
0.41TK


)+A,


(3.3)


where A is a constant and R is a gas constant 8.314 J K' mole


. But, we did not see such


an increasing behavior of C/T implying the ineligibility of the TCKE in this system.


Table 3-


Summary of Kondo temperature TK using Eq.


(3.3) for all our concentrations


x<0. 17.


concentration (x) TK (K)
0.07 6
0.10 10
0.125 11








As we dilute the U-concentration from 0.17 to 0.07


the lattice constants increase due to


the larger atomic size of Th than U giving rise to a decrease of both TK and TRKKY


assume that the TA corresponds to a magnetic phase transition,


. If we


we see in Figure 3-7 that


the long range correlations (TRKKY) are dominant over the on-site interaction (TK) in our


system


because


decreases


as the


coupling


constant


between


local


magnetic


moments and the conduction electrons decreases.


Amitsuka et al.


[1994] also suggested a possibility of "channel reduction"


that there is a cross-over from the


TCKE with a magnetic ground state F


such


to the usual


one-channel Kondo effect in high magnetic fields and at low temperatures.


But it is not


probable, because it always generates the Kramers doublet as the lowest state so that a

Curie-law susceptibility is expected even along the hard axis (in this case a-axis) and this


contradicts


almost


T independent


behavior


Ca lm


Thus,


such


a magnetic


dependence of the specific heat can not be explained by the simple


TCKE as shown by


both the decrease of C/T with fields and the inadequate argument of the channel reduction

to explain the FL behavior in magnetic field.


There is another NFL system of Uo.2Yo.sPd3,


where the physical properties such as


specific heat and magnetic susceptibility were suggested to obey


TCKE [Seaman et al.,


1991;


Maple


et al.


, 1995].


Also,


as the


theory


[Tsvelik,


1985;


Sacramento


Schlottmann, 1989b] predicts, there seems to be a remnant entropy {R In2)


=OK


[Seaman et at.,


1991].


Thus, C/T should increase at low temperatures, i


ST/TK


<0.1




























































































o-0.4





































0.36


I I 5
*
a S .
*
S.. *
S*
.
S
S
S
S
-
S
S
S
S
a
S
S
a
a
U
S
S
- a
S

S.
S
a
S S
S S
S
S
S
a

..5**' 0.405


"-Se

4.
'Pr


- 7


0.395
-S
a
S
S
a
S
S
S.
S
a
a S

S
I
S SS
a S
---S...
U.JL13

a
SS a a
S
a
a
a SS
SS
SS
a

1 S

0.375

0.5 1 1.5 2 2.5



a S I a I A A I I A


(K)



































I-'


ci:


0.7








0


O







r-











S-- p ---


0.2























400


- 200


E

U
C1


.5 0


Log o


0.5


(K)


C Q.nX la ot nf T

C:,,,,, 1















350


250


150


100





































TRKKY


Magnetic 4f-metal


Magnetic CKS


Non-magnetic CKS


2/w






62



observed by Andraka and Tsvelik [1991] at 0.35 K and 14 T (there should be about order


of one increase in C/T for T/TK


< 0.01 and H/TK


- 0.3 from the Figure 2-3c) indicating the


ineligibility of the TCKE theory to Uo.2


Susceptibility.


Y0.5Pd3.


Dc magnetic susceptibility measurements were performed from


room temperature down to


1.8 K in a commercial SQUID magnetometer.


No apparent


signature consistent with a magnetic anomaly was found in our samples in the investigated

range of temperatures-this is not surprising if we accept the possible relation between TA


and T,,


e.,TA ":(3


- 4) Tm so that Tm is expected below


However there was a


distinct difference between the zero-magnetic-field-cooled (ZFC) and field-cooled (FC)


susceptibilities


concentrations


investigated.


Moreover,


ZFC


some


concentrations flattened out at the lowest temperature investigated indicating that there


might be a possibility of an anomaly at temperatures lower than 1.8 K.


depicted in Figure 3-8 for


This tendency is


= 0.14.


It has been reported [Amitsuka and Sakakibara,


1994] that there was an excellent


scaling behavior in the xm for


x < 0.0


implying a single site Kondo effect and a fairly


good fitting of Xcm data was possible by the


TCKE as shown in the inset of Figure 3


However,


we suggest


interesting


to look


there


is a one-to-one


correspondence between TA and Tm by measuring xgm (even TA for better resolution) with


single crystalline samples for 0.07


x 0.14.


Because, if such a correspondence exists, it


























O
E
I
3
- 16

E
G)
U
E

>,
+'>


F~C


FC


p I 1 i i-L -


(K)


__






64


In summary, firstly we observed TA in p measurements, below which the intersite


interactions between local magnetic moments occur, for 0.


x < 0.17 at low


. This


anomaly at TA seems to be related to the onset of coherence, and can not be explained by


single-site


TCKE


interpretation.


Furthermore,


increase


resistivity


temperature for 0.3 K


coherence


20K contradicts the


Thus, the NFL behavior in UxThl-xRu2Si2 for 0.1


TCKE, instead implying the onset of


x < 0.17 seems to be due


to magnetic fluctuations at T


rather than the single-site TCKE.


in the U-dilute regime exhibits th


= 0 K or collective modes of excitations at low temperatures


Secondly, we know the specific heat of UxThi-xRu2Si2

NFL behavior. Also, thermodynamic measurements in


magnetic fields reveal that these systems transforms to the Fermi liquid regime from the

magnetic instability or magnetic intersite correlation regime caused by the destruction of


the intersite interactions between local magnetic moments.


Thirdly,


we observed a spin-


glass anomaly for concentrations 0.0


x <_ 0.17


in the FC and ZFC Xm measurements


using the polycrystalline samples.


Also


, the confirmation of the relation between Tm and TA using single crystalline


samples is desirable


to understand


the origins of Tm and


the logarithmic behavior of


Uo.o1Tho.99Ru2Si2 in Xm.


Although we have focused on the anomaly of TA and Tm in the


resistivity and magnetic susceptibility,


it is desirable to check if


our system obeys the


scaling behavior in the specific heat and magnetization measurements at several magnetic

fields as a fiurther work






65




3.3 Magnetism and its Connection to Non-Fermi Liquid Behavior in UI.xMxNNiAls
(M = Th. Pr. and Y1


Since there was a report of the discovery of a new heavy fermion system UNi2AI3


[Geibel et al., 1991c], there have been several studies to understand the system.


While we


were


conducting


doping


experiments


on the


U-site


UNi2AI3,


we found


unusual


temperature dependence of the physical properties inconsistent with Fermi liquid behavior


indicating a possible NFL system.


Thus,


we are going to investigate the doped system


more thoroughly and give a possible explanation for the origin of our newly discovered


[Kim W.W


3.3.1


.et a., 1993] NFL system.


UNi2A1


took


several


years


physicists


discover


new


heavy-fermion


superconductor, UNi2Al3,

as CeCu2Si2 [Steglich et al.


URu2Si2 [Schlabitz et al.,


[Geibel et al.,


1991c] after discovering the previous ones such


1979a], UBei3 [Ott et al., 1983], UPt3 [Stewart et al.


1986].


1984a]


Superconductivity takes place at


UNi2At3,


AFM transition at


TN = 4.6 K reflects a


weak


delocalization of 5f


electrons.


It has a hexagonal PrNi2AI3 crystalline structure, shown in Figure 3-9, with the


lattice parameters


5.207


A and c = 4.018


As we


see in Figure 3-9,


the U-U


distance is already larger than the Hill limit (3.4 A) [Hill,


1970] to exhibit heavy fermion


Tho .amnnl i annnsalsd tn rmnT/P cEAfnnnralrv nhbsec (tcmullv T TAI-1 which vYict


hbpah; inr


Te





If we look at X


vs. temperature as shown in Figure 3-10, there is a cusp at TN and a


broad maximum around


= 100


There is a flat region for


Tm in electrical


resistivity p


vs. T,


which is shown in Figure 3-11.


Also,


Geibel et al.


[1991c] found a


corresponding maximum in p around T,m after they subtracted the contribution from the

electron-phonon part, and suggested a transition from localized to weakly delocalized 5f

behavior in the spirit of the Kondo lattice concepts.


AFM


transition


not clear


in p,


is exhibited


a mean-field-type


relatively sharp transition at TN and a broad curve below


vs. Tas shown in Figure 3-12.


as high as H


TN down to the onset of Tc in


The TN is weakly depressed by an external magnetic


= 8 T as shown in the inset of Figure 3-12, resembling the case of, e.g.,


the heavy fermion antiferromagnet CeCu2Ge2 [de Boer et al.,


1987].


Magnetic entropy


released at TN gives a value of S


= 0.13 R ln2 indicating a rather small ordered U-moment.


This has been confirmed by neutron


scattering measurements [Schroder


et al.,


1994]


which give ordered moments rd= (0.24 + 0.10) pW/U-atom in the basal plane,


incommensurate with the nuclear lattice.


which is


However, positive-muon spin rotation (p'SR)


measurements [Amato et al.,


1992b] were reported such that the o = 0.1


pB/U-atom


along


c-direction


(perpendicular to


basal


plane)


commensurate


AFM


ordering.

The superconductivity is exhibited by a sharp transition in p, shown in the inset of


Figure 3-11, and by a broadened jump in the specific heat around at


Tc =


K, shown in


Figure 3-12.


The electronic specific heat coefficient


120 mJ K'2mole1'


is deduced,


S-~~ .- I ,.di TV .f I, m '7' ,r Tr fi


n






















0


At
Pd




































100 200


300




















1000


750


500


250


0


100


200


300


























200


150


~100


I


.*. .


200


170


10O






71



measurements of Tc with magnetic fields, the initial slope of the upper critical mag data

between Tc and 7 K shows a linear behavior, shown in the inset of Figure 3-11, usually


preceding the asymptotic low


T behavior, p


, of Fermi liquid.


From the netic field,


c2 = -


( jc2//)rTc, is also reported to be 1.4 T/K.


From Yo, Tc, po, H2, and assuming an


isotropic one band model, they estimate [Geibel et al.,


1991c] the effective carrier mass


= 70 mo, where mo is the mass of the bare electron.


3.3.2 Non-Fermi Liquid Behavior in Ui.xMxNbAl_{M


Thk Pr. and Y}


Since


our group


found


a possible


separation


single


effects


from


correlation effects in doping experiments [Kim J.S.


et al.,


1991; Jee et al.,


1990],


doped the parent system UNi2A3 on the U-site with Ce, La, Y, Th, and Pr in order to vary


observed


behavior.


While


we were


doing


our experiments,


we found


unusual


temperature dependence of the physical properties in, e.g., C/T,


x, and p inconsistent with


the FL behavior.


Thus,


we performed systematic studies to understand the origin of the


NFL behavior.

Samples were prepared via arc melting together the starting elements, followed by

(with exception of the sample #1 in UNi2Al3 discussed below) annealing for one week at


samples


maintained


PrNi2Ah3


crystalline


structure


with


lattice


parameters shown in


doped elements in


Table


Table 3-3


We also compare the physical properties of U and the


to help the understanding of the doping effects in these









The dc


magnetic


susceptibility Xdc


was


measured


samples.


The value


obtained at


1.8 K for our UNi2AI3 sample #


was about 8 % less than that found in the


discovery work by Geibel et al. [1991 c].


In addition, they saw a small (about 6 %) peak


Table 3


Parameters for Uo.9Mo.iNi2A13.


M = a (A) c (A) X (1.8 K)
_memu/formula unit]
U (parent) 5.184 4.023 4.55, 3.30, 3.95, 3.50 a
La 5.200 4.023 4.20
Y 5.184 4.024 5.35
Ce 5.188 4.030 4.20
Th 5.182 4.032 5.15
Pr 5.184 4.027 8.35
a) The values correspond to the sample #1 through #4 from the left.


Table 3-3.


Comparison of U and the doped elements.


at 4.8 K in Xdc (see


the inset in Figure 3-


10), whereas our data for sample #1 are, within


%, featureless in this region as shown in Figure 3-


As will be discussed below more


thoroughly, the sample dependence of the magnetic transition at TN is an important point.


Thus, weprepared three additional samples of UNi2Al3, whose Xdc (1.8 K


300 K) and


(1K


10 K) were measured (see Figures 3-


13 and 3-


We see a significant


atomic size electronic configuration effective magnetic moments
U~ -Y tetravalent (4+): Th U > Pr, U > Ce

U < La, Pr, Th, Ce trivalent (3+): La, Y, Pr, Ce Y, La, Th = 0






was annealed at


1000 C for six days,


while the subsequent samples were annealed in a


different furnace at 900 0C for seven days.


Unless the furnace used for sample #1


defective, the absence of the AFM transition shown in the C/T


Recently, there was a report [Schank et al.


UNi2AI3.


and Xdc, seems unusual.


1994] of the influence of off-stoichiometry on


They did see the absence of AFM transition and superconductivity down to 40


mK in UNi2.05A12.95, while they found about a 10 % suppression of TN, and Tc"~


with a much broader transition width in UNi1.95A13.05.


0.66 K


From these results we see that the


off-stoichiometry of the Ni (the excess) and Al (the deficiency) is very crucial to the

magnetic order and the superconductivity in UNi2A13.


show C/T


vs. T2for Uo.9Ceo.0Ni2Al3 in Figure 3-


14 and for Uo.9Mo.1Ni2Al3 (M


, Th, La, and Pr) in Figure 3-


. The 10 % doping destroys the AFM order completely


and the C/T at low temperatures seems to diverge (except for Ce doping).


For the small


peak around


K in the 10


o Ce-doped sample, shown in C/T


vs. T


we do not


see a


corresponding anomaly in Xdc down to 1.8 K.


We checked the temperature dependence of


the 5f electronic contribution of specific heat over temperature Csf/T of 10 % Y


Th, La


and Pr doped systems.


As shown in Figure 3-


16, a in T dependence for more than one


decade of temperatures is observed in the 10 % Th- and Pr-doped systems.


we did not see a broad in T dependence of Csf /T for the


Even though


0 % Y-doped systems for T


we saw a In T dependence down to about 0.3 K leaving about a decade of NFL


temperature behavior, shown in Figure 3


-16 (all NFL systems mentioned in section 3-1


show the logarithmic temperature dependence of C/T due to magnetic ions).


The 10 %









we estimate Kondo temperature using the formula (3.3),


we have 77 K, 69 K, and


for Pr, Th, and Y 10 % doped systems, respectively.

The question arises: how does this unusual behavior change upon further doping


For instance, the shrinking of the T range,


where In T dependence of C/T is observed, is


seen upon further U-doping in Uo.2Yo.sPd3 [Seaman et al.,


991].


In UCu3.sPdi.s


[Andraka


and Stewart,


993],


varying the Pd to


UCu4Pd totally destroys the In


T dependence;


instead giving rise to C/T


cT 0.32 from 1 to 10 K.


In our systems, the temperature range


over which this In T behavior is observable, on the other hand, shrinks upon increasing Th


(or decreasing U) content, up to 3


.2 K for 20 % Th and


2 K for 30 % Th as shown in


Figure 3-


other words,


unusual


behavior is


too limited


T to


significant credence.


As seen in Figure 3


-18, using Th doping as a representative example,


the temperature at which the upturn in C/T begins is depressed with more doping and the

negative slope at low temperatures is steeper for more Th doping resulting in the deviation

from the In T dependence in C/T.


The low Tvalues of Xdc vary as detailed in Table 3


The Xdc results for 1.8 K


< 9K of


= 0.1 Th and Pr obey T in dependence, shown in Figure 3-


9, as predicted by


TCKE for the nonmagnetic ground state [Cox, 1987a and 1987b].


The theory says that


we can express magnetic susceptibility Xm as Xm


- nT l' (refer to Eq.


28) where nr is


proportional to the T independent van Vleck susceptibility, Xvv,


and inversely proportional


to the CEF


splitting.


The coupling via conduction electrons between the nonmagnetic



















































100


200


300


(K)


P .mira2...12


IIrLA~ .r*.J


MaGnetic suscentibilitv as a function of T between


8 K and 100 K fnr fnwir


I

























C-'


100


100


E150



















140


100


100











































.5 0


Log10


0.5
(K)


Figure


electronic


contribution


specific


over temperature,


moaaorpAd fr TL ,,Pr^ .iN'LAl. T L ^Th.


.Ni-.Al,


T ^V .NLAl. an T ^T a .NMiAI. ik nirnttArl




































0.5 1


Loglo


(K)

















160


140


120


100










we have seen the sample dependence in the parent system,


we prepared a second sample


of Uo.,Tho. Ni2AI3.


The data also show Xdc


dependence.


On the other hand,


found that Xde of the 10 % Y-doped system exhibits a more singular behavior in the T 12


scale than the


Th- and Pr-doped systems as shown in Figure 3-19.


Thus, the


doped


system


follows


logarithmic


temperature


dependence


rather


dependence


as shown


Figure


3-20.


Since


quadrupolar


susceptibility,


where


aspherical charge distribution of the 5f ions play the role of a pseudospin, is usually too


small to see a response, Xde for Y


0 % doped sample may be described by the effect of


magnetic ground state as also suggested [Amitsuka and Sakakibara, 1994] in the U-dilute


UxThi.xRu2Si2.


However, as we will discuss thoroughly in the specific-heat measurements


by a small amount of doping, it seems to be unlikely that we could ignore the intersite

correlations in the U-concentrated (90 %) systems.


As we showed in


Table 3


there are differences for


Pr, and


Non-


magnetic


Th and Y


doped systems exhibit a smaller Xdc values at low temperatures than


the magnetic Pr doped one.


Also, the different T


dependence in Xdc seems to be more


related to the atomic size of doped elements, i.e.,


Th and Pr are larger than


Y (which is


almost same in size with U) as shown in


Tables


and 3-3 rather than the electronic


configuration and the magnetic moment of each element.


Furthermore, we measured the electrical resistivities of 10 % Th, Pr, and Y


doped


T 'n


--


--





















8.7


O
E


E
.3



.


5.1


(1)7


2.2 3


1
(K


tI;mlri


)rrn nra ro


arl nn n fi


1rl1 ** *3t, Eti WVI EtCtI*ItI iluttJ*ll t.ia *.~tI.. *I


TT,.Th, ,N;, dl,


IIIIIIIIIV II




















/"1'


4.9


0.2


0.7


1.2


Loglo


(K)




































(K)










for about 8.0 K


< 20 K saturating at lower temperatures as shown in Figure 3-21.


decrease


resistivity


at lower


temperatures


contradicts


TCKE,


where


opposite behavior is expected because of Kondo scattering.


Thus, the observed positive 6


seems to be related to the onset of coherence and the correlated scattering rather than a


single-ion scattering.

[Lbhneysen et at, 1


This kind of behavior having positive 6 is observed in CeCus.9Auo


994] out of the several NFL systems, and also observed in high-Tc


superconducting


oxides over


a wide temperature range


leading to


proposal


of a


marginal Fermi liquid [Varma et al.,


1989].


The resistivity p for the above three systems


of 10 % doped with Th, Pr, and Y varies linearly in T with a smaller positive 6 value for


0.3 K


1.0 K approaching residual resistivity (the data of p for 0.3 K


1.0 K


were indistinguishable in the T and T2 scales due to the scatterings of data).


To understand the origin of the NFL behavior in our systems,


we doped small


amount of Th in U.-xThxNi2Al3 (x


= 0.0025


0.005


and 0.01


) as shown in Figure 3


The magnetic transition temperature, as may be measured by the position of the maximum


in the specific heat anomaly,


decreases with increasing doping at the rate of about


K/%Th,


while the size of the anomaly, AC, decreases by 40 % for


= 0.005.


Magnetic


susceptibility, Xdc, for these series of samples shows a maximum at about 4.2


K (3.7 K) for


x = 0.0025(0.005) as shown in Figure 3-23,


undoped UNi2Al3.


while there is a peak at about


If the decreasing rate of TN is linear for Th doping, estimated


K for the


about
























180


" 150


120


0 50


100


Figure 3-22


C/Tvs. T2 for UL.xThxNi2Al3, x = 0.0 (sample #2), 0.0025,


0.005, and 0.01


normalized per U-mole.


The suppression of magnetism is clearly seen to be achieved with


extremely small doping levels.


Note the divergence in C/T as T


->-0 is


already present in


yr Al


0


.I'


-an I *ff i h )\ f ^i nn y / i ^ ^^ rnn.aa TO^Y r ^ w a n arnrl n a i f rt rI I n an at ,+ n


r- I


-I


I .1 i' \


I -




























0.005

-0 00
0
0
o


0 v

v 0.0025 v


V

V


V
, Y I,


(K)










In T dependence below about 3 K resulting in a more saturation than the


= 0.01


which are shown in Figure 3-


We also performed specific heat C measurements on Uo.9TholNi2A3 in magnetic


We found about a


2 % decrease of C at H


= 14 T at 1 K and almost no change for 4


10 K as shown in Figure 3-24.


This small magnetic field dependence of C in the


doped


system


is not


surprising


we remember


there


is almost


no magnetic


dependence of the AFM anomaly in the parent system, shown in Figure 3-12.


If this


system follows the TCKE,


where we estimated TK


~ 70 K using Eq.


(3.3), there should be


an increase of C/T of order of one at 14 T and 1 K as can be seen in Figure


2-3c (T/TK


0.014 and H/TK


~ 0.2,


where we assumed there is no change of TK in magnetic field)


which was not observed.


However, we can not explain our system in terms of the scaling


theory suggested by


Tsvelick and Reizer [1993], either.


For instance,


we do not see a


power law dependence of Xdc as a function temperature which is necessary to obey the

scaling properties.

It is also interesting to note that the upturn in C/T observed at low temperatures in


Ui-xMxNi2Al3


with several doping elements,


is already present above


TN in the parent


compound, as seen in Figures 3-14 and


3-22.


The broad upturn above TN is apparently


not due


simply


a broadened


AFM


transition


with


entropy


spread


out to higher


temperatures due to sample inhomogeneity.


Instead,


we see in Figure


that the


maoncftirf trnroitinmn rcac p E t rlnfi1 hrylnd n it c cunnrsed tn 1wr ftmneratiuree

















125


115


105


5 10


(K)










concentrations.


Thus, this fact indicates that the disorder interpretation [Dobrosavljevic et


al., 1992] seems not to be correct, because for weak disorder-as one would expect for


parent


compound-the


theory


predicts


unusual


temperature


dependence


ultralow temperatures.


Thus,


we see that


dilution


causes


a suppression


to lower


temperatures and


results


disappearance of TN


for more doping.


90 %


concentration, where we found the NFL behavior of C/T, p, and X at low T, seems to be


still close to the magnetic instability region.


Therefore, it seems to us that there may be a


relatively broad crossover region between (weakly) magnetic and non-ordering in which


we are finding the NFL behavior in C, x, and p in the Ui-xMxNi2AI3 (M =


Th, Pr, and Y)


systems.


In summary, we found the new system U0.9Mo.1Ni2A3 (M =


Th, Pr, and Y) which


exhibits the NFL behavior in thermodynamic, transport, and magnetic properties.


the resistivity being linear in temperature at least for 1.0 K


Firstly,


< 20 K (the Pr-doped one


exhibited the same behavior in a less wide range) contradicts the Fermi-liquid theory.


Also, the monotonic increase of resistivity with temperature for 0.3 K


20 K can not


be explained by the single-ion TCKE, but seems to be related to the onset of coherence


and the correlated scattering.


Secondly, the T mn (Th and Pr doped) and In T (Y


doped)


dependence in Xm were observed as a sign of the NFL behavior.


The difference between


- 0