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Magnetism and the Kondo effect in cerium heavy-fermion compounds cerium-aluminum-3 and cerium-lead-3

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Magnetism and the Kondo effect in cerium heavy-fermion compounds cerium-aluminum-3 and cerium-lead-3
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Pietri, Richard, 1971-
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viii, 198 leaves : ill. ; 29 cm.

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Doping ( jstor )
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Electronics ( jstor )
Magnetic fields ( jstor )
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Magnetism ( jstor )
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Thesis (Ph. D.)--University of Florida, 2001.
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Includes bibliographical references (leaves 189-197).
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Printout.
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Vita.
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by Richard Pietri.

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Full Text
MAGNETISM AND THE KONDO EFFECT IN CERIUM HEAVY-FERMION
COMPOUNDS CERIUM-ALUMINUM-3 AND CERIUM-LEAD-3
By
RICHARD PIETRI
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE
UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2001


ACKNOWLEDGMENTS
I would like to dedicate this work to my parents Gilberto Pietri and Palmira
Santiago, who made it possible for me to complete my education. There is no
way to measure the amount of support and advice I have received from these two
wonderful human beings. I give thanks to an all-powerful, everlasting God for my
parents, and for the opportunity to pursue my goals and dreams. I also thank my
relatives for all their support during my years at UF.
The most influential person in this project was my research advisor, Dr. Bohdan
Andraka. He was the source behind many of the ideas on this dissertation. He
was also a great mentor in the lab, from whom I learned countless experimental
tricks. He has my deepest appreciation. The second most influential person was
Prof. Greg Stewart, an endless source of information. I thank him very much for
letting me work in his lab. His written work inspired me throughout my gradu
ate career. I would also like to thank my other committee members, Prof. Mark
Meisel, Prof. Pradeep Kumar, and Prof. Cammy Abernathy for their patience in
reading this work, for many discussions, and for their advice regarding this dis
sertation. My appreciation also goes to people whom I worked with in the lab
over many years. I thank Dr. Jungsoo Kim and Dr. Steve Thomas for their train
ing and technical advice, and Josh Alwood and Dr. Hiroyuki Tsujii for help in
the lab and with some of the experiments. Greg Labbe and the people at the
Cryogenics Lab were also very helpful, especially while using the magnet dewar.
Other people in this field I would like to acknowledge are Prof. Kevin Ingersent, for
many discussions about my research and for an excellent collaboration; Prof. Peter
Hirschfeld for introducing me to the theory of heavy-fermions and to the Kondo


effect; and Dr. Ray Osborn and Dr. Eugene Goremychkin, whose work motivated
part of this study, for very enlightening discussions over the last year and during
the 2000 APS March Meeting. I am indebted to Dr. Youli Kanev and my good
friend Dr. Mike Jones for developing the DT^X UF thesis template, which greatly
simplified all of the formatting work, and to my fellow graduate students, especially
Rich Haas, Dr. Tony Rubiera, and Brian Baker for interesting physics discussions
and advice. My thanks go also to Susan Rizzo and Darlene Latimer for all the
grad-school related paperwork and for taking care of my registration over the years.
Finally, my life would have been unbearable without the company and emo
tional support of many people here in Gainesville, FL. They helped me stay
motivated and cope with the ups and downs of Physics Graduate School. I would
like to thank my dearest friends James Bailey, Ferdinand Rosa, Dr. Carlos (Caco)
Ortiz, Ivn Guzmn, Clinton Kaiser, Dr. Fernando Gmez, Soraya Benitez, Cristine
Plaza, Diana Serrano, Jorge Carranza, Franco Ortiz, Lyvia Rodriguez, Anthony
Wells, Diana Hambrick, and Charles and Sarah Reagor. I apologize to the countless
others who are not on this list, including the people at the Southwest Recreation
Center, the Worldwide Church of God, Latin nights at the Soul House, Saoca,
La Sala, Rhythm, and all the tailgators over the years.
m


TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ii
ABSTRACT vii
CHAPTERS
1 INTRODUCTION 1
2 THEORETICAL BACKGROUND 6
2.1 Landau Fermi-Liquid Theory 6
2.1.1 Theoretical Basis for a Fermi-liquid 7
2.1.2 Thermodynamic and Transport Properties 10
2.2 Localized Magnetic Moments in Metals 11
2.2.1 Electronic States of Magnetic Ions 12
2.2.2 Anderson Model 14
2.3 Single-ion Kondo Model 18
2.4 Anisotropic Kondo Model 20
2.5 Kondo Lattice 27
2.6 Non-Fermi-Liquid Effects 30
3 PROPERTIES OF CeAl3 AND CePb3 34
3.1 Properties of CeAl3 34
3.1.1 Crystal Structure 34
3.1.2 Specific Heat 36
3.1.3 Magnetic Susceptibility 37
3.1.4 Transport Measurements 40
3.1.5 Nuclear Magnetic Resonance 42
3.1.6 Muon Spin Rotation 45
3.1.7 Neutron Scattering 48
3.1.8 Chemical Substitution Studies 48
3.2 Properties of CePb3 51
3.2.1 Crystal Structure 51
3.2.2 Specific Heat 51
3.2.3 Sound Velocity Measurements 54
3.2.4 Transport Measurements 58
3.2.5 Magnetic Susceptibility 60
3.2.6 Neutron Scattering 63
3.2.7 Chemical Substitution Studies 65
IV


4 MOTIVATION 68
4.1 Importance of CeAl3 and CePb3 68
4.2 Objectives 70
4.2.1 Magnetism and Heavy-Fermion Behavior in Ce Kondo Lattices 70
4.2.2 Ground State of CeAl3 71
5 EXPERIMENTAL METHODS 73
5.1 Sample Preparation 73
5.1.1 Synthesis 73
5.1.2 Annealing 77
5.2 Diffraction of X-Rays 78
5.3 Magnetic Measurements 79
5.4 Specific Heat Measurements 80
5.4.1 Equipment 82
5.4.2 Thermal Relaxation Method 86
5.5 Experimental Probes 89
5.5.1 Experiments on CeAl3 90
5.5.2 Experiments on CePb3 91
6 STRUCTURAL AND THERMODYNAMIC PROPERTIES OF CeAl3 AL
LOYS 93
6.1 Lattice Parameter Study of CeAl3 Alloys 93
6.1.1 Lanthanum Doping: Cei_xLaxAl3 96
6.1.2 Yttrium Doping: Cei_xYxAl3 100
6.1.3 Mixed Doping: Ceo.8(Lai_xYx)0.2Al3 108
6.1.4 Summary 113
6.2 Thermodynamic Measurements of Cei_xLaxAl3 Alloys 116
6.2.1 Magnetic Susceptibility 116
6.2.2 Specific Heat 118
6.2.3 Discussion 127
6.3 Thermodynamic Measurements on Cei_xYxAl3 Alloys 134
6.3.1 Magnetic Susceptibility 134
6.3.2 Specific Heat 137
6.3.3 Discussion 139
6.4 Thermodynamic Measurements on Ce0.8(Lai_xYx)0.2Al3 Alloys . 141
6.4.1 Magnetic Susceptibility 141
6.4.2 Specific Heat 144
6.4.3 Discussion 147
6.5 Heat Capacity of Ce0.8La0.2Al3 and Ce0.3La0.7Al3 in Magnetic Fields 153
6.5.1 Results 154
6.5.2 Discussion 157
v


7 MAGNETIC FIELD STUDY OF CePb3 ALLOYS 165
7.1 Specific Heat of CePb3 in Magnetic Fields 165
7.2 Single-Ion Kondo Behavior of Ceo.6Lao.4Pb3 in Magnetic Fields . 175
7.2.1 Results 175
7.2.2 Discussion 179
8 CONCLUSION 184
8.1Summary 184
8.1.1 Ideas for Future Work 187
REFERENCES 189
BIOGRAPHICAL SKETCH 198
vi


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
MAGNETISM AND THE KONDO EFFECT IN CERIUM HEAVY-FERMION
COMPOUNDS CERIUM-ALUMINUM-3 AND CERIUM-LEAD-3
By
Richard Pietri
August 2001
Chairman: Bohdan Andraka
Major Department: Physics
Measurements of the lattice parameters, magnetic susceptibility, and specific
heat between 0.4 and 10 K in magnetic fields up to 14 T have been conducted on
Cei_xMxAl3 alloys, with M = La (0 of CePb3 and Ce0.6Lao.4Pb3 was also measured up to 14 T. The above experiments
were performed to study the anomalies in the specific heat of CeAl3 and CePb3,
and to better understand the interplay between magnetism and Kondo behavior
in the ground state of Ce heavy-fermion systems.
Data for x-ray diffraction of Cei_xMxAl3 confirmed an anisotropic lattice
volume expansion for M = La (decreasing c/a ratio) and a contraction for M =
Y. The low-temperature magnetic susceptibility and specific heat of Cei_xLaxAl3
are consistent with Doniachs Kondo necklace model. The electronic coefficient
7 decreases with Y concentration, and has a nonmonotonic dependence for M
= La with a minimum at x 0.2. The temperature position of the anomaly
Tm has a maximum around x = 0.3 for La doping. The lack of a suppression
vn


of Tm for Y x < 0.2 suggests a dependence of this maximum on the absolute-
value change in c/a. Magnetic field measurements on La-doped CeAl3 alloys
revealed that the field dependence of Tm is inconsistent with the anisotropic Kondo
model, with Tm for Ceo.sLao.2Al3 decreasing only by 0.4 K at 14 T. Experiments
on Ceo.8(Lai_xYa;)o.2Al3 revealed that C/T oc \ oc T~1+x for x = 0.4, with A
comparable to that of heavy-fermion alloys with scaling similar to that associated
with a quantum Griffiths phase.
Specific heat measurements up to 14 T on polycrystalline CePb3 indicated
a shift in X^ to lower values, disappearing for H > 6T. The ratio A/72 is field-
dependent below 6T. Studies on Ceo.6Lao.4Pb3 revealed that the electronic specific
heat AC of this alloy can be described by the single-ion Kondo model in magnetic
fields, with T/c 2.3K. A previously undetected anomaly in C/T was found below
2K, shifting toward higher temperatures with increasing field. This maximum
appears to be a feature of the Kondo model in magnetic fields.
vm


CHAPTER 1
INTRODUCTION
Over the last century, our current understanding of the metallic state developed
as a result of substantial experimental and theoretical work based on the discov
ery of the electron by J. J. Thomson in 1897 and the advent of modern quantum
physics. The behavior of solids has long been described in terms of the dynam
ics of its constituents, electrons and nuclei; with the former being responsible for
electrical conduction and dominating the thermodynamic properties at very low
temperatures. This single-electron picture of the solid state has been remarkably
successful in describing the properties of many body systems that, as a whole,
are much more than a simple array of atoms. The current picture of a lattice
of ions embedded in a gas of electrons obeying Fermi-Dirac statistics is justified
by the theoretical framework set by Landau on his Fermi-liquid theory, for which
he won the Nobel Prize in 1962. Based on the principle of adiabatic continuity,
the theory states that the metallic state at low temperatures can be described
quantum-mechanically in terms of a fluid of weakly-interacting particles (Fermi-
liquid, see Chapter 2). The properties of this quantum fluid are similar in form
to those of a gas of noninteracting electrons. Landaus Fermi-liquid theory has
been successfully applied to a variety of systems, including liquid 3He and normal
metals like Au and Ag. It is one of the foundations of modern condensed matter
physics, rivaled in its scope only by the standard model of particle physics.
Since the development of Fermi-liquid theory, the synthesis of new materials
displaying unusual properties presented challenges to this well-established descrip
tion of condensed matter systems. A large number of these materials exhibit strong
1


2
electron correlations in their normal (paramagnetic) state, stretching the limits of
applicability of Fermi-liquid theory. In some materials, the effect of these interac
tions is reflected in the deviations of their thermodynamic and transport properties
from the predictions of this theory. This group includes the normal state of high-
temperature superconductors and non-Fermi-liquid systems [1, 2, 3]. In others,
their normal-state properties remarkably agree with Fermi-liquid theory, despite
the presence of strong interactions between electrons and even the coexistence with
a magnetic phase. It is in this group that we find most heavy-fermion compounds.
Heavy-fermion sytems are alloys where one of their constituents is a member
of the lanthanide (Ce, Yb) or actinide (U, Np) family. They are so called because
the effective mass of the particles dominating the thermodynamics, which have
half-integer spin (fermions), is hundreds of times that of a free electron (heavy).
Extensive reviews on these systems have been written over the last two decades [4,
5, 6, 7, 8]. In these systems, the interactions between localized / electrons and the
conduction band reduce the / magnetic moment and give rise to a Fermi-liquid
like state at low temperatures. The large effective mass m* is a consequence of the
large density of states at the Fermi energy N(0).
The most widely used experimental parameter to determine both the density
of states and the effective mass of these particles is the Sommerfeld coefficient
of the specific heat 7. In Fermi-liquid theory, 7 is proportional to both m* and
iV(0). The specific heat of metals in their normal state at low temperatures is
approximated by the following formula [9, 10]:
C = yT + 0T3, (1.1)
where 7 is the electronic contribution and (3 is the Debye contribution from lattice
vibrations. Values of 7 for heavy-fermion compounds typically range from several
hundred to several thousand mJ/K2mol, compared to less than one for normal
metals like Cu and Au. The presence of additional contributions to the specific


3
heat makes the determination of 7 more difficult, and 7 is usually represented as
the extrapolated value of C/T at zero temperature.
The heavy-fermion character is also reflected in other properties, like mag
netic susceptibility and electrical resistivity. The magnetic susceptibility at high
temperatures follows the Curie-Weiss form [9, 10],
C
x~ r + eow
where C is the Curie constant and cw is the Curie-Weiss temperature. At lower
temperatures, the susceptibility reaches a constant value (~10 to 100 memu/mol),
proportional to the density of states N{0) according to Fermi-liquid theory. The
electrical resistivity of metals at very low temperatures is given by
P Po + AT2. (1.3)
Here, p0 is the temperature-independent term due to scattering off impurities and
defects, and A is the Fermi-liquid term. Values for A in heavy fermions are in
the order of tens of /iQcm/K2, much larger than those corresponding to normal
metals.
An intriguing fact of heavy-fermion systems is that the observed Fermi-
liquid properties are not exclusive to the normal state of these materials. The
variety of ground states for these compounds [5, 6] ranges from nonmagnetic, as
in UPt4Au [11], to antiferromagnetic (UCu5, U2Zni7, CeAl2) to superconduct
ing (UBei3, CeCu2Si2), to both magnetic and superconducting (UPt3, URu2Si2,
UPd2Al3, UNi2Al3). The presence of magnetism and/or superconductivity in these
compounds indicates that the heavy Fermi-liquid ground state coexists with a dif
ferent phase.
This unconventional ground state, when tuned as a function of pressure,
magnetic field, and/or chemical disorder, can completely move away from Fermi-
liquid behavior. These non-Fermi-liquid (NFL) alloys have been widely studied


4
during the last decade [3, 12]. Their thermodynamic and transport properties are
characterized by power laws in temperature. Theoretical models for the description
of these effects are currently under development. Examples of these systems [3, 12]
include UCu5_xPdx, CeCu6-xAux, Ui_xYxPd3, Ce7Ni3 (pressure-induced NFL),
and CeNi2Ge2 [13], U2Pt2In, and U2Co2Sn [14] (NFL compounds).
Among the many unresolved issues in heavy-fermion materials is the coex
istence of magnetic and Fermi-liquid degrees of freedom giving rise to the ground
state. In addition, a recent interpretation of the ground state in terms of an
anisotropic interaction between / electrons and the conduction band has been
proposed for these systems [15]. Both topics are confronted in this dissertation
by studying structural and thermodynamic properties of two well-studied canoni
cal heavy-fermion compounds: CeAl3 and CePb3. Cerium-based compounds were
chosen because of their simpler electronic configuration. There is only one 4/ spin
per Ce ionic site, as opposed to two or three 5/ spins per U ionic site. The ground
state properties of the above compounds are not well understood, despite more
than 20 years of study. The experiments presented here will help clarify these
issues in order to motivate further discussion of these topics on both theoretical
and experimental grounds.
The outline of the dissertation is as follows: The necessary theoretical back
ground behind heavy-fermion physics is presented in Chapter 2. The chapter
begins with an overview of Landaus Fermi-liquid theory, followed by a discussion
of the energies involved in the determination of the ionic ground state and mag
netic moments in metals. The Kondo effect, the mechanism responsible for the
Fermi-liquid state at low temperatures in heavy fermions, is then presented along
with its anisotropic version. The concept of a Kondo lattice is also introduced,
and the consequences of extending the Kondo model to a concentrated system
are discussed. Chapter 3 gives an experimental review of the essential physical


5
properties of both CeAl3 and CePb3. It is then followed by a discussion of the
motivation behind this study (Chapter 4). Chapter 5 gives a general description of
the experimental apparatus and methods used in this dissertation. The results of
structural and thermodynamic measurements on CeAl3 and CePb3 alloys are then
explained in Chapters 6 and 7, respectively. Finally, Chapter 8 summarizes the
main findings of the dissertation and elaborates on its contributions to the field.
The dissertation ends by pointing out unresolved issues and elaborating on ideas
for future studies.


CHAPTER 2
THEORETICAL BACKGROUND
This chapter discusses the current theoretical models describing the charac
teristics and behavior of heavy-fermion systems, such as Fermi-liquid theory, ionic
configurations in solids, and the Kondo effect.
2.1 Landau Fermi-Liquid Theory
Landaus theory of interacting fermions at low temperatures [16] stands as
one of the most remarkable achievements of theoretical condensed matter physics.
It has often been compared to the standard model of elementary particle physics,
as far as its scope and prediction of physical properties is concerned. The basis
of its success is the adaptation of the Fermi gas model of noninteracting electrons
to a system of interacting fermions at low densities and energies. This mapping
allows for a single-particle description of thermodyamic and transport properties
of Fermi systems like liquid 3 He and normal metals like copper, silver, and gold.
Although Landaus Fermi-liquid theory has been successfully applied in a large
number of condensed-matter systems, its validity relies on a series of assumptions
that apply mostly to weak interactions and isotropic scattering between fermions.
Heavy-fermion systems, often described as having a Fermi-liquid ground state,
exhibit strong many-particle correlations that lead to magnetic order in many cases.
The relation between magnetism and Fermi-liquid behavior in heavy fermions is
at present not fully understood. Nevertheless, the theory has been successful
in predicting the properties of these compounds. In this section, the differences
6


7
between Fermi-gas and Fermi-liquid models are outlined, followed by a description
of thermodynamic and transport properties of the Fermi liquid.
2.1.1 Theoretical Basis for a Fermi-liquid
For a system of noninteracting particles obeying Fermi-Dirac statistics, with
mass m, momentum p and spin a, the probability of finding a particle with energy
e is given by the Fermi distribution function n(e) [17],
n(e)
1
X _|_ e{e-n)/kBT
(2.1)
where kB is Boltzmanns constant and pi = £p, the Fermi energy. The spins are
assumed to be quantized along the 2-axis.
In the absence of an external field, the energy of a particle becomes e = ep
p2/2m, and the ground state distribution is given by
1 P< Pf
nPa =
(2.2)
I 0 p > pF
where Pf is the Fermi momentum. The ground state energy of the system E0 is
equal to
£o = E"p£p- (2.3)
pa
The total energy is the sum of the ground state energy and the excitation energies
of the system. The number of excitations is given by the difference between the
ground-state and excited-states distribution functions:
8fipa = Tlpcr npai (2*4)
where 8npa > 0 corresponds to a particle excitation and 8npa < 0 to a hole excita
tion. Since the excitation energies depend on the number of excitations, the total
energy of the system can be expressed as
E Eq + ^ ] Ep 8npa.
pa
(2.5)


8
Despite the strong electrostatic forces between electrons in a solid, the Fermi
gas model for noninteracting electrons is capable of describing their behavior in
metals. At metallic electron densities, the kinetic and Coulomb energy terms are
comparable in magnitude to each other. The justification for the predictions of this
model come from their close resemblance to those of the interacting case. Through
adiabatic continuity [16], it is possible to label the states of an interacting Fermi
system in terms of the states of a Fermi gas. When the interaction potential is
treated as a perturbation, and is turned on slowly enough to prevent a change in
the eigenstates of the Hamiltonian, there is a one-to-one correspondence between
the initial and final states. The excitation energies of the final state are different
from those of the Fermi gas because of the additional interaction term in the
Hamiltonian. The final state has also the same entropy and can be described by the
same distribution function as the noninteracting Fermi gas. The system resulting
from the adiabatic perturbation is called a Fermi liquid. The excited states of a
Fermi liquid are no longer associated with independent electrons, but to negatively
charged, spin-1/2 fermions called quasiparticles, with an effective mass m* different
from that of a free electron. These quasiparticles have a sufficiently long lifetime
t between collisions at low temperatures. The condition for the applicability of
Fermi-liquid theory is that the uncertainty in the energy of a particle, of order
Ti/t oc (kBT)2, is much smaller than the width of the excitation spectrum of the
Fermi distribution function, of order kBT [18]:
h/r < kBT. (2.6)
This condition applies to a system with excitation energies much smaller than kBT.
Due to the mutual interaction between quasiparticles, the total energy of
the system is no longer represented by the sum of ground state and individual
excitation energies. As a consequence, each quasiparticle is under the influence
of a self-consistent field from other quasiparticles. This self-consistent field affects


9
both potential and kinetic energy terms of each individual quasiparticle. The
energy E then becomes a functional E{npa} of the distribution function. The
excitation (quasiparticle) energy, which itself is a functional of the distribution
function, (e = £{np(T}), has an additional term corresponding to the interaction
energy between two quasiparticles /pa.pV', each with momentum and spin p pV, respectively. This energy term is also a functional f{npa} of the distribution
function, so that the quasiparticle energy becomes an expansion in terms of the
number of excitations 8npa [19]:
£pa £pa T fpa,p'a' 8npiai -f- ..., (2-7)
p 'a'
where £pcr is the ground-state quasiparticle energy. As a result, the total energy of
the system is also an expansion in 8npa:
E Eq + 'y ] Epa Snpcr T y ^ fP(t p'a' 8fipa 5np> a' T ... (2-8)
P<7 pa p'a'
When considering an ensemble of quasiparticles with spins quantized along
different axes, the distribution function npa should be treated as a 2 x 2 matrix in
spin space, that is, as a linear combination of the Pauli matrices. In the absence of
higher-order scattering processes, like spin-orbit coupling, the interaction energy
can be expressed as the sum of symmetric and antisymmetric (spin-dependent)
terms
fpp' = /pp' + /pp' t-t\ (2.9)
where fpp, and fpp, are the symmetric and antisymmetric terms, respectively,
and r, r' are Pauli matrices. Both /*p, and fpp, are dependent on the angle
between p and p', and can be expressed as an expansion in Legendre polynomials,
with coefficients ff and /, in the case of isotropic scattering (spherical Fermi
surface). In some metals, the presence of crystal-field and spin-orbit coupling
effects significantly distorts the Fermi surface, changing the angular dependence of


10
/pp, and /pp/. The Landau parameters Fts and F are defined with respect to the
coefficients ff and / corresponding to isotropic scattering:
Ff = 1V(0) ft,
Ft = N(0) ft,
(2.10)
where N(0) is the density of states at the Fermi energy.
2.1.2 Thermodynamic and Transport Properties
Since the total energy of the system of quasiparticles is an expansion in terms
of the variation in the distribution function Snp(T, it follows that the thermodynamic
properties are expansions in powers of the temperature. The first term of the
expansion corresponds to the result for the noninteracting Fermi gas. Subsequent
terms are finite temperature corrections due to coupling with spin fluctuations
within the interacting fermion fluid.
The specific heat of a Fermi liquid is given by:
C = 'yT + aT3 In T + ... ,
(2.11)
where the Sommerfeld coefficient 7 is
27Fkl
7 =
klm* z
N(0) = TiT
(2.12)
3 ' 3 fit
The first term is linear in temperature, and proportional to the effective quasipar
ticle mass m*. The effective mass is related to the free-electron mass m by
- =1 + ^
(2.13)
where F* is one of the Fermi-liquid parameters. The second term in the specific
heat is a smaller correction and originates from quasiparticle coupling to spin
fluctuations.
The magnetic susceptibility is independent of the temperature to first order:
h2 72iV(0)
X = 2/rffiV(0) + ... =
4 1 + Fn
+ ... ,
(2.14)


11
where /eff corresponds to the quasiparticle effective magnetic moment, 7 is the
linear coefficient of the specific heat, and Ffi is a Fermi-liquid parameter. The
second term in the expansion is of order T2 In T.
The electrical resistivity due to quasiparticle scattering is inversely propor
tional to the time between collisions r, and proportional to the square of the
temperature [20]:
2 = 7r2e2m(76.06) / T_\2
P 16N(0)h3 \T*f )
where e is the electronic charge, m is the mass of a free electron, h is Plancks
constant, and TF is the effective Fermi temperature of the Fermi liquid.
2.2 Localized Magnetic Moments in Metals
Electrons in metals are not entirely free particles. They are constantly under
the influence of a periodic potential due to a charged lattice. In addition, the
distances between electrons are close enough for the Pauli exclusion principle to
play an important role in the formation of energy levels. In general, electrons with
energies in the vicinity of the Fermi energy tend to be delocalized and form part of
the conduction band. To a first approximation, the equation of motion of nearly-
free electrons is given in the Hartree-Fock form. Orbital states within a single ion
are formed by electrons with energies below £p, and are more localized. Their wave
functions retain some ionic character. For the most part, the thermodynamics of
a metallic system in its normal state can be described by taking into account
the individual contributions of quasiparticles (Fermi-liquid theory) and localized
free spins. However, in many systems, the lattice of localized electrons near or
below the Fermi level strongly interacts with conduction electrons. The resulting
potential can have a major effect on the thermodynamics not accounted for by
nearly-free electron models. In order to understand the behavior of 4/ magnetic


12
moments in metals, it is important to have a knowledge of the interactions that
give rise to their formation.
2.2.1 Electronic States of Magnetic Ions
The localized states of electrons in metals are similar to those of free magnetic
ions [21]. For each energy level n, there are (2s + l)(2/ + l) degenerate states, where
n, /, and s are the principal, orbital, and spin quantum numbers, respectively. The
degeneracy is partially lifted by the electron-electron Coulomb interaction, of order
10 eV. These energy levels, called multiplets, are filled up according to Hunds rules
and the Pauli exclusion principle. Once all 2(2/ + 1) levels are fully occupied, the
sum total of spin and orbital angular momenta equals zero, so that a filled shell
has no magnetic moment.
In an incompletely filled shell, one of two relevant interactions responsible
for lifting any additional degeneracies is spin-orbit coupling. The spin of each
orbiting electron couples with an effective magnetic field due to its motion about
the nucleus. The effective field is proportional to the orbital angular momentum
of the electron. The total spin-orbit interaction is then given by
nso = A(L-S) = gnlz + (L-S), (2.16)
where g is the electron p-value, gB is the Bohr magneton, Zeff is the effective
atomic number, and L and S are the total orbital and spin angular momenta,
respectively. The coefficient A is positive when the shell is less than half-filled, and
negative for more than half-filled. The coupling between L and S has an effect on
the eigenstates of the ionic Hamiltonian. Both operators are no longer constants
of the motion, and the states are now labeled by the total angular momentum
J = L + S. As a consequence, the degenerate states of each multiplet split into
25+1 levels for L > S or 2L+1 levels for L < 5, each carrying a 2J+1 degeneracy.


13
The second interaction responsible for the splitting of degenerate energy lev
els of a multiplet is due to the surrounding ions. Crystal-field effects represent the
influence of Coulomb interactions from neighboring charges on localized states.
The crystal-field contribution is given by the net Coulomb energy due to point
charges located at the different crystallographic sites, and by the direct Coulomb
interaction between the outermost localized orbitals of surrounding ions. To a first
approximation,
^cef ~ ^cEF(r) = ~e^2 i i > (2-17)
i ij lr rV?'l
where Rj and Zej are the position vector and charge of the jth ion, respectively,
and r and e indicate the position and charge of the electrons. The potential
Keep can be expressed in polar coordinates and expanded in terms of the spherical
harmonics Ylm{6, ). The result is an expansion in powers of (r) and of the angular
momentum operators L2 and Lz (or J2, Jz). The crystal-field interaction partially
lifts the degeneracy of the ionic states. The number of states is determined by
the symmetry of the crystal structure, and typically increases for structures of low
point-group symmetry.
In solids with magnetic ions, the relative strength of spin-orbit and crystal-
field energies depends on the localized character of the wave function corresponding
to the incompletely-filled shell. The spin-orbit interaction increases as the distance
from the nucleus decreases (Hso oc (1/r3)). The crystal-field contribution HCef, on
the other hand, increases with the radial extent of the wave function. For electrons
in incomplete d orbitals, HcEF > Hso due to their direct interaction with orbitals
from neighboring ions. In contrast, electrons in incomplete / orbitals are very
localized and reside close to the nucleus. Therefore, the spin-orbit interaction is
very large (> 0.1 eV), and the crystal-field contribution 7YCef comparatively smaller
(> 0.01 eV). As a consequence, the lowest-lying multiplet is first split by the spin-


14
orbit interaction, and each of these levels is split further by the crystal field. The
ground state of the system is the crystal-field ground state. For example, in Ce3+,
there is only one 4/ electron (S |), and the lowest-lying multiplet corresponds
to L = 3. Hso splits the multiplet into two 6-fold degenerate levels: \J = |) and
| J = |). The lowest-energy level (J = |) is then split by 7YCEF into a doublet
and a quartet for cubic crystal symmetry and into three doublets in the case of
hexagonal symmetry. For a crystal-field doublet ground state, the effective total
angular momentum of Ce3+ is J = \.
2.2.2 Anderson Model
The fundamental problem in magnetic alloys (including heavy-fermion sys
tems) is the coexistence and interaction of the electron liquid with localized atomic
orbital states. From this point of view, the conduction band is formed primarily
of electrons in the outermost s and p shells, and the localized states consist of d
or / orbitals in iron-group and rare-earth ions, respectively. The following discus
sion will focus on localized / states. Electrons in a partially-filled / shell have
a finite probability of mixing and are free to interact with the conduction band
if their energy is close to the Fermi level. The interaction with the conduction
electrons regulates the average occupancy and magnetic moment of the / level.
This problem was described by Anderson [22] in the following Hamiltonian for a
single impurity embedded in a free-electron environment:
n^ = Ho + Hof + Hff + Hcf, (2.18)
The first term is the unperturbed free-electron Hamiltonian:
Wo = E£k"i- (219>
kcr
Here, is the energy of a free-electron state with wave number k and spin and rika is the number operator


15
Tlkcr Q'kcr^'kcri (2.20)
with aj^ and aka the creation and anihilation operators, respectively, for a free
electron state with labels k and a. The second term is the unperturbed energy of
the localized / level:
tto/ = ££/n/a, (2.21)
G
where Ef corresponds to the energy of the / level and
nfa = a)aafa- (2-22)
The third term represents the on-site Coulomb repulsion between two / elec
trons of opposite spin:
Tiff = UrifiTifi, (2.23)
with U the Coulomb integral between the two / states, and n/j and n/ the number
operators for / states with up and down spin, respectively. The last term denotes
the mixing between conduction electrons and the / orbital:
Hcf = ^2 Vkf(ak*afv + a/aaka)- (2.24)
k G
Here 14/ is the hybridization matrix element between localized and conduction
electronic states.
The effect of the Anderson Hamiltonian on the localized / states depends on
the relative magnitudes of the Coulomb and mixing terms. The Coulomb repulsion
U determines the separation of the up and down spin / levels with respect to each
other. The hybridization term 14/ is responsible for a broadening of the / levels,
which determines the overlap between the lowest / state and the Fermi energy.
These levels are represented by a Lorentzian of width 2T, where
r = 7r|vk/|2Jv(o),
(2.25)


16
and N(0) is the density of states at the Fermi energy. Figure 2.1 illustrates the
density of states of up and down-spin free-electrons and localized levels for different
relative strenghts of Coulomb repulsion and mixing width. For U |\4/|, the
localized up and down-spin levels (d or /) have a small width 2r and are well
separated by U. The down-spin level resides far above the Fermi energy and is
therefore unoccupied, favoring the formation of a strong local magnetic moment. If
the energy of the up-spin state is close to the Fermi energy in the limit U > oo, the
localized moment couples strongly with the conduction band (Kondo effect). This
scenario corresponds to integer valence, and is conducive to the formation of the
heavy-fermion state when the impurity concentration is of the order of Avogadros
number and the magnetic ions achieve the periodicity of the crystal lattice. For
U ~ 114/1, both localized levels are significantly broad and might overlap with the
Fermi energy due to a reduction in U. An overlap with the conduction band results
in partial occupancy of both up and down-spin levels, leading to mixed valence and
the formation of a weak local magnetic moment. In the limit |I4/| 0, both
levels have the same energy and occupancy and the impurity loses its magnetic
moment.
By studying the limit in which F<^Ef, Schrieffer and Wolff [24] were able to
perform a canonical transformation on the Anderson Hamiltonian that eliminates
the hybridization term 14/ Instead, the transformed Hamiltonian is expressed in
terms of Ho, Hof, H//, and an exchange interaction between /-ion and conduction
electron spins
Kx = -EJkk'Sk-S/, (2.26)
kk'
where Sk and S/ are the spin polarization of the conduction electrons and the spin
of the impurity, respectively, and Jkk/ the exchange coupling constant. Close to
the Fermi level, k, k' ~ k/r, and Jkk> becomes


17
NE) NU nH
NUE)
L2r
ni (a
NU NUE) NU
Figure 2.1: Spin-up and spin-down electronic density of states distributions for a
localized d orbital embedded in a sea of conduction electrons. Upper left: U =
|Vk/| = 0; upper right: U|14/|; lower left: U|Vk/|; lower right: U 0) (from Mydosh, 1993) [23].


18
JkFkF J 2|VkF/| + U) < (2.27)
where J is the Kondo coupling constant. In this manner, the Anderson Hamilto
nian effectively transforms into the Kondo Hamiltonian in the limit T W(0)J<1).
2.3 Single-ion Kondo Model
The Kondo problem is that of a single localized magnetic impurity in a metal
lic host. This scenario corresponds to the above-mentioned U oo limit of the
single-impurity Anderson model, with Ef close to the Fermi level. The following
discussion refers to the case of a spin-| impurity in a sea of conduction electrons, as
in the crystal-field ground state of Ce3+. As the temperature decreases, the local
ized / orbital hybridizes with the conduction band, spin-flip scattering increases,
and a scattering resonance appears near the Fermi level, known as the Kondo
or Abrikosov-Suhl resonance. The Hamiltonian describing these processes is the
Kondo (or s-d) Hamiltonian, of the form
^Kondo=-jE^)(^-S),
(2.28)
where J is the effective coupling constant between / and conduction electrons (as
in Eq. 2.27), S is the localized spin, and s and r represent the zth conduction-
electron spin and position vector, respectively. In the case where both Ef and
U + Ef are symmetric with respect to the Fermi energy (U/2 \ep Ef |),
\VkFf\2
J OC
I £f Ef I
(2.29)
where £p is the Fermi energy. A perturbation treatment of 7iKondo beyond the
Born approximation leads to an expansion of the thermodynamic and transport
properties in powers of JN(0) In(kBT/D). Here, iV(0) is the density of states at the


19
Fermi energy and D is the bandwidth of scattering states. The electrical resistivity
was calculated by Kondo [25] using third-order perturbation theory:
kBT\
P = Pb 1 + 2JN{0) In
D
(2.30)
The constant term
3 77T7T J2 0(0 ^
PB = 2^hte~FS{S + l)'
(2.31)
obtained from the Born approximation, is a residual resistivity term due to the
presence of the magnetic impurity. The third-order term diverges at low tempera
tures. The specific heat and magnetic susceptibility due to the impurity are given
by
C = (-J7V(0))47t2S(S + l)fcB ( 1 + 4JiV(0) In
kBT
D
+ ...
(2.32)
and
X =
gyBs(g + i)
3/crT
kBr
1 + JN(0) ^1 JN(0) In D
-l
(2.33)
respectively. The perturbation treatment for J < 0 breaks down at a temperature
fcBr* = Z)exp(-^y (2.34)
The temperature T'k is called the Kondo temperature.
At low temperatures (T TV), the impurity spin strongly couples with
the conduction electron spin polarization, forming a many-body singlet that com
pletely suppresses the localized magnetic moment at T = 0. In this range, the
thermodynamic and transport properties can be described by Fermi-liquid theory
due to the absence of an impurity spin. The zero-temperature susceptibility of the
impurity is inversely proportional to the Kondo temperature [26],
(2.35)
1 \2 1.29
Xo = I -z9Pb
nkBTK'
and the linear coefficient of the specific heat 7 is given by


20
7=1-29^. (2.36)
The ratio of the magnetic susceptibility to the electronic specific heat coefficient
7, called the Wilson ratio, is given by
Xo = 3 fg¡iB\2
7 2\TrkB)
This value is twice that corresponding to the noninteracting electron gas.
The exact solution to the Kondo Hamiltonian and its thermodynamic prop
erties in terms of T < Tk and T > Tk and a range of magnetic fields were
obtained using the Bethe ansatz [26, 27, 28, 29]. The above equations follow the
exact solution obtained with this method. Numerical solutions for the specific heat
and the magnetic susceptibility of a spin-^ impurity in different magnetic fields are
illustrated in Figs. 2.2 and 2.3. The zero-field specific heat reaches a maximum
at a temperature just below Tk- Both the magnitude and the temperature posi
tion of the maximum increase with field, reaching a shape corresponding to the
Schottky anomaly of a free uncompensated spin-| at large fields gfiBH kBTx,
where g is the g-factor of the magnetic impurity. The zero-field magnetic suscep
tibility shows a Curie-like increase for T > Tk, and then saturates until it reaches
a temperature-independent value well below Tk. A maximum associated with the
Schottky anomaly of the specific heat appears around Tk for g[iBHjkBTK = 2 [30].
Its temperature position increases, while its magnitude decreases with increasing
field.
2.4 Anisotropic Kondo Model
The anisotropic Kondo model (AKM) [31, 32] refers to the problem of a
single magnetic impurity coupled to the conduction electrons via an anisotropic
exchange interaction J>J||, Jj., where The Hamiltonian is given by


susceptibility
21
10- 10-* 10* 10 10 10* 10
Figure 2.2: Specific heat of a S = | Kondo impurity as a function of T/TK for
different magnetic fields (H > gg,BH/kBTK) [30].
Figure 2.3: Magnetic susceptibility of a S = | Kondo impurity as a function of
T/Tk for different magnetic fields (H > g¡iBH/kBTK) [30].


22
Hakm = Y, 4,A* + ^ (4TCfc'i5 + 4|Cfc'T5+) +
k,a Z fcfc'
(cfc|cfc'T cfcicfcU)5z + gfiBhSz, (2.38)
z jfcfc'
where 4a and are the conduction electron creation and anihilation operators,
5+ and S'- are the impurity spin raising and lowering operator eigenvalues, and Sz
is the impurity spin value in the z direction. The first term in 7YAKM represents the
conduction-electron energies, the second and third terms represent the in-plane
(J) and easy-axis (Jy) exchange interactions between a localized spin and the
conduction electrons, respectively, and the last term corresponds to the Zeeman
energy due to a local magnetic field h applied only to the impurity spin S. The
Kondo temperature for an anisotropic exchange interaction (Jy < 0) is given in
terms of Jy and J_ as [21, 33]
kBT^ = Dex p
-1
MO) yjf Jl
x tanh 1
(2.39)
where N(0) is the density of states and D is the bandwidth. The exponential
dependence of the Kondo temperature in the parameter J\\ is qualitatively similar
to the J dependence of Tk in the isotropic case.
The Hamiltonian for an anisotropic Kondo interaction has been used suc
cessfully to evaluate the properties of the spin-boson Hamiltonian [34, 35, 36, 37],
which describes the dissipation in the dynamics of a two-level system by an Ohmic
bosonic bath. A mapping of the spin-boson model [38] onto the AKM has been
exploited to calculate the thermodynamic properties of the former model. Further
more, the parameters of the spin-boson model have recently been used to describe
the properties of the AKM applied to the heavy-fermion system Cei_a;LaxAl3 [15].
The spin-boson Hamiltonian has the form


23
7"SB c\ ^ c\ ^ ^ ^Ol
z z a
\qo ^ E ,?* t ; (a + 4)- (2-40)
2 a yj TTIqUJch
Here ox and az are Pauli matrices, A is the tunneling energy between the two
states and e is an external bias applied to the system. The third term corresponds
to the energy of the bosonic bath and the last term represents the coupling of the
two-level system to the bath, with coupling constants Ca. In the case of Ohmic
dissipation, the spectral function of the system is J{u) = 2n a uj for u> coc, where
a is a measure of the strength of the dissipation and uc is a cutoff frequency. For
q^O, the tunneling energy A (h = 1) is renormalized into
aaaa + ) +
1
Ar = A
(2.41)
with Ar/kB equivalent to the Kondo temperature Tk in the AKM.
The low temperature behavior of both spin-boson and AKM systems is that
of a Fermi liquid. The linear coefficient of the specific heat per total mole is given
by [35, 36]
7x2kl
7
a
3At
Na = a
7r2 R
3T¡
K
(2.42)
where Na is Avogadros number and R = kBNA is the gas constant, and the
magnetic susceptibility of the spin-boson model per total mole at T = 0 is
_ g2glNA = g2v2BNA
XsB 2Ar 2kBTK
where g is the ^-factor of the impurity spin. The susceptibility of the AKM at
T = 0 differs from Xsb by a factor of a: Xakm =c*Xsb- The Wilson ratios for both
models are related as follows:
d 4 7T2kl Xakm 0
/tAKM 0 7
3 (j/b)2 7


24
R
SB
4 7r2kl Xsb
3(^b)2 7
2
a
(2.44)
where RAKU=aRSB.
The thermodynamic properties of the AKM are given in terms of the exchange
interactions (J||) and (J), and therefore can also be expressed in terms of the
parameters a and Ar of the spin-boson model [35, 36]:
Ar p Jj_,
2
(2.
Figure 2.4 illustrates the temperature dependence of the static susceptibility and
specific heat as C/T for different values of the dissipation a and e = 0. The
parameter a is a good measure of the Kondo anisotropy of the system, since
it decreases sharply with increasing J\\. Both curves are universal functions of
(T/Ar) ~ (T/Tk). For e = 0, the electronic coefficient of the specific heat is given
by 7 = a/Ar, and C/T reaches a maximum at a temperature corresponding to
Ar for a < 0.3. This maximum is reduced in magnitude with increasing a. The
susceptibility expressed as kBTxsB has a finite value at T = 0, as in the isotropic
Kondo model, and reaches the free-spin value at high temperatures. The main
effect of a is to increase the temperature at which this latter value is attained. The
temperature Ar indicates the crossover between Kondo and free-spin behavior.
The behavior for a finite bias e>0 is described in Fig. 2.5 for a = 0.2. The
quantity e is equivalent to a magnetic energy gpBh acting on the impurity spin in
the AKM. The temperature Ar is renormalized by e, and becomes [37]
Ar = ^A? + e2. (2.46)
a =
1-1 tan"
7T
npJ\\
The effects of a field on the specific heat are a strong reduction of 7, an attenuation
of the maximum in C/T, and an increase of its temperature position given by
Ar. The low-temperature susceptibility strongly decreases as a function of the


25
parameter e. It also shows a maximum for fields of order Ar and above, with a
temperature position that increases with Ar.
2.5 Kondo Lattice
Certain types of metallic compounds, including heavy-fermion systems, can
be described as a lattice of Kondo impurities embedded in a metallic host [39,
40, 41]. This class of materials is commonly referred to as concentrated Kondo
systems. In these alloys, a giant Abrikosov-Suhl resonance of width Tk appears
in the density of states near the Fermi level for T T^. In the case of spin-
| Kondo scatterers, the resonance lies right at the Fermi energy. This feature
indicates the crossover to a strong-coupling regime in the scattering between /
and conduction electrons, growing in size as the number of impurities approaches
Avogadros number NA. Consequently, there is a substantial increase in the density
of states at £p. Figure 2.6 illustrates the evolution of the Abrikosov-Suhl resonance
for different temperatures. In heavy-fermion compounds, the 4/ level is located
well below the Fermi energy. As a result, the localized orbital has integer valence.
The large resonance in the density of states has an effect on the effective mass
m*, as indicated by Fermi-liquid theory. At high temperatures (T T/e), the
Abrikosov-Suhl resonance disappears, and the system behaves as an ensemble of
classical free spins.
Two other characteristics of the Kondo lattice are the appearance of coherence
effects and interactions between magnetic impurities. Below a temperature Tcoh,
the electronic properties change from those described by scattering off independent
Kondo impurities to those reflecting the periodicity of the lattice via Blochs theo
rem. This crossover is usually described in terms of a maximum in the temperature
dependence of the specific heat as C/T and the electrical resistivity around T ~Tcoh.
A consequence of coherence is an increase of indirect exchange interactions between
impurity spins. At distances larger than the 4/ radius (r4f <0.5) but less than


MxJT)
26
Figure 2.4: Thermodynamic properties of the anisotropic Kondo model for e = 0
and different values of a. a) Specific heat expressed as ArC/kBT vs T/Ar. b)
Universal static susceptibility curves expressed as kBTxSb vs T/Ar [37].


27
o 1/5
ct= 1/5
Figure 2.5: Thermodynamic properties of the AKM for a 0.2 and different values
of e (in units of Ar). a) Specific heat as ArC/kBT vs kBT/Ar. b) Susceptibility
curves expressed as Arxsb vs kBT/Ar [37].


28
Figure 2.6: Density of states of a nonmagnetic Kondo lattice at different temper
atures, showing the evolution of the giant Abrikosov-Suhl resonance [39].


29
the size of the Kondo compensation cloud for a single impurity, the presence of
closely-spaced uncompensated spins leads to the Ruderman-Kittel-Kasuya-Yosida
(RKKY) interaction between localized / orbitals
Wrkky = J(r)Si-Sj, (2.47)
where
/7V\ J cos(2kFr)
J{r) ~ { ]
is the RKKY coupling at large distances, J is the Kondo coupling, and kF is
the Fermi wavevector. In most heavy-fermions J{r) leads to antiferromagnetic
coupling between impurity spins.
The state of a concentrated Kondo system depends on the competition between
the two energies represented by the Kondo and RKKY temperatures TK and TRKKY.
This competition has been described in a simple form through the Kondo necklace
model, developed by Doniach [42, 43]. Both TF and TRKKY depend on the Kondo
coupling J and the concentration of magnetic impurities. The Doniach model relies
on the assumption that the ground state of the system depends on the relative
magnitude of the coupling J only. The phase diagram for this model is shown in
Fig. 2.7. The Kondo temperature depends exponentially on the parameter J, as
discussed previously, while TRKKY ~ J2 N(0). At low values of J, Trkky>Tk, the
material is a magnetic 4/ metal, and the Kondo effect is absent. As J increases,
Tk>Trkky, the Kondo effect appears before magnetic order, and the material is a
magnetic Kondo lattice. At even larger values of J (7k 3>TRKKY), magnetic order
disappears altogether and the material is a nonmagnetic Kondo lattice. Heavy-
fermion compounds exist in the region around the magnetic-nonmagetic phase
boundary, and those with a magnetic ground state exhibit mostly antiferromag
netic order.


30
A modified form of the Doniach diagram has been recently proposed [44, 45]
to account for the effect of intersite magnetic correlations on the Kondo tempera
ture in the nonmagnetic region. Instead of continuing to increase exponentially as
in the single-impurity case, Tk reaches a saturation value, after which it decreases
slightly with increasing J. Thus, Tk in nonmagnetic Kondo lattices may not nece-
sarily follow single-impurity behavior. On the other hand, a complete theoretical
explanation of the effect of magnetic interactions on the Kondo temperature has
yet to be developed.
At a value of the Kondo coupling J = Jc, the magnetic ordering temperature
Tm approaches zero at a critical point. The ground state of some heavy fermions at
or near Jc is neither magnetically ordered nor Fermi-liquid-like. A large number of
intermetallics falling in this category are commonly referred to as non-Fermi-liquid
(NFL) systems. Their thermodynamic and transport properties can in some cases
be described by either logarithmic divergences or power-law behavior according to
different theoretical models [3, 12].
2.6 Non-Fermi-Liquid Effects
Current models of non-Fermi-liquid phenomena can be divided into two
groups: theories describing a possible single-ion origin to these effects and those
attributing them to intersite interactions. A member of the first group is the
two-channel quadrupolar Kondo effect [46], a particular scenario within the more
general multichannel Kondo problem [47]. The quadrupolar Kondo effect consists
of the quenching of a nonmagnetic quadrupolar level by two degenerate conduction-
electron bands, and has been used to explain the properties of heavy-fermion
systems like Ui_xThxBei3 [48]. In this model, NFL behavior is associated with
fluctuations of the quadrupolar degrees of freedom, rather than spin fluctuations.
Another possible single-ion mechanism towards non-Fermi-liquid behavior
is Kondo disorder [49, 50, 51]. The material exhibits a random distribution of


31
the quantity pJ, where p is the density of states and J is the Kondo coupling
constant. Thus, variations in either the Kondo couplings or the local density of
states gives as a result a distribution of Kondo temperatures. The probability
distribution function P{Tk) = P(pJ) d(pJ)/dTx acquires a log-normal form for
strong disorder:
P(TK) = (4*,)-* exp ln2[poJe~" ln(£F/r*)]} <2-49>
where po is the average density of states, and u is a dimensionless parameter cor
responding to the amount of disorder in the system. For weak disorder, P[Tk)
takes the form of a Gaussian. At a given temperature T, there are regions where
the local Kondo temperature T/<- probability of having uncompensated spins at T 0, P{Tk 0)^0, the thermo
dynamic properties are dominated by the contribution from free spins, leading to
non-Fermi-liquid behavior.
The first model involving collective behavior applied to NFL alloys was based
on a description of the physical properties in terms of their proximity to a quantum
critical point (QCP). The system exhibits critical fluctuations of the order param
eter in the vicinity of a quantum phase transition at T * 0 [52, 53, 54, 55, 56].
At finite temperatures, the characteristic frequency uj* associated with the critical
fluctuations of the order parameter is much smaller than the transition temper
ature Tc, so that the system behaves classically at hcu* C kBTc [56]. A quantum
phase transition at T = 0 is not achieved by a change in temperature, but rather
by a change in a parameter of the Hamiltionian. Under this model, non-Fermi-
liquid effects in heavy-fermion systems arise as a consequence of a near-zero anti
ferromagnetic transition temperature, so that a quantum-mechanical treatment is
necessary. The thermodynamic properties are dominated by the collective modes
due to critical fluctuations rather than by Fermi-liquid-like elementary excitations,
and are described by various scaling laws [53, 54] depending on the effective dimen-


32
sionality and the nature of the magnetic transition. As a result, the system is said
to have a generalized (non-Landau) Fermi-liquid ground state, with an enhanced
quasiparticle mass m* due to the presence of long-range spin fluctuations [57].
A recent explanation for NFL behavior relies on the competition between
anisotropic Kondo and RKKY interactions in a disordered system [58, 59]. Around
the QCP corresponding to Jc, for Tk > TRKKY, free spins arrange into clusters,
which increase in size as Tk >TRKKY. The spin clusters form a granular magnetic
phase, coexisting with the metallic phase, and the system exhibits a Griffiths
singularity at zero temperature [60]. Non-Fermi-liquid effects are attributed to the
dynamics of large spin clusters in the Griffiths phase. A percolation limit for these
clusters is reached at the QCP, which for Tc 0 leads to an antiferromagnetic,
spin-glass, or ferromagnetic transition [58]. The temperature dependences of the
thermodynamic properties obey power laws, with exponents determined by the
crystal symmetry and the values of the local exchange constants. The nonuniversal
nature of these exponents offers a common description of NFL effects in heavy-
fermion alloys within the Griffiths phase model.


33
Figure 2.7: Phase diagram of the Kondo lattice [39], illustrating the different
dependences of Tk and TRKKY on the parameter J/W, where J represents the
Kondo coupling and W is the bandwidth. The dependence of the magnetic ordering
temperature Tm on J/W dictates the regions corresponding to magnetic metal,
magnetic concentrated Kondo system (CKS), and nonmagnetic CKS.


CHAPTER 3
PROPERTIES OF CeAl3 AND CePb3
This chapter gives an overview of structural, thermodynamic, transport, and
magnetic properties of CeAl3 and CePb3 alloys that are relevant to the problems
addressed in this dissertation.
3.1 Properties of CeAl3
3.1.1 Crystal Structure
The compound CeAl3 crystallizes in the hexagonal Ni3Sn structure (DO19),
Pearson symbol hP8, space group P63/mmc, number 194. This structure con
sists of two alternating hexagonal layers. The most recently published lattice
parameter measurements give a = 6.547 and c 4.608 [61]. The above val
ues correspond to a c/a ratio of 0.704, much smaller than the close packed ratio
(0.816), and a lattice volume V = 171.05 3. A study of the structure of rare-
earth trialuminides[62] attributed the formation of a particular structure and its
c/a ratio to the rare-earth/aluminum ratio Rre/RAi This ratio is largest for the
hexagonal LaAl3, PrAl3, and CeAl3, and smallest for Yb, Tm and Sc trialuminides,
which crystallize in the cubic Cu3Au structure. As Rre/RA\ decreases, the crystal
structure is modified from hexagonal to cubic, the layer stacking changes, and the
c/a ratio increases.
Figure 3.1 shows the idealized (Ni3Sn) unit cell of CeAl3. The cell contains
two formula units. The atom positions with respect to the origin are given in
Table 3.1 in terms of the lattice parameters a (x, y axes) and c (z axis). Figure 3.2
is an extended scheme showing the hexagonal stacking and the periodicity of the
34


35
Figure 3.1: Hexagonal Ni3Sn structure of CeAl3.
Figure 3.2: Hexagonal Ni3Sn structure of CeAl3 (extended scheme).


36
Table 3.1: Cell Content of Ni3Sn structure of CeAl3 [64].
Atom
Multiplicity
(Wyckoff notation)
X
Coordinates
y
z
Ce
2c
1/3
2/3
1/4
2/3
1/3
3/4
Al
6 h
0.833
0.666
1/4
0.833
0.167
1/4
0.334
0.167
1/4
0.167
0.334
3/4
0.666
0.833
3/4
0.167
0.833
3/4
unit cell. Each Ce atom has 6 A1 nearest neighbors, at a distance dCe.M = 3.27 ,
and 6 Ce nearest neighbors at a distance dCe.Ce 4.428 [63]. The central Ce
atom is surrounded by six nearest neighbors (3 A1 and 3 Ce atoms) above and six
below the basal plane. It is important to point out that all nearest neighbors are
located in the layers above and below the central Ce atoms, and their distances are
not along the c-axis direction, but rather at an angle. These off-axis neighboring
distances might have some implications regarding the hybridization between Ce
and A1 atoms, as well as the effects of the RKKY interaction on the magnetic
properties of CeAl3 (see Chapter 7).
3.1.2 Specific Heat
Early measurements of the specific heat of CeAl3 below 10 K proved to be
unreliable [65, 66] due to anomalies caused by the presence of the secondary phases.
Later measurements by Brodale et al. [67] demonstrated a significant reduction of
these anomalies. In their study, the low temperature specific heat showed a maxi
mum around 0.4 K when plotted as C/T vs T. The value of the electronic specific
heat coefficient 7 extrapolated from C/T vs T2 is 7 = 1250 mJ/K2 mol. This max
imum in C/T has been the subject of intense controversy about the ground state of
CeAl3. It was initially proposed that its origin is due to the formation of a Kondo


37
lattice state in which the conduction electrons undergo coherent scattering [68].
Later experiments [69, 70, 71] suggested that the maximum was due to either
magnetic correlations or a possible antiferromagnetic order in this compound.
The anomaly in C/T has also been studied at different pressures and mag
netic fields. Magnetic field measurements up to 4 T [68] showed that both the
maximum and its temperature position decrease in field, while there is an increase
of C/T values below 0.2 K (see Fig. 3.3). Measurements above 1 K and at 23T[72]
indicated a decrease in C/T values below 4-5K (more than 15% at IK) and an
increase in values above the same temperature (around 20% near 10 K). These
results seem to indicate an initial increase of the electronic coefficient 7 with field,
followed by a marked decrease at higher fields. The pressure dependence of the
specific heat as C/T vs T is shown in Fig. 3.3 [73]. The specific heat is very sen
sitive to pressure. C/T values at 0.4 K were found to decrease with pressure as
P1/6. There is no sign of the specific heat anomaly at a pressure of 0.4kbar. The
coefficient 7 is reduced from 1250 mJ/K2 mol at atmospheric pressure to about
550mJ/K2 mol at 8.2kbar. Values of C/T are essentially constant below IK for
pressures around and above 2 kbar.
An attempt was also made to measure specific heat on very small single crys
tals of CeAl3 [74]. The results proved to be sample-dependent. Some of the crystals
showed peaks in the specific heat resembling antiferromagnetic phase transitions.
It remains to be understood whether there is any relationship between these peaks
in the specific heat and the maximum observed in C/T for polycrystalline samples.
3.1.3 Magnetic Susceptibility
Avenel et al. [75] measured the magnetic susceptibility of polycrystalline
CeAl3 down to 0.8 mK. The results show a broad maximum around 0.5 K, resem
bling the anomaly in C/T near 0.4 K (see Fig. 3.4). The susceptibility becomes
temperature independent below 40 mK (y(T = 0) 29.5 memu/mol), consistent


38
T {K)
Figure 3.3: Magnetic field and pressure dependence of the specific heat of CeAl3.
Upper part: C/T vs T of CeAl3 in magnetic fields up to 4 T (OT: circles, 2T:
diamonds, and 4T: triangles) [68]. Lower part: Pressure dependence of C/T vs T
for CeAl3 up to 8.2kbar [73].


X O 03 emu/mol)
39
T (K)
Figure 3.4: Magnetic susceptibility of CeAl3 below 10 K [75]. The inset shows the
inverse susceptibility.


40
with Fermi-liquid behavior. The inverse susceptibility follows Curie-Weiss law
above 150 K, with an effective magnetic moment close to that of a free Ce3+ ion,
/ieff = 2.54b, and cw = 30 6K. The susceptibility of single crystals above
4K was also measured with the field parallel (x||) and perpendicular (x) to the
c-axis [76]. The susceptibility along the c-axis X|| is at least three times as large as
X_l around 4 K, indicating a large anisotropic magnetic behavior.
3.1.4 Transport Measurements
Figure 3.5 shows the electrical resistivity of CeAl3 below 300 K. It can gener
ally be described by a Kondo-like increase down to 50 K, a maximum around 35 K,
possibly signaling the crossover from single-impurity to Kondo-lattice behavior,
and a sharp decrease below 10 K. At temperatures below 100 mK, the resistivity
has the form of a Fermi-liquid, with a coefficient A 35 /xQcm/K2 (see Fig. 3.5).
No sign of a magnetic phase transition (i.e. kink in the resistivity curve) has been
detected in electrical resistivity measurements around 0.4-0.5 K. When pressure is
applied, there is an increase in both the temperature and magnitude of the maxi
mum [77]. In addition, the A coefficient decreases, and resistivity values above the
temperature of the maximum are enhanced as pressure increases.
The low temperature magnetoresistance of polycrystalline samples was found
to change sign at a field of 2T, becoming positive at lower fields [79, 80]. The
results are shown in Fig. 3.6. The resistivity values are dependent on the field
direction with respect to the current. This anisotropic behavior increases with
applied field and at low temperatures. The magnetoresistance at 4.2 K and field
perpendicular to the current becomes less negative with increasing pressure for
fields larger than 2T [77]. In single-crystal measurements, the electrical resistivity
in zero field along the basal plane is more than twice that along the c-axis [76, 81].
The field dependence of the A coefficient parallel to the c-axis shows a peak around


41
p
2*0
220
200
180
160
1*0
120
IOO
80
60
*o
20
OAtj
ekclncol resistivity
O
too
200
T[X]
500
Figure 3.5: Transport measurements on CeAl3. Upper part: Electrical resistivity
below 300 K [78]. Lower part: p vs T2 below 100 mK [20].


42
2 T. The authors found this result to be in qualitative agreement with theoretical
models describing weakly-antiferromagnetic metals.
3.1.5 Nuclear Magnetic Resonance
Measurements on 27A1 nuclear magnetic resonance (NMR) on CeAl3 down
to 0.3 K by Nakamura et al. [82] are part of a series of microscopic measurements
arguing against the coherence interpretation of the anomalies in C/T and the mag
netic susceptibility. The temperature dependence of the spin-lattice relaxation rate
at 0.98 MHz increases by one order of magnitude at the lowest temperatures in a
nonlinear fashion. The relaxation rate reaches a maximum at 1.2 K. The authors
attributed this maximum to the onset of antiferromagnetic order at this tempera
ture. Later measurements by Wong and Clark [83] and Gavilano et al. [70] revealed
not only the absence of a maximum in the relaxation rate at low temperature, but
a Korringa-like (Ti T = const.) behavior below 0.6 K as well. The reason for these
discrepancies might be related to a large sensitivity of the ground state to lattice
strains and sample preparation for NMR measurements. Powdered samples have
grains with typical linear dimensions around 50 fim. The nonuniform strains cre
ated by preparing the powder can have a dramatic effect on the physical properties
of CeAl3 below 1 K. The presence of secondary phases can also have an effect on the
results, since it is more probable to find entire grains of either CeAl2 or Ce3Aln, as
proposed by Wong and Clark [83]. Gavilano et al. also measured the NMR spec
tra of partially oriented powder (c-axis along the direction of the applied field) at
6.968 MHz, and observed two distinct components (Fig. 3.7). They concluded that
these components correspond to two different regions of the sample being stud
ied: the spectral lines seen in Fig. 3.7 were attributed to a normal paramagnetic
phase, while the broad structure was ascribed to a phase where static magnetic
correlations take place. The Ce moments of this latter phase were estimated to be


43
P(B)
Figure 3.6: Magnetoresistance of CeAl3 down to 100 mK [79].


Echo intensity
44
Figure 3.7: NMR spectra of partially oriented powder at 6.968 MHz for different
temperatures [70].


45
less than 0.05B. The presence of magnetic correlations in CeAl3 argues against a
simple interpretation of its ground state in terms of a non-magnetic Fermi-liquid.
3.1.6 Muon Spin Rotation
The only muon spin rotation (SR) experiments on pure CeAl3 available to
date are those of Barth et al. [69, 84]. The authors measured the time-dependent
muon polarization on two polycrystalline samples, as seen in Fig. 3.8. The muon
polarization signal was described as the sum of several time-dependent components,
two of which correspond to the response of muons from different magnetic envi
ronments. The most significant finding was the detection of a spontaneous muon
spin precession frequency in zero field below 0.7 K from one of these components.
This Larmor frequency, proportional to the local magnetic field, has a very small
temperature dependence below 0.7 K. Its extrapolated value at T 0 is just above
3 MHz, which corresponds to an average local field of 220 G. In agreement with this
estimate, the muon precession signal could not be observed at an external applied
field of 750 G. Both the oscillating component and the fast relaxation of the muon
polarization are commonly associated with spin-density-wave behavior [85]. The
presence of the local field at the muon sites was interpreted as the development
of short-range, quasistatic magnetic correlations in CeAl3 below 0.7 K. As the
temperature decreases, these correlated moments, estimated to be around 0.5B,
develop some coherence in a spatially inhomogeneous manner. The appearance
of this almost percolative effect was attributed to magnetic frustration. Electron
paramagnetic resonance (EPR) measurements by Coles et al. on GdAl3 (Ni3Sn
structure) [86], also contributed to the development of this idea, arguing that the
magnetic behavior in CeAl3 might be mediated by frustrated antiferromagnetism
in the triangular sublattice of the hexagonal a-b planes.


- polarization (o.u.)
Figure 3.8: Muon polarization as a function of time in zero external field
T = 0.05, 0.5, and IK [69].


47
Energy transfer [meV]
Figure 3.9: Magnetic contribution to the inelastic scattering function of CeAl3 at
T 20 and 40 K [87]. The solid line is a fit to a three-Lorentzian model. The
dotted lines represent the individual fit components.


48
3.1.7 Neutron Scattering
Inelastic neutron scattering is one of the most direct methods of determining
electronic energies and crystal fields in metallic compounds. In CeAl3, the cerium
ions occupy positions of low point symmetry. In hexagonal structures, the Ce3+
\J = |) multiplet splits into three doublets under the influence of a crystalline
electric field (CEF): Ty : | |), T8 : | |), and r9 : | |). In cerium heavy-
fermion compounds, the neutron scattering spectrum can be described in terms
of two components: a quasielastic peak around zero energy transfer and a width
of order Tk at T 0, and an inelastic peak at an energy that coincides with the
characteristic energy of crystal-field excitations.
In addition to the quasielastic peak, the most recent measurements [87] dis
played a single inelastic peak at an energy e~6.4meV for T = 20 K (Fig. 3.9). With
the help of previous single-crystal magnetic susceptibility data [76], the authors cal
culated the crystal-field parameters for CeAl3 and determined the ground state to
be r9 : | |), followed by T8 : | |) at 6.1 meV (T = 71 K), and Ty : |
at 6.4 meV (T = 74 K). By comparing the parameters to those of other rare-earth
trialuminides with Ni3Sn structure, they concluded that the hybridization of Ce
4/ electrons with the conduction band is the dominant contribution to the CEF
potential, as proposed by some theories of the Kondo effect in crystal fields [88].
Thus, the hybridization is responsible for both Kondo and CEF energy scales.
3.1.8 Chemical Substitution Studies
By far the most interesting doping studies on CeAl3 to date are those of La
impurities on the Ce sites. Recent specific heat studies of Cei_xLaxAl3, performed
after evidence for magnetic correlations was found for the pure compound [69, 84],
added to the already existing controversy about the nature of the anomalies in
CeAl3. An enhancement of the anomaly in C/T was found for 0 < x < 0.2 [71],
and a corresponding peak appears in the specific heat, as seen in Fig. 3.10. The


49
magnetic susceptibility also shows an enhancement in its corresponding maximum,
with a temperature around 2.5 K for x = 0.2. A T3 dependence of the specific
heat below this maximum for the La-doped alloys led to the conclusion that the
anomalies represented the development of an antiferromagnetic transition. Two
reasons for this development were proposed. The first one is the application of a
negative chemical pressure by the larger La atoms and a subsequent decrease in
hybridization between / ions and conduction electrons. This effect is in accordance
with the Kondo necklace model (see Chapter 2). The second possibility is the
reduction of magnetic frustration in the basal-plane triangular lattice of Ce ions [86,
89]. As the Ce ions are substituted by non-magnetic La atoms in the triangular
sites, a number of the Ce moments are relieved from the frustration constraint and
are free to interact with others. This explanation relies on the assumption that the
in-plane interactions are much stronger than the interactions between two adjacent
planes.
More recent neutron scattering and SR studies on Cei_xLaxAl3 [15, 90] have
shown that the temperature at which the maximum in the specific heat for a; = 0.2
develops coincides with both the appearance of an inelastic peak in the neutron
scattering function and the divergence of the SR relaxation rate. The divergence
of the muon relaxation rate was interpreted as evidence for either short-range mag
netic correlations, as found for pure CeAl3 [69, 84], or long-range magnetic order
of small moments. Bragg scattering on powdered samples did not show evidence
of long range order within the resolution of the measurement. The magnitude of
the Ce moments was estimated as <0.05B. The position of the inelastic peak for
x = 0.2 is weakly temperature-dependent, with an estimated energy of 0.54 meV
at T = 0. It was argued that the magnetic correlations in this sample were too
small to be responsible for the behavior of both the inelastic peak and the thermo
dynamics below 2 K. In the search for an alternate explanation, the specific heat


50
and the inelastic peak were described in terms of the anisotropic Kondo model
(discussed in Chapter 2), which shows a similar response function and a maximum
in C/T for specific parameter values. This interpretation was not able to account
for the magnetic behavior inferred from the SR results. Instead, the AKM proved
to be useful in providing an explanation for the anomalies in terms of a single-ion
mechanism, rather than cooperative behavior. Numerical results for the specific
heat of the AKM will be compared to specific heat measurements in magnetic field
of La-doped CeAl3 alloys in Chapter 6.
Only one study reports doping of CeAl3-based alloys on the A1 ligand sites [61].
Corspius et al. found that the alloys were single-phased for doping levels less than
x 0.1, and that substitution of Ga, Si, and Ge contracts the lattice, while Sn
expands it. All of the above elements have the same effect on the specific heat
and the magnetic susceptibility. The anomaly in C/T for the pure compound is
shifted to higher temperatures, as much as 4.2 K for Ce(Al0.9Sn0.i)3. A maximum
at a slightly higher temperature is also seen in the susceptibility between 0.1 and
70 kG. The maxima were attributed to the development of an antiferromagnetic
phase transiton. All samples except those with Ga impurities exhibit discrepan
cies between zero-field-cooled and field-cooled susceptibilities, and only those above
x 0.1 show a time-dependent maximum (spin-glass-like). The development of an
apparent phase transition in the thermodynamic properties does not seem to be
exclusively related to an isotropic volume change of the hexagonal lattice, since
these features were seen in alloys with both smaller and larger lattice parameters
than those of CeAl3. Instead, the authors argued that the change in the tem
perature position of the anomaly in C/T is related to the absolute-value change
(increase or decrease) in the c/a ratio.


51
Table 3.2: Cell Content of Cu3Au structure of CePb3 [64].
Atom
Multiplicity
(Wyckoff notation)
X
Coordinates
y
z
Ce
la
0
0
0
Pb
3c
1/2
1/2
0
1/2
0
1/2
0
1/2
1/2
3.2 Properties of CePb3
3.2.1 Crystal Structure
The compound CePb3 crystallizes in the face-centered cubic Cu3Au struc
ture, Pearson symbol cP4, space group Pm3m, number 221. The Ce sites cor
respond to the corners of the cube, while the Pb atoms occupy the face-centered
positions. The structure forms directly from the melt at 1170C on the Ce-Pb
phase diagram [91]. Unlike CeAl3, there are no secondary phases that might af
fect the physical properties and the formation of single crystals of this compound.
The lattice constant is a = 4.8760.002 [92], corresponding to a lattice volume
V = 115.93 3.
Figure 3.11 shows the Cu3Au unit cell of CePb3. The cell contains one
formula unit. The atomic coordinates with respect to the origin are given in units
of a in Table 3.2. In an fee structure, the Ce atoms have 6 Ce nearest neighbors at
a distance equal to the lattice constant, and 12 Pb nearest neighbors at a distance
dce-Pb ~ci/y/2 3.448 .
3.2.2 Specific Heat
The low-temperature specific heat, plotted as C/T vs T2, is shown in Fig. 3.12.
It has a peak around 1.1 K due to an antiferromagnetic transition. The magnitude
of the peak is close to 3.5 J/K2mol, and the extrapolated electronic coefficient 7
reaches a value around 1000 mJ/K2mol. The effect of high magnetic fields was


(mJVK Ce mol)
52
4000
3000
2000
o
1000 L
0
Figure 3.10:
A A
m
Ce La R 1
1 x x 3
x-0.05
K-0. 1
x-0.2
*...! I 4 ... .1 I 1 . .
1 2 3 4 5 6 ?
T CK)
Specific heat of Cei-^La^-A^ alloys (x 0.05, 0.1, and 0.2) [71].
Figure 3.11: Cubic CU3AU structure of CePb3.


53
Figure 3.12: Specific heat plotted as C/T vs T2 of CePb3 between 0.6 and 4K.
The inset shows C/T vs T2 from 1.5 to 10 K [93].


54
first studied by Fortune et al. [94]. Magnetic fields between 10 and 20 T were found
to suppress the antiferromagnetic state and reduce the electronic coefficient.
Specific heat studies under pressure [95] revealed the existence of a pressure-
induced magnetic phase above 0.7 GPa. Below the critical pressure, the antiferro
magnetic temperature is suppressed down to 0.6 K; above 0.7 GPa, the temper
ature of this pressure-induced type-II antiferromagnetic phase increases from 0.6 K
to 1 K at 1.3 GPa. Figure 3.13 illustrates the temperature-pressure phase diagram,
with T/v decreasing up to 0.7 GPa and increasing at higher pressures. This behav
ior is rather unusual since a continuous decrease of T/v with pressure is expected for
Kondo lattices, especially when the Kondo temperature TK is about three times
as large as the transition temperature, as in CePb3 [96]. In addition, contrary to
other Ce Kondo lattices like CeC^-zAu^, (x > 0.1) [97], and CeRu2Ge2 [45], no
pressure-induced suppression of to zero was observed for this compound.
3.2.3 Sound Velocity Measurements
The temperature dependence of elastic constants was determined from mea
surements on a CePb3 single crystal along the (100) and (110) directions [98]. Fig
ure 3.14 illustrates the magnetic field dependence of the relative change in velocity
of an elastic mode in the (110) direction at 10 MHz. Two phase boundaries (indi
cated by arrows) can be distinguished at 0.38 K. The lower one signals the antifer
romagnetic phase transition. The high-field boundary corresponds to an unknown
phase, possibly a spin-flop state [98]. The exact nature of this field-induced phase
remains to be determined by neutron diffraction experiments. Nevertheless, the
discovery of this field-induced transition in the (110) direction motivated further
investigation of the properties of CePb3 single crystals in magnetic fields.


55
Figure 3.13: Transition temperature-pressure phase diagram for CePb3 up to
1.4 GPa [95]; the graph shows specific heat measurements (crosses), neutron scat
tering (circles), and transport measurements (triangles). The broken line indicates
a crossover between two distinct magnetic phases (see text).


56
Ll l 1 1
0 5 10 15 20 B (T)
Figure 3.14: Magnetic field dependence of the relative change in sound velocity for
the (cn Ci2)/2 elastic mode at 10 MHz [98].


57
Figure 3.15: Magnetic contribution to the electrical resistivity of CePb3 at H = 1T
below room temperature. The inset shows the resistivity between 0.2 and 4 K at
H = 0.93 T [93].


58
3.2.4 Transport Measurements
In order to measure the electrical resistivity of CePb3, it is important to
measure in magnetic fields of order 1T in order to suppress the superconducting
transition due to the presence of Pb on the surface of the sample [93]. The reaction
of CePb3 with oxygen from air causes the separation of the two elements, eventually
followed by oxidation of Ce and Pb. Figure 3.15 displays the magnetic resistivity
between 0.2 and 4 K. It shows a logarithmic, Kondo-like increase from room tem
perature down to 40 K, followed by two maxima, and finally by a drop below 2 K.
The maximum around 20 K has been attributed to the decrease in Kondo scatter
ing due to a depopulation of the excited crystal-field levels [99]. The maximum
at 3.3 K is thought to be due to a coherence effect of the Kondo lattice. There is
also a rapid change in slope around 1 K, indicative of the antiferromagnetic phase
transition, as shown in the inset to the figure.
The pressure dependence of the magnetic resistivity was measured on a single
crystal [99]. There is a shift of the maximum at 3.3 K toward higher temperatures.
Only one broad maximum was detected for pressures above 11.5kbar. This result
is consistent with an increase of the Kondo temperature T'k- The magnetore
sistance was recently measured along the (110) crystallographic direction [100].
Two field-induced anomalies were found for the magnetoresistance curves below
400mK at 5 and 9.5T, respectively (see Fig. 3.16). The resistivity increases up
to 5T, decreasing sharply above the first transition, and becoming almost field-
independent after the second. A magnetic field-temperature phase diagram was
constructed, in good agreement with previous sound velocity measurements. The
angle dependence near the (110) direction was also measured in order to verify the
orientational dependence of the field-induced phase above 5 T, detected by sound
velocity measurements. A large increase in the magnetoresistance was observed as
the field direction was rotated toward the (10 0) direction, at which point the sharp


59
Figure 3.16: Magnetoresistance curves between 1 and 16 T for temperatures in the
range 20mK to 8K. The magnetic field is along the (110) direction [100].


60
drop at 5 T could not be detected. The low-temperature resistivity was found to be
proportional to T2 with a field-dependent A coefficient. At 5T, A reaches a max
imum, the range of T2 dependence becomes smaller, and the resistivity acquires
a linear term, all coinciding with the field-induced transition. This enhancement
of A with field points to a corresponding enhancement of the specific heat coeffi
cient 7, as the ratio A/72 is expected to remain constant for heavy fermions [101].
At 10 T, there is a small bump in the A coefficient, indicating a transition to a
ferromagnetically-polarized paramagnetic state [100].
3.2.5 Magnetic Susceptibility
Measurements of the magnetic susceptibility on a CePb3 polycrystal below
4K [102] revealed a maximum at 1.25 K, similar to that found for the specific
heat at 1.1 K. Figure 3.17 shows the data measured at 2.6 kG. This maximum
is reminiscent of an antiferromagnetic phase transition, and coincides with the
appearance of a maximum in the specific heat at 1.1 K. The estimated value of
x(T = 0) is somewhere between 32 and 33 memu/mol. The inverse susceptibility
follows a Curie-Weiss behavior, and gives a high temperature effective moment
= 2.5 B, and a Curie-Weiss temperature 0CW = 25 K. An investigation of
the pressure dependence of the inverse susceptibility [99] found an increase of 0CW
from 0 to 15kbar, a trend consistent with an increase of Tk-
Recently, the ac susceptibility of a CePb3 single crystal was measured as
a function of crystallographic direction to verify the phase diagram and the field-
induced (presumably spin-flop) phase transition [103]. Their phase diagrams along
the (1 00) and (11 0) directions indicated that the range of the field-induced phase
depends on the crystallographic direction. Between 20 and 600 mK, with H
(10 0), the range is about IT, while for H || (110), it is close to 5T. The phase
diagram determined from ac susceptibility data along (11 0) is in agreement with
previous studies, as shown in Fig. 3.18.


61
Figure 3.17: Magnetic susceptibility of a CePb3 polycrystal below 4K at H
2.6kG [102],


62
e
X
i 1 r
Paramagnetic State
H//<110>
~~Ol
A
tV
'<5
Spin-Flop phase
a-
\
\
\
Xt
o -
Antiferromagnetic State
\
Qa \
X
X
X
M
' %
w
J i_
0.0 0.2 0.4 0.6 0.8 1.0
12
Temperature (K)
Figure 3.18: Phase diagram (H T) for CePb3, with the field along the (110)
direction (Solid circles: ac susceptibility [103], open circles: sound velocity [98],
and open triangles: magnetoresistance [100]).


63
3.2.6 Neutron Scattering
Neutron scattering studies are essential in the determination of the ordered
moment at low temperatures and the crystal-field parameters of heavy-fermion
systems. The CU3AU cubic structure of CePb3 provides a high degree of crystal
symmetry. In the cubic environment of Ce3+ ions in CePb3, the crystal-field (CEF)
potential splits the | J = |) multiplet into a T7 doublet and a T8 quartet [104]:
|r7> = a| !> 6| T !>
_ *>l §> + I T 1>
where a = (|)1 / 2 and 6 = (|)1/f2.
(3.1)
The magnetic scattering function of polycrystalline CePb3 is shown in Fig. 3.19,
which shows the inelastic, quasielastic, and elastic peaks. A fit to the scattering
function [105] determined that the ground state is the T7 doublet. The CEF
splitting between the doublet and the first excited state is around 72 K [106].
Bragg scattering studies on a single crystal led to the conclusion that the magnetic
structure of CePb3 is antiferromagnetic, and that the moments are aligned along
the (100) direction [106]. The magnetism is incommensurate, with a modula
tion amplitude of 0.55//b at 30 mK. A similar incommensurate structure has also
been detected for CeAl2 [107], another cubic heavy-fermion compound. Vettier et
al. [106] concluded from a comparative study of Ce Kondo lattices that cubic com
pounds are more magnetic than those with a large crystal anisotropy, like CeAl3,
CeCu6, and CeCu2S2. This statement has important implications regarding a
possible role of crystalline anisotropy in regulating the competition between the
Kondo and RKKY energy scales.


64
Figure 3.19: Magnetic neutron scattering function of a CePb3 polycrystal [105].
The solid line is a fit to the data. The dashed line represents the determined
quasielastic component, and the dash-dotted line corresponds to the inelastic com
ponent.


65
3.2.7 Chemical Substitution Studies
Alloying studies on the Ce sites of CePb3 were first reported using La [96].
These studies are particularly important and have fundamental significance, because
they constitute evidence of single-impurity effects in a concentrated heavy-fermion
system. The specific heat, magnetic susceptibility, and electrical resistivity all
scale with Ce concentration. Electrical resistivity measurements revealed that the
crystal-field splitting is also unaffected by La doping. The electronic specific heat
data for alloys with La x = 0.4, 0.6, and 0.96 are shown in Fig. 3.20, along with the
theoretical prediction for S = The Kondo temperature is constant throughout
the series, implying a constant value of J. The transition temperature T/v goes to
zero near a La concentration x = 0.2. The suppression of magnetism as a result
of a lattice expansion upon La substitution seems to indicate that the decrease
in Trkky with respect to Tk is due to an increase in the average Ce-Ce distance,
rather than to an overall change in J. Indeed, Cei_xLaxPb3 is a unique system in
the sense that Tk and the coupling J seem to remain unaffected by La doping.
While thermodynamic and transport properties of Cei_xLaxPb3 seem to be
unaffected by the electronic environment surrounding the Ce3+ ions, experiments
on Cei_xMxPb3 (M = Y, Th) [109] confirmed that the single-impurity scaling
observed by La doping on the Ce sites is the exception rather than the rule. Instead,
a rather unusual behavior is observed upon either Y or Th doping. The magnetic
susceptibility at 1.8 K increases with Y concentration. The Kondo susceptibility
is inversely proportional to Tk, so this result implies an unusual decrease of the
Kondo temperature as the lattice contracts (increasing J). Substitution of Th on
the Ce sites also contracts the lattice, and at the same time leads to magnetic-like
anomalies in both specific heat and susceptibility for x 0.3, 0.5. The differences
in the outer electronic structure between Ce, Y, and Th seem to play an important
role in the evolution of the ground state properties of Cei_xMxPb3.


AC(^mole-CeK)
66
Figure 3.20: Electronic specific heat vs T/Tk for Cei_xLaxPb3 alloys, x = 0.4, 0.6,
and 0.96 [96]. The data are in good agreement with the prediction from the spin-|
Kondo specific heat [108]. The only adjustable parameter is T¡< = 3.3 K.


67
Chemical substitution studies were also performed on both /-ion and ligand
sites of the CePb3 structure. In Ce(Pbi_a;Mx)3 studies with M = Tl, In, and
Sn [110, 111], the antiferromagnetic transition temperature decreased toward zero
for a Sn concentration x = 0.4, and increased for both Tl and In. For the latter
two dopants, there is a maximum towards the center of the x phase diagram.
Substitution of Sn for Pb on the ligand sites suppresses Tyv and greatly increases
the Kondo temperature [112, 113].


CHAPTER 4
MOTIVATION
This chapter begins with a discussion on the importance of the study of CeAl3
and CePb3, followed by a presentation of the objectives of the current study.
4.1 Importance of CeAl3 and CePb3
Both CeAl3 and CePb3 are canonical, well-documented heavy-fermion sys
tems, with values of the 7 coefficient surpassing 1 J/K2mol, crystal-field doublet
ground states, and a low temperature resistivity characteristic of Kondo lattices.
Studies on these compounds over the last 25 years made a substantial contribution
to the standard interpretation of heavy-fermion systems, based on the Kondo effect
and Fermi-liquid theory. However, deviations from this standard model have
been observed in these and other compounds through the coexistence of mag
netic order and heavy electrons, the presence of unaccountable anomalies in the
thermodynamic properties, and non-Fermi-liquid effects. These are all topics of
current interest, yet they are among the least understood aspects of heavy-fermion
physics. Any information obtained from the study of the above two compounds
might be utilized in the development of new interpretations for the heavy-fermion
state. The current work will concentrate on the coexistence of heavy fermions
and magnetic order in CePb3, the nature of the anomaly seen in the specific heat
(plotted as C/T) of CeAl3, and the heavy-fermion behavior of both compounds in
magnetic fields.
In 1975, specific heat and electrical resistivity measurements below 100 mK
by Andres, Graebner, and Ott led to the discovery of CeAl3 as the first heavy-
68


69
fermion compound [20]. Despite its significance in the field of strongly-correlated
electron systems, CeAl3 is probably one of the least understood among these com
pounds. Ever since its discovery, it has been considered a canonical, nonmagnetic
heavy-fermion system. Yet later experimental results (see Chapter 3) challenged
its nonmagnetic status, and pointed to a possible magnetically-ordered ground
state for CeAl3. Whether the ground state in this compound is magnetic or not
has been a long-standing debate, and remains an important topic in the study of
heavy-fermion systems.
The compound CePb3 ranks among the most extensively studied magnetic
Kondo lattices. The magnetic transition has little effect in reducing the large value
of the electronic specific heat coefficient, 7 1000 mJ/K2 mol. The electrical re
sistivity has a large T2 coefficient, A 45 /iQcm/K2, and the ratio A/72 is around
4 x 10~5 OcmK2 mol2/J2. When taking into account the relatively large value of
7 for this compound, the above suggests that the ground state is some superposi
tion of ordered local moments and heavy electrons. Very little is known about the
nature of the magnetic ground state of heavy-fermion materials. Measurements of
thermodynamic properties of paramagnetic and magnetic states in this compound
may be useful to understand the coexistence of magnetic order and heavy electrons.
Another important characteristic of CePb3 is the observation of single-ion
scaling of thermodynamic and transport properties in a concentrated 4/ system.
The study of Cei-xLa^Pbs by Lin et al. [96] revealed that the normal state of
alloys over the range (0 (see Chapter 3). It is the only Ce heavy-fermion system to date exhibiting such
behavior. The reason why such a concentrated system can exist with apparently
noninteracting 4/ sites remains unclear.


70
4.2 Objectives
4.2.1 Magnetism and Heavy-Fermion Behavior in Ce Kondo Lattices
The studies on CeAl3 and CePb3 alloys presented in this dissertation are
motivated by a fundamentally important topic in heavy-fermion research: the
need for a full understanding of the interdependence between magnetic correlations
and/or magnetic order and the heavy-fermion state. The ground state of rare-earth
intermetallics is generally described in terms of the competition between two energy
scales, Tk and TRKKY, discussed in Chapter 2. The former represents a single-ion
effect due to the local Kondo interaction between conduction electrons and the /
orbital. The latter portrays a collective effect due to indirect exchange interactions
between ionic spins. The schematics of this delicate balance were shown in Fig. 2.7.
For Trkky > Tk, magnetic order occurs and the moments are unquenched at zero
temperature. The size of the moments is close to that corresponding to the crystal-
field ground state. Concentrated Kondo systems falling into this category have
relatively low values of 7, of order 100mJ/K2mol (e.g., CeCu2 and CeAl2 [6]).
Whenever Tk TRKKY, the Kondo effect develops without magnetic order. This
regime corresponds to most nonmagnetic Kondo lattices, with Kondo temperatures
larger than 10 K. For Tk>Trkky, the formation of heavy electrons occurs, with 7
values in excess of several hundred mJ/K2mol. This is the least understood area
of the Doniach phase diagram. The applicability of this model to heavy-fermion
Kondo lattices, in particular to CeAl3 alloys, will be discussed as part of a study
on the anomaly present in this system.
Two empirical correlations have been postulated in order to distinguish between
magnetic and nonmagnetic heavy-fermion ground states: the Wilson ratio R and
the Kadowaki-Woods ratio. The experimental Wilson ratio R [5] is defined as
n2klxo/l2efl, where y0 is the zero-temperature susceptibility and /eff is the effective
moment at room temperature. Values of R are usually much larger for magnetically-


71
ordered than for nonmagnetic Kondo lattices [5]. Nevertheless, the experimental
ratios for CeAl3 and CePb3 are both around 0.7, a value within the range corre
sponding to nonmagnetic heavy fermions. Thus, this ratio does not seem to account
for the magnetic order observed in CePb3, as well as for a possible magnetic order
in CeAl3.
In most heavy-fermion compounds, the empirical relation A/72 lies somewhat
close to the Kadowaki-Woods ratio A/72 = 1 x 10-5 QcmK2 mol2/J2 [101]. This
ratio is about an order of magnitude larger than that corresponding to transition-
metal alloys. The magnetic field dependence of this relation has not been exten
sively studied. The ratio A/72 has been observed to remain constant with field in
nonmagnetic CeCus.gAuo.i [114], the only published study of the field dependence
of this ratio. In order to verify whether A/72 remains the same for both param
agnetic and ordered states, it would be of interest to explore the field dependence
of this ratio in a magnetically-ordered heavy-fermion system.
Previous thermodynamic and transport measurements on Ce0.6La0.4Pb3 [96]
suggested a single-ion mechanism for the heavy-fermion behavior in this system. A
study of the specific heat in magnetic field of Ce0.6Lao.4Pb3, a nonmagnetic coun
terpart of CePb3, was conducted in this dissertation to search for further evidence
of a single-ion Kondo origin for the heavy-fermion state in Ce-based systems.
4.2.2 Ground State of CeAl3
The experiments on CeAl3 alloys presented in this dissertation are motivated
by the existing controversy about the ground state of CeAl3. The nature of the
anomalies in the thermodynamic properties of CeAl3 systems below 1 K is not well
understood. It is a major topic of interest in the field of strongly-correlated electron
systems. There are at least three competing interpretations for the origin of these
anomalies. One explanation is that the weak maxima seen in C/T and in the
magnetic susceptibility between 0.3 and 0.5 K is due to a reduction in the density


72
of states caused by the formation of coherent states in the Kondo lattice [68].
Another interpretation argues for an unconventional ground state in which heavy
electrons coexist with either magnetic correlations or magnetic order. There is
now enough evidence [61, 70, 69, 71] for the existence of magentic correlations
below 1 K in CeAl3 through NMR and /rSR studies, casting serious doubt on the
so-called coherence interpretation [68]. However, it is not clear at the present time
whether the magnetic correlations are short-ranged, frustrated, or whether they
lead to long range order. The third and most recent interpretation suggests that the
anisotropic Kondo model provides an alternative explanation to the ground state
properties, as driven by single-ion dynamics, and dependent on the anisotropy of
the Kondo interaction [15, 90]. Under this point of view, the question remains of
how to reconcile the presence of magnetic correlations in CeAl3 with a single-ion
Kondo description of its thermodynamic features.


CHAPTER 5
EXPERIMENTAL METHODS
5.1 Sample Preparation
5.1.1 Synthesis
Alloys used in this dissertation were synthesized by melting its respective
constituents in an Edmund-Biihler arc furnace under a high-purity argon atmo
sphere. The arc-melting apparatus consisted of a stainless-steel vacuum chamber
with a water-cooled copper crucible at the bottom and a hydraulic mechanism sup
porting an electrode at the top. The tip of the electrode is made out of a tungsten
alloy, and it is capable of carrying well over 100 A of current.
Prior to melting, each of the consituent elements was carefully cleaned to
eliminate any oxide layer on the surface, and later weighed to an accuracy of
0.03 mg. Their molecular weights and stoichiometric ratios were used to calcu
late the appropriate relative masses. The total mass of an average sample was
about 500 mg, and the diameter of a sample bead ranged between 0.5 and 1cm.
The Cu hearth on the arc-melter was thoroughly cleaned to avoid the presence
of unwanted impurities during sample preparation. The element with the high
est vapor pressure was placed on the Cu crucible below those with lower vapor
pressures. This procedure minimizes direct contact between the Ar arc and the
material with highest vapor pressure, therefore reducing its mass loss, and mini
mizing the discrepancy between predicted and actual stoichiometries for the alloy
being synthesized. The chamber was then pumped and subsequently flushed with
high-purity Ar. After this procedure was repeated three to four times, the cham-
73


Temperature
74
Figure 5.1: Phase diagram of Ce-Al [91].


75
ber was filled to 0.5 atm of Ar gas. In order to avoid the unwanted presence of
oxygen and water vapor, two measures were taken. First, the high-purity Ar goes
through a purifier before entering the arc-furnace. Second, a zirconium bead is
placed inside the furnace and melted before sample synthesis. Zirconium is known
for its high absorbing capacity for oxygen.
At the start of the melting process, a relatively low current was sent through
the tungsten electrode. The arc was moved slowly towards the elements to avoid
any thermal stresses and motion or splashing of material due to the arc pressure.
During melting, enough time was allowed for the liquid components to mix via arc
pressure. To ensure homogeneity, the above process was repeated several times and
the sample bead was turned over after each melt. The mass loss during melting
was obtained as a percentage difference (typically < 0.1 0.3%) between the total
masses before and after sample synthesis.
Alloys of CeAl3
Alloys of Cei_xMa;Al3 (M = La, Y) were synthesized using the purest avail
able materials: cerium and lanthanum from Ames Laboratory, and Johnson Matthey
(AESAR) aluminum (99.999% purity). The weighing of constituents required spe
cial attention due to the sensitivity of the crystal structure of CeAl3 to small
changes in the relative concentration of Ce and A1 atoms. The synthesis of CeAl3
alloys is always accompanied by the formation of a large amount of the secondary
phases CeAl2 and Ce3Aln. The presence of these unwanted phases is substantially
reduced by proper annealing conditions.
The cerium-aluminum phase diagram has been studied by several groups [91],
its latest addition being CeAl3 [62]. It contains four other compounds: Ce3Aln,
CeAl2, CeAl, and Ce3Al (see Fig. 5.1). Both CeAl2 and Ce3Al form directly
from the liquid solution, CeAl and Ce3Aln form peritectically, and CeAl3 forms
peritectoidally at 1135C. A peritectic reaction is one in which the compound


76
melts incongruently [115], that is, the composition of the liquid just above the
melting point has a different composition than the solid before melting. Only part
of the solid forms a liquid solution, with the remaining part forming crystallites
floating around in the liquid. As the temperature reaches the melting point, the
mixture solidifies into a single phase. The peritectoid reaction in CeAl3 is similar
to a peritectic reaction, except that the compound does not melt into a liquid-
crystallite mixture. Rather, it separates into a solid phase mixture of CeAl2 and
/?-Ce3Aln, which in turn melts into CeAl2 crystallites embedded in a liquid solution
matrix.
The transformation of a mixture of Ce-Al neighboring phases into the CeAl3
phase upon cooling has a marked effect on the way samples crystallize. The pres
ence of secondary phases is the cause of many sample dependences of thermo
dynamic and transport measurements. Polycrystals synthesized by arc melting
consist of a mixture of CeAl3 with large amounts of CeAl2 and Ce3Aln. Anneal
ing has been found to reduce the proportion of secondary phases to the point of
becoming undetectable by conventional x-ray diffraction methods. Magnetic sus
ceptibility measurements on annealed samples are an efficient way of detecting the
above second phases, since CeAl2 is antiferromagnetic below 3.8 K, and Ce3Aln is
ferromagnetic with transitions at 3.2 and 6.2 K [116]. Specific heat data has also
been used successfully by some groups to detect irregularities at these tempera
tures.
Alloys of CePb3
Lanthanum-doped CePb3 alloys were made using Ames Laboratory Ce and
La, and Johnson Matthey Pb with 99.9999% purity. Special care was also taken
in the making of both CePb3 and Ce0.6La0.4Pb3 due to the large vapor pressure of
lead. Therefore, Ce should be melted first, then Pb. Unfortunately, this procedure
was not enough to significantly reduce Pb mass loss due to vapor pressure at


77
0.5 atm of Ar gas. In order to compensate for this mass loss, an additional 3%
of the calculated mass for Pb was added to the constituents before the first melt.
The mass loss for each bead after melting was mostly due to lead, usually around
3%. The sample was remelted in case the mass loss was less than the extra amount
of Pb. Correspondingly, more Pb was added in the event that the mass loss was
greater than expected. After melting the sample, the stoichiometry was verified
by recalculating the atomic percentages based on the final mass of the sample.
CePb3-based alloys are generally free of any secondary phases except pure Pb,
which can precipitate in the surface as the alloys react with air. As a result, the
samples were kept in a vacuum container along with Drierite acting as a moisture
absorber.
5.1.2 Annealing
Annealing helps relieve stresses inside the samples not removed during crys
tallization. It also reduces the amount of unwanted secondary phases in the final
melt. Typical annealing temperatures range between 2/3 and 3/4 of the melting
point of the alloy.
The final beads were broken into smaller pieces using a ceramic mortar instead
of a metal crusher to avoid the presence of iron impurities in the samples. Part of
each original bead was wrapped in a clean tantalum foil and placed inside a quartz
tube. The tubes were pumped and flushed with Ar gas several times. Right before
sealing, the Ar pressure inside was reduced to lOOmtorr. The quartz tubes were
then placed inside a Lindberg furnace and annealed according to a previously
tested prescription. Alloys of Cei_xLazAl3 were annealed at 830C for two weeks,
while those of Cei_xYxAl3 were annealed at 800C for two weeks, then 850C for
five days. Both CePb3 and Ceo.6La0.4Pb3 were annealed at 800C for one week. In
all cases, annealing started with the furnace already at annealing temperature. At


78
the end of the prescribed annealing period, the samples were immediately removed
from the furnace and left to cool down at ambient temperature.
5.2 Diffraction of X-Rays
Measurements of x-ray diffraction were used as a means to verify whether
the arc melting and annealing processes led to the formation of the desired crystal
structure. Prom the diffraction pattern, it was also possible to determine the lattice
parameters and the presence of secondary phases in the sample. The principle
behind the diffraction of x-rays in crystals is based on Braggs Law:
A = 2d sin 9, (5.1)
which for a first order (n = 1) spectrum relates the known Cu Ka wavelength to the
diffraction angle 6 and the distance between lattice planes d. The lattice constants
are then calculated from d and the intersection points of the lattice planes for the
desired space group number, given in terms of the Miller indices (hkl).
The experimental setup consisted of a Phillips APD 3720 diffractometer, an
x-ray source with a water-cooled power supply, and a computer for data acquisition.
The APD 3720 consists primarily of x-ray beam slits, the sample holder, and
an electronic counter. Both the counter and the sample holder rotate about a
horizontal axis so that the angle of rotation of the counter is always twice that of
the holder. This latter angle corresponds to the angle of incidence/reflection from
the sample plane 9. The x-ray beam is of known wavelength: a Cu Ka line with
A = 1.540562 .
Powder samples were ground out of annealed pieces from the original beads
using a ceramic mortar. About 1 cm2 of powder was then glued to a glass slide using
a 7:1 amyl acetate collodion mixture. With the slide in place, the diffractometer
power supply was set to 40 kV and 20 mA. The detector angular speed was set


79
to 6/min, and its range to 5 < 29 < 120. The counting rate was set to 1000
counts/sec. All measurements were performed at room temperature.
The angular positions of the resulting intensities were compared to the the
oretical positions and reflection indices obtained from a structure-generating soft
ware. This procedure allows for identification of secondary-phase intensity lines
larger than the background intensity (~ 5% of maximum intensity line). For a
cubic system (i. e. CePb3 alloys), the indices for primary-phase lines are obtained
from the following equation [117]:
sin2 9 = Y~x{h2 + k2 + l2).
4 a2
Similarly, for a hexagonal system (CeAl3 alloys),
(5.2)
sin 9 =
4 (.h2 + k2 + l2) Z2
3 a2 + c2
(5.3)
The indices (h k l) and the angles 29 for the highest and narrowest intensity lines
were entered as data points into a least-squares fitting program, along with the
wavelength and structure type. The room-temperature lattice parameters and
their uncertainties were then obtained from a least-squares fit using one of the
above two equations, depending on the structure type of the sample.
5.3 Magnetic Measurements
All magnetization and magnetic susceptibility measurements were conducted
using a Quantum Design Magnetic Property Measurement System (MPMS) SQUID
magnetometer. The apparatus consisted of a liquid He dewar, the sample probe
assembly, the electronic console with temperature and gas controllers, the He gas
handling system, and a Hewlett Packard computer. The probe assembly is inserted
inside the dewar; it contains the sample space, thermometers, the sample heater,
an impedance controlling He flow, a superconducting magnet producing fields up
to 5.5 T, and the sample transport mechanism. The temperature is regulated by
the flow of He gas through the sample space and by the sample heater. Below


80
approximately 4.2 K, the liquid-helium vapor inside a pot is pumped in order to
reach temperatures down to 2 K.
The technique used for magnetization measurements on the MPMS detects
the change in flux induced by the sample under an applied field using a super
conducting quantum interference device (SQUID) amplifier. The sample is first
enclosed in a 0.5cm-long plastic straw segment, which is slid into a drinking straw
at the end of the support tube, serving as the sample holder. During each mea
surement, the sample is moved upward along the axis of a series of pick-up coils
connected to the SQUID. The SQUID voltage is read at different position intervals
accross the scan length. This voltage is proportional to the change in flux detected
by the coils, which in turn is proportional to the magnetization of the sample.
The accuracy of magnetization measurements is generally around 3%, while the
precision at a fixed temperature can be as low as 0.01%.
Magnetization curves as a function of magnetic field can also be obtained by
measuring at the lowest temperature (2 K) and measuring at each field, sweeping
the field from 0 to 5T. The magnetization (in emu/mol) is obtained by multiplying
the signal by the molecular weight of the sample and dividing by its mass. The
magnetic susceptibility x = M/H (in memu/mol) is calculated from the signal
measured at a fixed field (typically 1 kG), multiplied by the molecular weight of the
alloy, and divided by its mass and the applied field. Each measurement sequence is
fully automated, and uses a version of the MPMS software from Quantum Design.
The convention used for units of magnetization and magnetic susceptibility in this
dissertation follows from the literature on heavy-fermion systems (e.g., Refs. [5]
and [6]).


81
block
thermometer
Cu block
brass can
Figure 5.2: View of the cryostat used for zero-field specific heat measurements
betwen 1 and 10 K.


82
5.4 Specific Heat Measurements
This section will discuss the necessary cryogenic and electrical equipment to
measure specific heat of small samples (< 100mg) with large heat capacity, and
the thermal relaxation method [118, 119, 120] used for this purpose.
5.4.1 Equipment
Electronic
The experimental setup for the measurement of specific heat in both zero
and magnetic fields by the thermal relaxation method consisted of three cryostats,
a liquid-He dewar, two Keithley 220 and a Keithley 224 programmable current
sources, a Keithley 195A, 196 digital multimeter for thermometer voltage measure
ments, an EG&G Model 124A lock-in amplifier for platform thermometer current
detection, a variable decade resistor and a resistance box with three internal resis
tances. The resistance box is connected to the decade resistor in a Wheatstone
bridge configuration. A more detailed explanation of the equipment is provided
elsewhere [118, 119, 120, 121]. A Dell PC was used for data acquisition and anal
ysis. The computer was interfaced to the digital equipment using an AT-TNT
Plug and Play GPIB board from National Instruments. A 12-bit resolution Keith
ley Metrabyte DAS-1402 A/D converter board interfaced the PC to the lock-in
amplifier. The data acquisition was monitored using two PC-based programs for
thermal conductance and specific heat measurements, respectively. The software
was designed by the author using Lab VIEW version 5.1 for Windows 95/98.
Cryogenic
The cryostats used for zero-field measurements are illustrated in Figs. 5.2
and 5.3. Figure 5.2 shows the probe used in the temperature range 1-10 K. The
electrical connections are enclosed by a brass can attached to a taper joint by
pumping on the enclosure. The cooldown procedure consisted of precooling in


83
liquid nitrogen for about 15 to 60 minutes, insertion into a dewar, and subsequent
transfer of liquid He into the dewar, which reduces the temperature to 4.2 K. A
temperature of 1 K was achieved by pumping the He vapor out of the dewar/probe
assembly for about an hour.
Measurements in the range 0.4-2 K were conducted using the cryostat described
in Fig. 5.3. After reaching a temperature of 4.2 K following the procedure above,
the 4He pot was filled with liquid He from the bath by opening the needle valve,
and 3He gas was transferred into the 3He pot. The needle valve was then closed,
and the 4He pot was pumped out to reach a temperature between 1 and 2 K. Al
though this temperature can be sustained for many hours, the 4 He pot can be
easily refilled if necessary. In order to reach a temperature of 0.4 K, the following
method was used. A Cu container full of activated charcoal resides at the lower
end of a rod inside the 3He-gas enclosure. At 1 K, the 3He gas condenses inside.
As the charcoal container is lowered towards the 3He pot, the condensed 3He is
attracted to the charcoal, which acts as an adsorption pump. Temperatures below
1 K could be achieved in 20 minutes and sustained up to several hours with this
technique. Once the charcoal saturates with 3He, it was warmed up to release the
gas and the above process was repeated.
Specific heat measurements in magnetic field were conducted in a specially-
designed dewar from Cryogenic Consultants Limited (CCL). The additional elec
tronic equipment consisted of a GenRad 1689M RLC DigiBridge, used to measure
the capacitance of a thermometer used above 1 K, a CCL superconducting magnet
and a magnet power supply. The magnet is made of two inner coil sections of
niobium-tin wire and two outer coil sections of niobium-titanium wire. The cryo
stat used below 1 K is the same as in Fig. 5.3, and the one used between 1-10 K
is illustrated in Fig. 5.4. The main difference between them is the lack of a 3He
enclosure for the higher-temperature probe.


84
Figure 5.3: View of the 3He inner pot cryostat used in both zero and magnetic
field specific heat measurements between 0.4 and 2 K.


85
Figure 5.4: View of the 4He inner pot cryostat used for specific heat measurements
in magnetic fields at temperatures between 2 and 10 K.


86
All cryostats have a similar electronic design. They are equipped with radiation
shields from top to bottom, and the wires are coupled to the He bath by a heat
sink, as shown in Figs. 5.3, and 5.4. Additional wires are soldered from the heat
sink to the Cu block, and wrapped around the 4He pot to ensure thermal equi
librium. The temperature of the block is regulated by a heater made of wrapped
manganin wire. It is monitored by a Lake Shore calibrated Ge thermometer in
the range 1-10 K, and by a Speer carbon resistor between 0.4 and 2K. In mag
netic fields, a Lake Shore capacitance thermometer was used above 1 K due to its
negligible field dependence, and the Speer resistor was used from 0.4-2 K for its
known magnetoresistance [122]. All thermometers are linked to the block using
thermally-conductive Wakefield grease.
Sample Platform
The sample resides at the bottom of the cryostat, attached to a sapphire
platform by Wakefield grease. A flat surface at the bottom of the sample is impor
tant in order to establish optimum thermal contact between platform and sample.
The platform is thermally linked to a copper ring, as shown in Fig. 5.5. Two types
of platforms were used in this study. Each platform has four wires soldered to
silver pads attached to the ring by thermally-conductive Stycast. The two pairs of
wires are connected to the platform heater and thermometer, respectively, using
EpoTek H31LV silver epoxy. The platform heater is an evaporated layer of 7%Ti-
Cr alloy. For measurements between 1-10 K, the platform thermometer used was
an elongated piece of doped Ge, and the platform wires were made of a Au-7%Cu
alloy. A thin piece of Speer carbon resistor and Pt-10%Rh platform wires were
used for measurements between 0.4 and 2 K.


87
Figure 5.5: Top view of the sample-platform/Cu-ring assembly at the bottom of
the cryostat.


88
5.4.2 Thermal Relaxation Method
A thermal relaxation technique consists of calculating the time constant of
the temperature decay of the sample linked to a heat bath by a small thermal
resistance [118, 119, 120]. The electrical analog of the system is that of an RC
circuit, where the time constant is proportional to the capacitance. When heat is
applied to the platform-sample system by means of a small current (in /xA), the
temperature increases from a base value T0 by an amount AT. When the current
is turned off, the system temperature T(t) decays exponentially to T0:
T(t) = T0 + ATe~t/Tl.
(5.4)
The time constant T\ is proportional to the total heat capacity (sample plus plat
form) Ctotal:
^total
Tl = ,
K,
(5.5)
where k, is the thermal conductance of the wires linking both platform and sample
at T = T0 + AT, and the Cu ring at T = T0. The time constant was obtained
by measuring the time decay of the off-null voltage signal from a Wheatstone
bridge using a lock-in amplifier. Two arms of the Wheatstone bridge consisted
of a resistance box and the platform thermometer. By adjusting the resistance of
the box it is possible to balance the bridge and obtain the platform thermometer
resistance. The platform temperature is extracted from a previous calibration of
the platform thermometer. The accuracy of the time constant measurement in the
temperature range 0.4-10 K is 1-3%. The thermal conductance is given by
k =
P
AT'
(5.6)
Here, P IV is the power applied to the platform heater. The above equations
are valid under the assumption of an ideal thermal contact (Avsample ~ oo) between
sample and platform. In the event of a poor thermal contact between the sample


89
and the sapphire (/isamPie~^) the temperature decay can generally be described as
the sum of two exponentials
T(t) = T0 + Ae~t/n + Be~t,T\ (5.7)
where A and B are measurement parameters and r2 is the time constant between
sample and platform temperatures. The total heat capacity can be calculated
from Ti, r2, and k. The thermal conductance is measured separately by applying a
current to the platform heater, calculating the power P IV, and calculating AT
as a result of the power applied to the heater. The accuracy of this measurement
between 0.4-10 K is 5%. The sample heat capacity is calculated by subtracting
the heat capacity of the addenda (sapphire platform, wires, silver epoxy, platform
thermometer, and thermal grease) from the total heat capacity. Finally, the specific
heat is obtained by multiplying by the molecular weight and dividing by the sample
mass.
5.5 Experimental Probes
In order to accomplish the objectives discussed in the previous chapter, two
mechanisms for the study of thermodynamic properties were used in this disser
tation: alloying and magnetic fields. Alloying is a powerful tool that allows for
changes in the electronic structure, the lattice constants, and the properties of a
system. Magnetic fields allow to probe the energy scales relevant to heavy-fermion
systems at low temperatures and test their thermodynamic properties against the
oretical predictions.
The two main types of doping on heavy-fermion compounds are Kondo-hole
and ligand-site doping. The first one consists of replacing the magnetic ion by a
nonmagnetic counterpart (e.g., La or Y instead of Ce). In this method, there is a
reduction of the number of magnetic moments in the sample and some disorder in
their electronic environment. In addition, the lattice structure changes significantly


90
due to an atomic size difference between the / ion and the dopant ion. Doping with
La usually leads to a lattice volume expansion, while Y substitution corresponds
to the application of a positive chemical pressure. Ligand-site doping consists of
substituting the ligand atoms of one species by another. The main effect here is
a dramatic change in the electronic environment of the magnetic ions, changing
the value of the local exchange constants. Maximum atomic disorder is introduced
using this method, which could complicate the analysis of properties. It is of
current interest to investigate the extent to which each method of doping affects
the electronic properties.
The measurement of thermodynamic properties as a function of applied mag
netic field is an important, though not often implemented tool in the study of heavy
fermions. The relevant energy scales, both single-site and cooperative, are small
enough that magnetic fields easily accessible in a laboratory can help determine
their overall magnitude and their role in determining physical properties. The mag
netic behavior of heavy-fermion compounds ranges from short-range correlations to
non-Fermi-liquid behavior to long-range antiferromagnetic order. Magnetic fields
are useful in understanding the different types of magnetic behavior through a
comparative study of changes in the density of states, the entropy, the specific
heat, and the magnetic characteristic temperature. Various theoretical models,
including the single-impurity Kondo description, have different predictions for the
magnetic field response of thermodynamic properties. Therefore, the use of mag
netic fields as an external parameter is a convenient way of testing the applicability
of these models. Specific heat measurements in magnetic field on CePb3 and CeAl3
alloys will be presented in this dissertation in order to study the trends followed
by parameters relevant to both Kondo and magnetic degrees of freedom in these
systems.


91
5.5.1 Experiments on CeAl3
A doping study of the lattice parameters, specific heat, and magnetic sus
ceptibility of Cei_xMxAl3 alloys has been conducted, with M = La concentrations
0 < x < 1, and M = Y concentrations 0 < x < 0.2. The evolution of the lat
tice parameters and their ratio c/a with La/Y concentration x was investigated
to determine how the relative variation of a with respect to c and changes in the
lattice volume are related to trends in the thermodynamic properties. In addition,
the specific heat, the anomaly in C/T, the magnetic susceptibility, and the Wilson
ratio expressed as x/l of Cei_xLaxAl3 were studied over the whole concentration
range to search for evidence for a magnetic origin of the anomaly in this system
by comparing the concentration dependence of Tk and the temperature Tm of the
anomaly in C/T, with their dependence on the parameter J based on Doniachs
Kondo necklace model. The coupling J is proportional to the hybridization, which
is expected to decrease with La concentration (expansion of the lattice).
The specific heat of Ce0.8La0.2Al3 and Ce0.3La0.7Al3 was measured in magnetic
fields up to 14 T to compare to the predictions of the anisotropic Kondo model [15,
36, 37] and to search for clues regarding the magnetic character of the ground
state in these alloys. The measured field dependence will allow to determine a
connection between the maxima in C/T and those of the AKM. The specific heat
data of Y-doped samples will be compared to data as a function of pressure for
CeAl3 to distinguish between the effects of chemical and hydrostatic pressure on
the anomaly in C/T.
Additional Ceo.8(Lai_xYx)0.2Al3 samples with x = 0.09,0.4 were also pre
pared for specific heat and magnetic susceptibility studies. In this system, yttrium
doping of Ce0.8La0.2Al3 was conducted to create a similar hybridization environ
ment to that of CeAl3 by reducing the lattice volume to that of the undoped
compound. Thermodynamic measurements will allow to test the magnetic inter-


92
pretation of the anomaly in C/T by assuming a constant coupling J, yet reducing
TRKKY by increasing the Ce-Ce distance with respect to CeAl3.
5.5.2 Experiments on CePb3
In CePb3, the increase in the A coefficient of the electrical resistivity along
(110) points to a possible enhancement of the heavy-fermion state in magnetic
fields based on the proportionality between A and 7. A study of the specific heat
of a CePb3 polycrystal in magnetic fields will be presented in order to describe
the changes of the Fermi-liquid parameters 7 and A/72 as a function of mag
netic field. The phase diagram obtained from these measurements will be com
pared to previous magnetoresistance results along (110) to search for evidence of
the field-induced transition detected by previous sound velocity and magnetoresis
tance measurements, and for possible non-Fermi-liquid effects. The data should
be helpful in understanding the effects of a magnetic transition on the nature of
the heavy-fermion state.
Results from measurements of the heat capacity of Ceo.6La0.4Pb3 in magnetic
fields up to 14 T will also be discussed in order to investigate further the single
impurity nature of the paramagnetic heavy-fermion state of CePb3. The electronic
contribution to the specific heat below 10 K will be compared to predictions for the
S \ single-impurity Kondo model in magnetic fields. The above measurements
on CePb3 and Ce0.6Lao.4Pb3 allow for an analysis of the electronic coefficient 7 and
the Kondo state in both nonmagnetic and magnetic heavy-fermion systems.


Full Text

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MAGNETISM AND THE KONDO EFFECT IN CERIUM HEAVY-FERMION COMPOUNDS CERIUM-ALUMINUM-3 AND CERIUM-LEAD-3 By RICHARD PIETRI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2001

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ACKNOWLEDGMENTS I would like to dedicate this work to my parents Gilberto Pietri and Palmira Santiago, who made it possible for me to complete my education. There is no way to measure the amount of support and advice I have received from these two wonderful human beings. I give thanks to an all-powerful everlasting God for my parents and for the opportunity to pursue my goals and dreams. I also thank my relatives for all their support during my years at UF. The most influential person in this project was my research advisor Dr. Bohdan Andraka. He was the source behind many of the ideas on this dissertation. He was also a great mentor in the lab from whom I learned countless experimental tri c ks. He has my deepest appreciation. The second most influential person was Prof. Greg Stewart an endless source of information. I thank him very much for letting me work in his lab. His written work inspired me throughout my gradu ate career. I would also like to thank my other committee members, Prof. Mark Meisel, Prof. Pradeep Kumar, and Prof. Cammy Abernathy for their patience in reading this work, for many discussions, and for their advice regarding this dis sertation. My appreciation also goes to people whom I worked with in the lab over many years. I thank Dr. J ungsoo Kim and Dr. Steve Thomas for their train ing and technical advice, and Josh Alwood and Dr. Hiroyuki Tsujii for help in the lab and with some of the experiments. Greg Labbe and the people at the Cryogenics Lab were also very helpful, especially while using the magnet dewar. Other people in this field I would like to a cknowledge are Prof. Kevin Ingersent, for many discussions about my research and for an excellent collaboration; Prof. Peter Hirschfeld for introducing me to the theory of heavy-fermions and to the Kondo ii

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effect; and Dr. Ray Osborn and Dr. Eug ene Goremychkin who se work motivated part of this study, for very enlightening discu ss ion s over the la st year and during the 2000 APS March Meeting. I am indebted to Dr. Youli Kan ev an d m y good friend Dr. Mike Jones for developing the ]}'IE)( UF thesis template which greatly simplified all of the formatting work, and to my fellow graduate students, especially Rich Haas, Dr. Tony Rubiera, and Brian Baker for interesting physics discussions and advice. My thanks go also to Susan Rizzo and Darlene Latim er for a ll the grad-school related paperwork and for taking care of my registration over the years. Finally, my life would have been unbearable without the company and emo tional support of many people here in Gainesville FL. They helped me stay motivated and cope with the ups and downs of Physics Graduate S c hool. I would like to thank my dearest friends James Bailey Ferdinand Rosa, Dr. Carlos ( Caco ) Ortiz, Ivan Guzman, Clinton Kaiser Dr. Fernando Gomez, Soraya Benftez Cristine Plaza, Diana Serrano, Jorge Carranza Franco Ortiz, Lyvia Rodrfguez Anthony Wells Diana Hambrick, and Charles and Sarah Reagor. I apologize to the countless others who are not on this list including the people at the Southwest Recreation Center, the Worldwide Church of God, Latin nights at the Soul House Saoca La Sala, Rhythm, and all the "tailgators" over the years lll

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TABLE OF CONTENTS ACKNOWLEDGMENTS ABSTRACT CHAPTERS 1 INTRODUCTION 2 THEORETICAL BACKGROUND 2.1 Landau Fermi-Liquid Theory ... 2.1.1 Theoretical Basis for a Fermi-liquid 2.1.2 Thermodynamic and Transport Properties 2.2 Localized Magnetic Moments in Metals . 2.2.1 Electronic States of Magnetic Ions 2.2.2 Anderson Model 2.3 Single-ion Kondo Model 2.4 Anisotropic Kondo Model 2 5 Kondo Lattice . . . 2.6 Non-Fermi-Liquid Effects 3 PROPERTIES OF CeAh AND CePb 3 3.1 Properties of CeAh .. 3.1.1 Crystal Structure . . 3.1.2 Specific Heat .. .. 3.1.3 Magnetic Susceptibility 3.1.4 Transport Measurements 3.1.5 Nuclear Magnetic Resonance 3.1.6 Muon Spin Rotation .... 3.1.7 Neutron Scattering ..... 3.1.8 Chemical Substitution Studies 3.2 Properties of CePb 3 .. 3.2 1 Crystal Structure ... . . 3.2 2 Specific Heat .... . . 3.2 3 Sound Velocity Measurements 3.2.4 Transport Measurements 3.2.5 Magnetic Susceptibility . .. 3 2.6 Neutron Scattering . . . 3.2. 7 Chemical Substitution Studies lV page ii vu 1 6 6 7 10 1l 12 14 18 20 27 30 34 34 34 36 37 40 42 45 48 48 51 51 51 54 58 60 63 65

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4 MOTIVATION 68 4.1 Importance of CeAh and CePb 3 . . 68 4.2 Objectives . . . . . . . . . . 70 4.2.1 Magnetism and Heavy-Fermion Behavior in Ce Kondo Lattices 70 4.2.2 Ground State of CeAh . . . . 71 5 EXPERIMENTAL METHODS 5.1 Sample Preparation 5.1.1 Synthesis . 5.1.2 Annealing .. 5.2 Diffraction of X-Rays 5.3 Magnetic Measurements 5.4 Specific Heat Measurements 5.4.1 Equipment ..... 5.4.2 Thermal Relaxation Method 5.5 Experimental Probes ..... 5.5.1 Experiments on CeA1 3 5.5.2 Experiments on CePb 3 6 STRUCTURAL AND THERMODYNAMIC PROPERTIES OF CeA1 3 AL73 73 73 77 78 79 80 82 86 89 90 91 LOYS . . . . . . . . 93 6.1 Lattice Parameter Study of CeA1 3 Alloys 93 6.1.1 Lanthanum Doping: Ce 1 _xLaxAh 96 6.1.2 Yttrium Doping: Ce1-x YxAh . 100 6.1.3 Mixed Doping: Ceo s(La1-x Yx)o.2Ah 108 6.1.4 Summary . . . . . . . 113 6.2 Thermodynamic Measurements of Ce 1 _xLaxAh Alloys. 116 6.2.1 Magnetic Susceptibility 116 6.2.2 Specific Heat . . . . . . . . . 118 6.2.3 Discussion . . . . . . . . . . 127 6.3 Thermodynamic Measurements on Ce 1 _x YxAh Alloys 134 6.3.1 Magnetic Susceptibility 134 6.3.2 Specific Heat . . . . . . . . . 137 6.3.3 Discussion . . . . . . . . . . 139 6.4 Thermodynamic Measurements on Ce 0 8 (La 1 _x Yx)o 2 Ah Alloys 141 6.4.1 Magnetic Susceptibility 141 6.4.2 Specific Heat . . . . . . . . . . . 144 6.4.3 Discussion . . . . . . . . . . . . 147 6.5 Heat Capacity of Ce 0 8 Lao 2 Ah and Ce 0 3 Lao 7 Ah in Magnetic Fields 153 6.5.1 Results . 154 6.5.2 Discussion . . . . . . . . . . . . . . 157 V

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7 MAGNETIC FIELD STUDY OF CePb 3 ALLOYS . . . . 165 7.1 Specific Heat of CePb 3 in Magnetic Fields . . . . . . 165 7.2 Single-Ion Kondo Behavior of Ce 0 6 La 0 .4Pb 3 in Magnetic Fields 175 7.2.1 Results . 175 7.2.2 Discussion .... 8 CONCLUSION . . . 8.1 Summary . . . . 8.1.1 Ideas for Future Work REFERENCES ..... BIOGRAPHICAL SKETCH Vl 179 184 184 187 189 198

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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 MAGNETISM AND THE KONDO EFFECT IN CERIUM HEAVY-FERMION COMPOUNDS CERIUM-ALUMINUM-3 AND CERIUM-LEAD-3 Chairman: Bohdan Andraka Major Department: Physics By Richard Pietri August 2001 Measurements of the lattice parameters, magnetic susceptibility, and specific heat between 0.4 and 10 K in magnetic fields up to 14 T have been conducted on Ce 1 _xMxAh alloys, with M = La (0 ::;x::; 1) and Y (0 ::;x ::;0.2). The specific heat of CePb 3 and Ce 0 6 Lac>.4Pb 3 was also measured up to 14 T. The above experiments were performed to study the anomalies in the specific heat of CeA1 3 and CePb 3 and to better understand the interplay between magnetism and Kondo behavior in the ground state of Ce heavy-fermion systems. Data for x-ray diffraction of Ce 1 _xMxAh confirmed an anisotropic lattice volume expansion for M = La ( decreasing c/ a ratio) and a contraction for M = Y. The low-temperature magnetic susceptibility and specific heat of Ce 1 _xLaxAh are consistent with Doniach's Kondo necklace model. The electronic coefficient ,..., decreases with Y concentration, and has a nonmonotonic dependence for M = La with a minimum at x = 0.2. The temperature position of the anomaly Tm has a maximum around x = 0.3 for La doping. The lack of a suppression Vll

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of Tm for Y x < 0.2 suggests a dependence of this maximum on the absolute value change in c/ a Magnetic field measurements on La-doped CeA1 3 alloys revealed that the field dependence of Tm is inconsistent with the anisotropic Kondo model, with Tm for Ce 0 8 La 0 2 Al 3 decreasing only by 0.4 K at 14 T. Experiments on Ceo s(La1-x Yx)o 2Ah revealed that C /T ex X ex T-1+>. for x = 0.4, with A comparable to that of heavy-fermion alloys with scaling similar to that associated with a quantum Griffiths phase. Specific heat measurements up to 14 T on polycrystalline CePb 3 indicated a shift in TN to lower values, disappearing for H > 6 T. The ratio A/, 2 is field dependent below 6 T. Studies on Ce 0 6 La 0 4 Pb 3 revealed that the electronic specific heat /:lC of this alloy can be described by the single-ion Kondo model in magnetic fields, with T K 2.3 K. A previously undetected anomaly in C /T was found below 2 K, shifting toward higher temperatures with increasing field. This maximum appears to be a feature of the Kondo model in magnetic fields. Vlll

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CHAPTER 1 INTRODUCTION Over the last century, our current understanding of the metallic state developed as a result of substantial experimental and theoretical work based on the discov ery of the electron by J. J. Thomson in 1897 and the advent of modern quantum physics. The behavior of solids has long been described in terms of the dynam ics of its constituents, electrons and nuclei; with the former being responsible for electrical conduction and dominating the thermodynamic properties at very low temperatures. This single-electron picture of the solid state has been remarkably successful in describing the properties of many body systems that, as a whole, are much more than a simple array of atoms. The current picture of a lattice of ions embedded in a gas of electrons obeying Fermi-Dirac statistics is justified by the theoretical framework set by Landau on his Fermi-liquid theory, for which he won the Nobel Prize in 1962. Based on the principle of adiabatic continuity, the theory states that the metallic state at low temperatures can be described quantum-mechanically in terms of a fluid of weakly-interacting particles (Fermi liquid, see Chapter 2). The properties of this quantum fluid are similar in form to those of a gas of noninteracting electrons. Landau's Fermi-liquid theory has been successfully applied to a variety of systems, including liquid 3 He and normal metals like Au and Ag. It is one of the foundations of modern condensed matter physics, rivaled in its scope only by the standard model of particle physics Since the development of Fermi-liquid theory, the synthesis of new materials displaying unusual properties presented challenges to this well-established descrip tion of condensed matter systems. A large number of these materials exhibit strong 1

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2 electron correlations in their normal (paramagnetic) state, stretching the limits of applicability of Fermi-liquid theory. In some materials, the effect of these interac tions is reflected in the deviations of their thermodynamic and transport properties from the predictions of this theory. This group includes the normal state of high temperature superconductors and non-Fermi-liquid systems [1, 2, 3]. In others, their normal-state properties remarkably agree with Fermi-liquid theory, despite the presence of strong interactions between electrons and even the coexistence with a magnetic phase. It is in this group that we find most heavy-fermion compounds. Heavy-fermion sytems are alloys where one of their constituents is a member of the lanthanide (Ce, Yb) or actinide (U, Np) family. They are so called because the effective mass of the particles dominating the thermodynamics, which have half-integer spin (fermions), is hundreds of times that of a free electron (heavy). Extensive reviews on these systems have been written over the last two decades [4, 5, 6, 7 8]. In these systems, the interactions between localized f electrons and the conduction band reduce the f magnetic moment and give rise to a Fermi-liquid like state at low temperatures. The large effective mass m* is a consequence of the large density of states at the Fermi energy N(O). The most widely used experimental parameter to determine both the density of states and the effective mass of these particles is the Sommerfeld coefficient of the specific heat ,. In Fermi-liquid theory, is proportional to both m* and N(O). The specific heat of metals in their normal state at low temperatures is approximated by the following formula [9, 10]: C = ,T + {3T3, (1.1) where, is the electronic contribution and {3 is the Debye contribution from lattice vibrations. Values of, for heavy-fermion compounds typically range from several hundred to several thousand mJ /K 2 mol, compared to less than one for normal metals like Cu and Au. The presence of additional contributions to the specific

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3 heat makes the determination of, more diffi c ult a nd i s u s u a ll y r e pr ese n te d as th e extrapolated value of C /T at zero temper a tur e The heavy-fermion character is also reflected in oth e r properti e s lik e m ag netic susceptibility and electrical resistivity. The magnetic susceptibility at high temperatures follows the Curie-Weiss form [9 10], C X = T+0 c w ( 1.2 ) where C is the Curie constant and 0cw is the Curie-Weiss temperature. At lower temperatures, the susceptibility reaches a constant value (rvlO to 100 memu/mol) proportional to the density of states N(O) according to Fermi-liquid theory. The electrical resistivity of metals at very low temperatures is given by p =Po+ AT 2 (1.3) Here p 0 is the temperature-independent term due to scattering off impurities and defects, and A is the Fermi-liquid term. Values for A in heavy fermions are in the order of tens of n cm/K 2 much larger than those corresponding to normal metals. An intriguing fact of heavy-fermion systems is that the observed Fermi liquid properties are not exclusive to the normal state of these materials. The variety of ground states for these compounds (5, 6] ranges from nonmagnetic as in UPt 4 Au [11], to antiferromagnetic (UCu 5 U 2 Zn 17 CeAh) to superconduct ing (UBe 13 CeCu 2 Si 2 ), to both magnetic and superconducting (UPt 3 URu 2 Si 2 UPd 2 Ah, UNi 2 Ah). The presence of magnetism and/or superconductivity in thes e compounds indicates that the heavy Fermi-liquid ground state coexis t s with a dif ferent phase. This unconventional ground state, when tuned as a fun c tion of pre s sur e, magnetic field, and/or chemical disorder can completely move a wa y from Fermi liquid behavior. These non-Fermi-liquid (NFL) alloys hav e b een w id e l y st udi e d

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4 during the last decade [3, 12). Their thermodynamic and transport properties are characterized by power laws in temperature. Theoretical models for the description of these effects are currently under development. Examples of these systems [3, 12) include UCus-xPdx, CeCu6-xAux, U1-x YxPd3, Ce1Ni3 (pressure-induced NFL), and CeNi 2 Ge 2 [13), U 2 Pt 2 ln, and U 2 Co 2 Sn [14) (NFL compounds). Among the many unresolved issues in heavy-fermion materials is the coex istence of magnetic and Fermi-liquid degrees of freedom giving rise to the ground state. In addition, a recent interpretation of the ground state in terms of an anisotropic interaction between f electrons and the conduction band has been proposed for these systems [15). Both topics are confronted in this dissertation by studying structural and thermodynamic properties of two well-studied canoni cal heavy-fermion compounds: CeAh and CePb 3 Cerium-based compounds were chosen because of their simpler electronic configuration. There is only one 4f spin per Ce ionic site, as opposed to two or three 5 f spins per U ionic site. The ground state properties of the above compounds are not well understood, despite more than 20 years of study. The experiments presented here will help clarify these issues in order to motivate further discussion of these topics on both theoretical and experimental grounds. The outline of the dissertation is as follows: The necessary theoretical back ground behind heavy-fermion physics is presented in Chapter 2. The chapter begins with an overview of Landau's Fermi-liquid theory, followed by a discussion of the energies involved in the determination of the ionic ground state and mag netic moments in metals. The Kondo effect, the mechanism responsible for the Fermi-liquid state at low temperatures in heavy fermions, is then presented along with its anisotropic version. The concept of a Kondo lattice is also introduced, and the consequences of extending the Kondo model to a concentrated system are discussed. Chapter 3 gives an experimental review of the essential physical

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5 properties of both CeA1 3 and CePb 3 It is then followed by a discussion of the motivation behind this study (Chapter 4). Chapter 5 gives a general description of the experimental apparatus and methods used in this dissertation. The results of structural and thermodynamic measurements on CeAh and CePb 3 alloys are then explained in Chapters 6 and 7, respectively. Finally Chapter 8 summarizes the main findings of the dissertation and elaborates on its contributions to the field. The dissertation ends by pointing out unresolved issues and elaborating on ideas for future studies.

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CHAPTER 2 THEORETICAL BACKGROUND This chapter discusses the current theoretical models describing the charac teristics and behavior of heavy-fermion systems, such as Fermi-liquid theory ionic configurations in solids, and the Kondo effect. 2.1 Landau Fermi-Liquid Theory Landau s theory of interacting fermions at low temperatures [16] stands as one of the most remarkable achievements of theoretical condensed matter physics. It has often been compared to the standard model of elementary particle physics, as far as its scope and prediction of physical properties is concerned. The basis of its success is the adaptation of the Fermi gas model of noninteracting electrons to a system of interacting fermions at low densities and energies. This mapping allows for a single-particle description of thermodyamic and transport properties of Fermi systems like liquid 3 He and normal metals like copper, silver, and gold. Although Landau's Fermi-liquid theory has been successfully applied in a large number of condensed-matter systems, its validity relies on a series of assumptions that apply mostly to weak interactions and isotropic scattering between fermions. Heavy-fermion systems, often described as having a Fermi-liquid ground state, exhibit strong many-particle correlations that lead to magnetic order in many cases. The relation between magnetism and Fermi-liquid behavior in heavy fermions is at present not fully understood. Nevertheless, the theory has been successful in predicting the properties of these compounds. In this section, the differences 6

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7 between Fermi-gas and Fermi-liquid models are outlined, followed by a description of thermodynamic and transport properties of the F erm i liquid. 2 .1.1 Theoretical Basis for a Fermi-liquid For a system of noninteracting particles obeying Fermi-Dirac statistics, with mass m, momentum p and spin a, the probability of finding a particle with energy c is given by the Fermi distribution function n( c) [17], 1 n(c)----1 + e(c-)/kaT' (2. 1 ) where k 8 is Boltzmann s constant and = EF, the Fermi energy. The spins are assumed to be quantized along the z-axis. In the absence of an external field, the energy of a particle becomes c = c p = p 2 /2m, and the ground state distribution n~a is given by a -{ 1 P < PF npa 0 p > PF (2.2) where PF is the Fermi momentum. The ground state energy of the system Ea is equal to (2.3) The total energy is the sum of the ground state energy and the excitation energies of the system. The number of excitations is given by the difference between the ground-state and excited-states distribution functions: (2.4) where 8npa > 0 corresponds to a particle excitation and 8npa < 0 to a hole excita tion. Since the excitation energies depend on the number of excitations, the total energy of the system can be expressed as E =Ea+ LEP8npa pa (2.5)

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8 Despite the strong electrostatic forces between electrons in a solid, the Fermi gas model for noninteracting electrons is capable of describing their behavior in metals. At metallic electron densities, the kinetic and Coulomb energy terms are comparable in magnitude to each other. The justification for the predictions of this model come from their close resemblance to those of the interacting case. Through adiabatic continuity [16], it is possible to label the states of an interacting Fermi system in terms of the states of a Fermi gas. When the interaction potential is treated as a perturbation, and is turned on slowly enough to prevent a change in the eigenstates of the Hamiltonian, there is a one-to-one correspondence between the initial and final states. The excitation energies of the final state are different from those of the Fermi gas because of the additional interaction term in the Hamiltonian. The final state has also the same entropy and can be described by the same distribution function as the noninteracting Fermi gas. The system resulting from the adiabatic perturbation is called a Fermi liquid. The excited states of a Fermi liquid are no longer associated with independent electrons, but to negatively charged, spin-1/2 fermions called quasiparticles, with an effective mass m* different from that of a free electron. These quasiparticles have a sufficiently long lifetime T between collisions at low temperatures. The condition for the applicability of Fermi-liquid theory is that the uncertainty in the energy of a particle of order n/T ex (k 8 T)2, is much smaller than the width of the excitation spectrum of the Fermi distribution function, of order k 8 T [18]: (2.6) This condition applies to a system with excitation energies much smaller than k 8 T. Due to the mutual interaction between quasiparticles, the total energy of the system is no longer represented by the sum of ground state and individual excitation energies. As a consequence, each quasiparticle is under the influence of a self-consistent field from other quasiparticles This self-consistent field affects

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9 both potential and kinetic energy terms of each individual quasiparticle. The energy E then becomes a functional E { npa} of the distribution function The excitation ( quasi particle) energy, which itself is a functional of the distribution function, (c = E{ npa} ), has an additional term corresponding to the interaction energy between two quasi particles f pa p'a', each with momentum and spin p O' and p' 0' 1 respectively. This energy term is also a functional f { npa} of the distribution function, so that the quasiparticle energy becomes an expansion in terms of the number of excitations 8npa [19]: Epa = E~a + L fpa p'a' 8np'a' + ... p'a' (2.7) where E~a is the ground-state quasiparticle energy. As a result, the total energy of the system is also an expansion in c5npa: E = Eo + L E~a 8npa + 1 L fpa p'a' 8npa 8np 1 a'+... (2.8) pa pa p'a' When considering an ensemble of quasiparticles with spins quantized along different axes, the distribution function npa should be treated as a 2 x 2 matrix in spin space, that is, as a linear combination of the Pauli matrices. In the absence of higher-order scattering processes, like spin-orbit coupling, the interaction energy can be expressed as the sum of symmetric and antisymmetric (spin-dependent) terms (2.9) where J;P, and J;P, are the symmetric and antisymmetric terms, respectively, and -r, r' are Pauli matrices. Both J;P, and J;P, are dependent on the angle between p and p', and can be expressed as an expansion in Legendre polynomials with coefficients N and ft, in the case of isotropic scattering (spherical Fermi surface). In some metals, the presence of crystal-field and spin-orbit coupling effects significantly distorts the Fermi surface, changing the angular dependence of

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10 f ;P, and f;P,. The Landau parameters F,,S and Ft are defined with respect to the coefficients N and ft corresponding to isotropic scattering: F,,S = N(O) N, Ft= N(O) ft, where N(O) is the density of states at the Fermi energy. 2.1.2 Thermodynamic and Transport Properties (2.10) Since the total energy of the system of quasi particles is an expansion in terms of the variation in the distribution function 8npa, it follows that the thermodynamic properties are expansions in powers of the temperature. The first term of the expansion corresponds to the result for the noninteracting Fermi gas. Subsequent terms are finite temperature corrections due to coupling with spin fluctuations within the interacting fermion fluid. The specific heat of a Fermi liquid is given by: C = T + a T 3 In T + ... (2.11) where the Sommerfeld coefficient is 2 2k2 k2 = 7r s N(O) = am PF 3 31i 3 (2.12) The first term is linear in temperature, and proportional to the effective quasipar ticle mass m*. The effective mass is related to the free-electron mass m by m* 1 = 1 +-Fs m 3 1 (2.13) where Ft is one of the Fermi-liquid parameters. The second term in the specific heat is a smaller correction and originates from quasiparticle coupling to spin fluctuations. The magnetic susceptibility is independent of the temperature to first order: 2 1i2 ,2N(O) X = 2etrN ( 0) + ... = 4 1 + F8 + ... (2.14)

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11 where eff corresponds to the quasiparticle effective magnetic moment, 1s the linear coefficient of the specific heat, and F 0 is a Fermi-liquid paramet er. Th e second term in the expansion is of order T 2 ln T. The electrical resistivity due to quasiparticle scattering is inversely propor tional to the time between collisions T, and proportional to the square of the temperature [20]: = AT2 = 7r2e2m(76.06) (I_) 2 P 16N(0)h 3 T;, (2.15) where e is the electronic charge, m is the mass of a free electron h is Planck 's constant, and T; is the effective Fermi temperature of the Fermi liquid. 2.2 Localized Magnetic Moments in Metals Electrons in metals are not entirely free particles. They are constantly under the influence of a periodic potential due to a charged lattice. In addition, the distances between electrons are close enough for the Pauli exclusion principle to play an important role in the formation of energy levels. In general, electrons with energies in the vicinity of the Fermi energy tend to be delocalized and form part of the conduction band. To a first approximation, the equation of motion of nearly free electrons is given in the Hartree-Fock form. Orbital states within a single ion are formed by electrons with energies below cp, and are more localized. Their wave functions retain some ionic character. For the most part, the thermodynamics of a metallic system in its normal state can be described by taking into account the individual contributions of quasiparticles (Fermi-liquid theory) and localized free spins. However, in many systems, the lattice of localized electron near or below the Fermi level strongly interacts with conduction el ctrons. Th r su ltin g potential can have a major effect on the thermodynamics not account d for by nearly-free electron models. In order to understand th b havior of 4f m gn ti

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12 moments in metals it is important to have a knowledge of the interactions that give rise to their formation. 2.2.1 Electronic States of Magnetic Ions The localized states of electrons in metals are similar to those of free magnetic ions [21]. For each energy level n, there are (2s+l)(2l+l) degenerate states, where n, l, ands are the principal, orbital, and spin quantum numbers, respectively. The degeneracy is partially lifted by the electron-electron Coulomb interaction, of order l0eV. These energy levels, called multiplets, are filled up according to Hund's rules and the Pauli exclusion principle. Once all 2(2l + 1) levels are fully occupied, the sum total of spin and orbital angular momenta equals zero, so that a filled shell has no magnetic moment. In an incompletely filled shell, one of two relevant interactions responsible for lifting any additional degeneracies is spin-orbit coupling. The spin of each orbiting electron couples with an effective magnetic field due to its motion about the nucleus. The effective field is proportional to the orbital angular momentum of the electron. The total spin-orbit interaction is then given by 1-lso = ,\(LS) = g;Zeff (:3) 2~(LS), (2.16) where g is the electron g-value, 8 is the Bohr magneton, Zeff is the effective atomic number, and L and S are the total orbital and spin angular momenta, respectively. The coefficient ,\ is positive when the shell is less than half-filled, and negative for more than half-filled. The coupling between Land S has an effect on the eigenstates of the ionic Hamiltonian. Both operators are no longer constants of the motion, and the states are now labeled by the total angular momentum J = L + S. As a consequence, the degenerate states of each multiplet split into 2S + 1 levels for L > Sor 2L+ 1 levels for L < S, each carrying a 21 + 1 degeneracy.

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1 3 The second interaction responsible for th e s pli tt ing of d ege n e ra te e n e r gy l ev els of a multiplet is due to the surrounding ion s C rysta l-fi e ld e ff e ct s r e p rese nt th e influence of Coulomb interactions from neighborin g c h a rg es on lo ca liz e d s t ates. The crystal-field contribution is given by the net Coulomb en e rgy du e to poi nt charges located at the different crystallographic sites and by the dire c t Coulo mb interaction between the outermost localized orbitals of surrounding ion s. To a fi rst approximation, (2.17 ) where Rj and Zej are the position vector and charge of the jth ion, respectiv e l y, and r i and e indicate the position and charge of the electrons. The potential V c EF can be expressed in polar coordinates and expanded in terms of the spheric a l harmonics Yim ( 0 ). The result is an expansion in powers of ( r) and of the angul a r momentum operators L 2 and L z ( or J 2 J z ) The crystal-field interaction partiall y lifts the degeneracy of the ionic states. The number of states is determined by the symmetry of the crystal structure, and typically increases for structures of low point-group symmetry. In solids with magnetic ions, the relative strength of spin-orbit and crystal field energies depends on the localized character of the wave function corresponding to the incompletely-filled shell. The spin-orbit interaction increases as the distance from the nucleus decreases (Hso ex (1/r 3 ) ). The crystal-field contribution H c EF on the other hand, increases with the radial extent of the wave function. For electrons in incomplete d orbitals, HcEF > Hso due to their direct interaction with orbitals from neighboring ions. In contrast, electrons in incomplete f orbitals are very localized and reside close to the nucleus. Therefore the spin-orbit in t erac t ion is very large(> 0.1 eV), and the crystal-field contribution H c EF comparativel y sm a ll e r (2:: 0.01 eV). As a consequence, the lowest-lying multiplet is fir st spli t b y the s pi n

PAGE 22

14 orbit interaction and each of these levels is split further by the crystal field. The ground state of the system is the crystal-field ground state For example, in Ce 3 +, there is only one 4f electron (S = and the lowest-lying multiplet corresponds to L = 3. 1tso splits the multiplet into two 6-fold degenerate levels: IJ = ~) and I J = ~). The lowest-energy level ( J = ~) is then split by 7tcEF into a doublet and a quartet for cubic crystal symmetry and into three doublets in the case of hexagonal symmetry. For a crystal-field doublet ground state, the effective total angular momentum of Ce 3 + is J = 2. 2. 2 Anderson Model The fundamental problem in magnetic alloys (including heavy-fermion sys tems) is the coexistence and interaction of the electron liquid with localized atomic orbital states. From this point of view, the conduction band is formed primarily of electrons in the outermost s and p shells, and the localized states consist of d or f orbitals in iron-group and rare-earth ions, respectively. The following discus sion will focus on localized f states. Electrons in a partially-filled f shell have a finite probability of mixing and are free to interact with the conduction band if their energy is close to the Fermi level. The interaction with the conduction electrons regulates the average occupancy and magnetic moment of the f level. This problem was described by Anderson [22] in the following Hamiltonian for a single impurity embedded in a free-electron environment: (2.18) The first term is the unperturbed free-electron Hamiltonian: (2.19) Here, Eknkois the energy of a free-electron state with wave number k and spin CJ, and nkois the number operator

PAGE 23

1 5 (2 2 0 ) with aL and aka the creation and anihilation operators r e spectiv e ly for a fr ee electron state with labels k and CJ. The second term is the unperturbed e n e r gy o f the localized f level: ( 2 21 ) where E I corresponds to the energy of the f level and (2 22) The third term represents the on-site Coulomb repulsion between two f elec trons of opposite spin: (2.23) with Uthe Coulomb integral between the two f states, and nn and nn the number operators for f states with up and down spin respectively. The last term denotes the mixing between conduction electrons and the f orbital: 1tcf = z:= vkJ(alaafa + a}aaka ). ka (2.24) Here Vkf is the hybridization matrix element between localized and conduction electronic states. The effect of the Anderson Hamiltonian on the localized f states depends on the relative magnitudes of the Coulomb and mixing terms. The Coulomb repulsion U determines the separation of the up and down spin f levels with respect to each other. The hybridization term Vkf is responsible for a broadening of the f levels which determines the overlap between the lowest f state and the Fermi energy These levels are represented by a Lorentzian of width 2r where (2 25 )

PAGE 24

16 and N(O) is the density of states at the Fermi energy. Figure 2.1 illustrates the density of states of up and down-spin free-electrons and localized levels for different relative strenghts of Coulomb repulsion and mixing width. For U >> I Vkf I the localized up and down-spin levels ( d or f) have a small width 2r and are well separated by U. The down-spin level resides far above the Fermi energy and is therefore unoccupied favoring the formation of a strong local magnetic moment. If the energy of the up-spin state is close to the Fermi energy in the limit U--+ oo, the localized moment couples strongly with the conduction band (Kondo effect). This scenario corresponds to integer valence, and is conducive to the formation of the heavy-fermion state when the impurity concentration is of the order of Avogadro's number NA and the magnetic ions achieve the periodicity of the crystal lattice. For U I Vkf I, both localized levels are significantly broad and might overlap with the Fermi energy due to a reduction in U. An overlap with the conduction band results in partial occupancy of both up and down-spin levels, leading to mixed valence and the formation of a weak local magnetic moment. In the limit IVkJI >> U 0, both levels have the same energy and occupancy and the impurity loses its magnetic moment. By studying the limit in which r << E f, Schrieffer and Wolff [24] were able to perform a canonical transformation on the Anderson Hamiltonian that eliminates the hybridization term Vkf. Instead, the transformed Hamiltonian is expressed in terms of 1t 0 1t 01 riff, and an exchange interaction between /-ion and conduction electron spins rlex = L Jkk'sk S1, kk' (2.26) where Sk and Sf are the spin polarization of the conduction electrons and the spin of the impurity, respectively, and Jkk' the exchange coupling constant. Close to the Fermi level, k, k' '.:::'. kp, and Jkk' becomes

PAGE 25

17 N! (E) Nf (E) N! (E) Nf (E) 2r N ,1. (El Nj (fl N! (E} Nf (El Figure 2.1: Spin-up and spin-down electronic density of states distributions for a localized d orbital embedded in a sea of conduction electrons. Upper left: U = I vk/ I = O; upper right: u >> I vk/ I; lower left: u I vk/ I; lower right: u << I vk/ I; ( u = 0) (from Mydosh, 1993) [23).

PAGE 26

18 (2.27) where J is the Kondo coupling constant. In this manner, the Anderson Hamilto nian effectively transforms into the Kondo Hamiltonian in the limit r << E 1 ( or N(O)J << 1). 2.3 Single-ion Kondo Model The Kondo problem is that of a single localized magnetic impurity in a metal lic host. This scenario corresponds to the above-mentioned U oo limit of the single-impurity Anderson model, with E 1 close to the Fermi level. The following discussion refers to the case of a spinimpurity in a sea of conduction electrons, as in the crystal-field ground state of Ce 3 +. As the temperature decreases, the local ized f orbital hybridizes with the conduction band, spin-flip scattering increases, and a scattering resonance appears near the Fermi level, known as the Kondo or Abrikosov-Suhl resonance. The Hamiltonian describing these processes is the Kondo ( or s-d) Hamiltonian, of the form (2.28) where J is the effective coupling constant between f and conduction electrons ( as in Eq. 2.27), S is the localized spin, and Si and ri represent the ith conduction electron spin an:d position vector, respectively. In the case where both E I and U + E 1 are symmetric with respect to the Fermi energy (U /2 = lcF E1I), J IVkp/12 (2.29) ex lcF E1I' where c F is the Fermi energy. A perturbation treatment of 1-lKondo beyond the Born approximation leads to an expansion of the thermodynamic and transport properties in powers of J N(O) ln(k 8 T / D). Here, N(O) is the density of states at the

PAGE 27

19 Fermi energy and Dis the bandwidth of scattering states. The e l ectrical resistivity was calculated by Kondo [25] using third-order perturbation theory: The constant term 3 m1r J 2 PB= ---S(S + 1) 2 ne 2 h 4cp (2.30) (2.31) obtained from the Born approximation, is a residual resistivity term due to the presence of the magnetic impurity. The third-order term diverges at low tempera tures. The specific heat and magnetic susceptibility due to the impurity are given by C = ( ~J N(0)) 4 ir 2 S(S + l)k 8 ( 1 + 4J N(O) Ink;+ ... ) (2.32) and X = g2~S(S + 1) [1 + J N(O) (1 J N(O) In ksT)-1] 3k 8 T D (2.33) respectively. The perturbation treatment for J < 0 breaks down at a temperature (2.34) The temperature TK is called the Kondo temperature. At low temperatures (T << TK ), the impurity spin strongly couples with the conduction electron spin polarization, forming a many-body singlet that com pletely suppresses the localized magnetic moment at T = 0. In this range the thermodynamic and transport properties can be described by Fermi-liquid theory due to the absence of an impurity spin. The zero-temperature susceptibility of the impurity is inversely proportional to the Kondo temperature [26] ( 1 ) 2 1.29 Xo = 2 9 8 1rk 8 TK (2.35) and the linear coefficient of the specific heat is given by

PAGE 28

7rks = 1.29-T 6 K 20 (2.36) The ratio of the magnetic susceptibility to the electronic specific heat coefficient ,, called the Wilson ratio, is given by Xo = (gs ) 2 2 7r ks (2.37) This value is twice that corresponding to the noninteracting electron gas. The exact solution to the Kondo Hamiltonian and its thermodynamic prop erties in terms of T < T K and T > T K and a range of magnetic fields were obtained using the Bethe ansatz [26, 27, 28, 29]. The above equations follow the exact solution obtained with this method. Numerical solutions for the specific heat and the magnetic susceptibility of a spinimpurity in different magnetic fields are illustrated in Figs. 2.2 and 2.3. The zero-field specific heat reaches a maximum at a temperature just below T K. Both the magnitude and the temperature posi tion of the maximum increase with field, reaching a shape corresponding to the Schottky anomaly of a free uncompensated spinat large fields 8 H >> ksTK, where g is the g-factor of the magnetic impurity. The zero-field magnetic suscep tibility shows a Curie-like increase for T > TK, and then saturates until it reaches a temperature-independent value well below TK. A maximum associated with the Schottky anomaly of the specific heat appears around TK for 8 H/ksTK = 2 [30]. Its temperature position increases, while its magnitude decreases with increasing field. 2.4 Anisotropic Kondo Model The anisotropic Kondo model (AKM) [31, 32] refers to the problem of a single magnetic impurity coupled to the conduction electrons via an anisotropic exchange interaction J 1 11 J 1., where J 11 >> J 1.. The Hamiltonian is given by

PAGE 29

0.35 0 30 0 25 $ 0.20 0.15 0.10 0.0S 10~ 21 S=112 10 2 10 1 10 1 10 2 10> Fi g ur e 2. 2 : S pec ifi c h eat o f a S = Ko nd o impur ity as a fun ction o f T /TK for d iff ere n t magnet i c fi e l ds ( H ----t 8 H/ ks T K) [30] 1.8 H=O.O 1.4 S=ll2 0 = 1.0 fr 0 {I) 0.6 = (I) 0.2 10-3 10.:a 10 1 10 10 1 10 2 10s T/fK Fi g ur e 2.3: Magnet i c s u sce p t ibili ty o f a S = Kondo impurity as a function of T/T K for d iff ere n t mag n et i c fi e ld s ( H ----t 8 H /ksTK) [30].

PAGE 30

22 (2.38) where cL. and Cka are the conduction electron creation and anihilation operators s+ andsare the impurity spin raising and lowering operator eigenvalues and S z is the impurity spin value in the z direction. The first term in 1-lAKM represents the conduction-electron energies the second and third terms represent the in-plane (J1_) and easy-axis (J11) exchange interactions between a localized spin and the conduction electrons respectively and the last term corresponds to the Zeeman energy due to a local magnetic field h applied only to the impurity spin S. The Kondo temperature for an anisotropic exchange interaction (J11 < 0) is given in terms of J11 and J1_ as [21 33] k T = D exp x tanh -i -'----[ 1 Jll s K N(O) JJ1f Jl -J11 (2.39) where N(O) is the density of states and D is the bandwidth. The exponential dependence of the Kondo temperature in the parameter J11 is qualitatively similar to the J dependence of T K in the isotropic case The Hamiltonian for an anisotropic Kondo interaction has been used suc cessfully to evaluate the properties of the spin-boson Hamiltonian (34, 35, 36 37], which describes the dissipation in the dynamics of a two-level system by an Ohmic bosonic bath. A mapping of the spin-boson model (38] onto the AKM has been exploited to calculate the thermodynamic properties of the former model. Further more, the parameters of the spin-boson model have recently been used to describe the properties of the AKM applied to the heavy-fermion system Ce1-xLaxAh [15] The spin-boson Hamiltonian has the form

PAGE 31

23 (2.40) Here ax and az are Pauli matrices, is the tunneling energy between the two states and E is an external bias applied to the system. The third term corresponds to the energy of the bosonic bath and the last term represents the coupling of the two-level system to the bath, with coupling constants C 0 In the case of Ohmic dissipation, the spectral function of the system is J ( w) = 21r aw for w << we, where a is a measure of the strength of the dissipation and We is a cutoff frequency. For a =J 0, the tunneling energy (n = 1) is renormalized into (~)l~o ~r-~ We (2.41) with ~r/k 8 equivalent to the Kondo temperature TK in the AKM. The low temperature behavior of both spin-boson and AKM systems is that of a Fermi liquid. The linear coefficient of the specific heat per total mole is given by [35, 36] (2.42) where NA is Avogadro's number and R k 8 N A is the gas constant, and the magnetic susceptibility of the spin-boson model per total mole at T = 0 is (2.43) where g is the g-factor of the impurity spin. The susceptibility of the AKM at T = 0 differs from Xs 8 by a factor of a: XAKM = DX 88 The Wilson ratios for both models are related as follows:

PAGE 32

where RAKM = aRss R i 1r 2 k~ Xss ss 3 (gs)2 'Y 2 a 24 (2.44) The thermodynamic properties of the AKM are given in terms of the exchange interactions ( 111) and ( 11_), and therefore can also be expressed in terms of the parameters a and ~r of the spin-boson model [35 36]: ~r = pl1_, a= [1+ tan-1 (rr:J11 )f (2.45) Figure 2.4 illustrates the temperature dependence of the static susceptibility and specific heat as C /T for different values of the dissipation a and E = 0. The parameter a is a good measure of the Kondo anisotropy of the system since it decreases sharply with increasing 111. Both curves are universal functions of (T / ~r) rv (T /TK ). For E = 0 the electronic coefficient of the specific heat is given by 1 = a/ ~r and C /T reaches a maximum at a temperature corresponding to ~r for a < 0.3. This maximum is reduced in magnitude with increasing a The susceptibility expressed as k 8 TXss has a finite value at T = 0, as in the isotropic Kondo model and reaches the free-spin value at high temperatures. The main effect of a is to increase the temperature at which this latter value is attained. The temperature ~r indicates the crossover between Kondo and free-spin behavior. The behavior for a finite bias E > 0 is described in Fig. 2.5 for a = 0.2. The quantity E is equivalent to a magnetic energy 8 h acting on the impurity spin in the AKM. The temperature ~r is renormalized by E, and becomes [37] (2.46) The effects of a field on the specific heat are a strong reduction of 1 an attenuation of the maximum in C /T, and an increase of its temperature position given by Ar. The low-temperature susceptibility strongly decreases as a function of the

PAGE 33

25 parameter E. It also shows a maximum for fields of order llr and above with a temperature position that increases with llr. 2.5 Kondo Lattice Certain types of metallic compounds, including heavy-fermion systems, can be described as a lattice of Kondo impurities embedded in a metallic host (39 40, 41]. This class of materials is commonly referred to as concentrated Kondo systems. In these alloys, a giant Abrikosov-Suhl resonance of width T K appears in the density of states near the Fermi level for T << T K. In the case of spin Kondo scatterers, the resonance lies right at the Fermi energy. This feature indicates the crossover to a strong-coupling regime in the scattering between f and conduction electrons, growing in size as the number of impurities approaches Avogadro's number NA. Consequently, there is a substantial increase in the density of states at cp. Figure 2.6 illustrates the evolution of the Abrikosov-Suhl resonance for different temperatures. In heavy-fermion compounds, the 4f level is located well below the Fermi energy. As a result, the localized orbital has integer valence. The large resonance in the density of states has an effect on the effective mass m*, as indicated by Fermi-liquid theory. At high temperatures (T >> TK ), the Abrikosov-Suhl resonance disappears, and the system behaves as an ensemble of classical free spins. Two other characteristics of the Kondo lattice are the appearance of coherence effects and interactions between magnetic impurities. Below a temperature Teoh the electronic properties change from those described by scattering off independent Kondo impurities to those reflecting the periodicity of the lattice via Bloch 's theo rem. This crossover is usually described in terms of a maximum in the temperature dependence of the specific heat as C/T and the electrical resistivity around T~T coh A consequence of coherence is an increase of indirect exchange interactions between impurity spins. At distances larger than the 4f radius (r 41 < 0.5A) but less than

PAGE 34

..._ '-" :2 1.00 (a) 0.80 .._. ... 0.60 t,,..; -----0.40 t0 ------------0.20 0 00 2 1010 1 0.30 0.20 0.10 0.00 -3 10 ~1/5 a=l/4 -----o.=l/3 ---a-1/2 ----o.=2/3 fJ;=.3/4 a.=4/5 10-2 26 a=l/5 a.=1/4 ... _____ a=I/3 ---a=l/2 __ ..,... __ a.=2/3 o.=3/4 a=4/5 10 10 1 10i kaT/~ (b) Figure 2.4 : Thermodynamic properties of the anisotropic Kondo model for E = 0 and different values of a a) Specific heat expressed as ~rC/k 8 T vs T/~r b) Universal stati c susceptibility curves expressed as k 8 T Xs b vs T / ~r (37).

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er:-= l /5 0.30 r------,------------......----,.------, (a) -. 0.20 _______ _,,,., :2 -.. 1-0 0.10 ..,,. ,.._,. _,_,,.._._,. (b) 0.15 ....,. _______ 0.10 0.05 ; I I I I -e=O = 2 -4 -3 .... -E= 2 -'2 --; 2 -1 --= 2 0 ~E=2 +I ---e= 2 +2 ---E= 2 +3 --e= 2 +4 e=2 O.O~ Oi:;_ 2 ;;::;;;::;::~1~0~1 ;.;......-.-..1.0~...:..::..-1...i.:0;1 ..-.L~1=0~ 2 ,__...1...,..0 3 k 8 T/~, 27 Figure 2.5: Thermodynamic properties of the AKM for a = 0.2 and different values of E (in units of .6.r)a) Specific heat as .6.rC/k 8 T vs k 0 T/.6.r. b) Susceptibility curves expressed as .6.rXsb vs k 0 T/ .6.r [37).

PAGE 36

28 g{E) Figure 2.6: Density of states of a nonmagnetic Kondo lattice at different temper atures, showing the evolution of the giant Abrikosov-Suhl resonance [39].

PAGE 37

29 the size of the Kondo compensation cloud for a sin g l e impurit y, t h e p rese n ce of closely-spaced uncompensated spins leads to the Rud e rm a n-Kitt e l K as u ya -Yo s id a (RKKY) interaction between localized f orbitals where :J(r) rv J cos(2kpr) (2kpr) 3 (2 .4 7) (2.48) is the RKKY coupling at large distances J is the Kondo coupling and kp is the Fermi wavevector. In most heavy-fermions :J ( r) leads to antiferromagnetic coupling between impurity spins. The state of a concentrated Kondo system depends on the competition between the two energies represented by the Kondo and RKKY temperatures T K and TRKKY This competition has been described in a simple form through the Kondo necklace model developed by Doniach [42, 43]. Both TK and TRKKY depend on the Kondo coupling J and the concentration of magnetic impurities The Doniach model relies on the assumption that the ground state of the system depends on the relative magnitude of the coupling J only. The phase diagram for this model is shown in Fig. 2.7. The Kondo temperature depends exponentially on the parameter J as discussed previously, while TRKKY rv 1 2 N(O). At low values of J, TRKKY > TK the material is a magnetic 4f metal, and the Kondo effect is absent. As J increases TK >TRKKY, the Kondo effect appears before magnetic order and the material is a magnetic Kondo lattice. At even larger values of J (T K >> TRKKY), magnetic order disappears altogether and the material is a nonmagnetic Kondo lattice. Heavy fermion compounds exist in the region around the magnetic-nonmagetic ph as e boundary and those with a magnetic ground state exhibit mostly antiferromag netic order.

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30 A modified form of the Doniach diagram has been recently proposed [44, 45) to account for the effect of intersite magnetic correlations on the Kondo tempera ture in the nonmagnetic region. Instead of continuing to increase exponentially as in the single-impurity case, TK reaches a saturation value, after which it decreases slightly with increasing J. Thus, TK in nonmagnetic Kondo lattices may not nece sarily follow single-impurity behavior. On the other hand, a complete theoretical explanation of the effect of magnetic interactions on the Kondo temperature has yet to be developed. At a value of the Kondo coupling J = le, the magnetic ordering temperature TM approaches zero at a critical point. The ground state of some heavy fermions at or near Jc is neither magnetically ordered nor Fermi-liquid-like. A large number of intermetallics falling in this category are commonly referred to as nonFermi-liquid (NFL) systems. Their thermodynamic and transport properties can in some cases be described by either logarithmic divergences or power-law behavior according to different theoretical models (3, 12). 2.6 Non-Fermi-Liquid Effects Current models of non-Fermi-liquid phenomena can be divided into two groups: theories describing a possible single-ion origin to these effects and those attributing them to intersite interactions. A member of the first group is the two-channel quadrupolar Kondo effect (46), a particular scenario within the more general multichannel Kondo problem (47). The quadrupolar Kondo effect consists of the quenching of a nonmagnetic quadrupolar level by two degenerate conduction electron bands, and has been used to explain the properties of heavy-fermion systems like U 1 _x ThxBe 13 (48]. In this model, NFL behavior is associated with fluctuations of the quadrupolar degrees of freedom, rather than spin fluctuations. Another possible single-ion mechanism towards non-Fermi-liquid behavior 1s Kondo disorder (49, 50, 51). The material exhibits a random distribution of

PAGE 39

31 the quantity pJ, where p is the density of states and J is the Kondo c ouplin g constant. Thus variations in either the Kondo couplings or th e lo ca l d e n s i ty of states gives as a result a distribution of Kondo temperatures. Th e prob a bilit y distribution function P(TK) = P(pJ) d(pJ)/dTK acquires a log-normal form for strong disorder: 1 1 { 1 2 } P(TK) = ( 41rut 2 1 ( /T ) exp -ln [p 0 Je-u ln(cp/TK )] TK n cp K 41ru (2.49) where p 0 is the average density of states, and u is a dimensionless parameter cor responding to the amount of disorder in the system. For weak disorder P(TK) takes the form of a Gaussian. At a given temperature T, there are regions where the local Kondo temperature TK <
PAGE 40

32 sionality and the nature of the magnetic transition. As a result, the system is said to have a 'generalized' (non-Landau) Fermi-liquid ground state, with an enhanced quasi particle mass m* due to the presence of long-range spin fluctuations [57]. A recent explanation for NFL behavior relies on the competition between anisotropic Kondo and RKKY interactions in a disordered system [58, 59]. Around the QCP corresponding to le, for TK > TRKKY, free spins arrange into clusters, which increase in size as TK-+TRKKY The spin clusters form a granular magnetic phase, coexisting with the metallic phase, and the system exhibits a Griffiths singularity at zero temperature [60]. Non-Fermi-liquid effects are attributed to the dynamics of large spin clusters in the Griffiths phase. A percolation limit for these clusters is reached at the QCP, which for Tc i= 0 leads to an antiferromagnetic, spin-glass, or ferromagnetic transition [58]. The temperature dependences of the thermodynamic properties obey power laws, with exponents determined by the crystal symmetry and the values of the local exchange constants. The nonuniversal nature of these exponents offers a common description of NFL effects in heavy fermion alloys within the Griffiths phase model.

PAGE 41

.,,.. ,,, .,,.. / / ,, / / / I I I I I TK I I / I ,,.,,. I ,,, 1 ,,, ,,,"' TRKKY I ,,, / .,,.. / .,,.. .,,.. /_,,.,, ------------+----------'l~------~/W Magnetic 4f-metal Magnetic CKS Non-magnetic CKS 33 Figure 2. 7: Phase diagram of the Kondo lattice [39], illustrating the different dependences of TK and TRKKY on the parameter J /W, where J represents the Kondo coupling and W is the bandwidth. The dependence of the magnetic ordering temperature TM on J /W dictates the regions corresponding to magnetic metal magnetic concentrated Kondo system (CKS), and nonmagnetic CKS.

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CHAPTER 3 PROPERTIES OF CeA1 3 AND CePb 3 This chapter gives an overview of structural, thermodynamic, transport, and magnetic properties of CeAh and CePb 3 alloys that are relevant to the problems addressed in this dissertation. 3.1 Properties of CeAh 3.1.1 Crystal Structure The compound CeAh crystallizes in the hexagonal Ni 3 Sn structure (DO 19 ), Pearson symbol hP8, space group P6 3 /mmc, number 194. This structure con sists of two alternating hexagonal layers. The most recently published lattice parameter measurements give a= 6.547 A and c = 4.608A [61]. The above val ues correspond to a c/ a ratio of 0. 704, much smaller than the close packed ratio (0.816), and a lattice volume V = 171.05 A 3 A study of the structure of rare earth trialuminides[62] attributed the formation of a particular structure and its c/ a ratio to the rare-earth/ aluminum ratio RRd RAi This ratio is largest for the hexagonal LaAh, PrAh, and CeAh, and smallest for Yb, Tm and Sc trialuminides, which crystallize in the cubic Cu 3 Au structure. As RRd RA 1 decreases, the crystal structure is modified from hexagonal to cubic, the layer stacking changes, and the c/ a ratio increases. Figure 3.1 shows the idealized (Ni 3 Sn) unit cell of CeAh. The cell contains two formula units. The atom positions with respect to the origin are given in Table 3.1 in terms of the lattice parameters a (x, y axes) and c (z axis). Figure 3.2 is an extended scheme showing the hexagonal stacking and the periodicity of the 34

PAGE 43

35 Figure 3.1: Hexagonal Ni 3 Sn structure of CeAh. Figure 3.2: Hexagonal NbSn structure of CeAh (extended scheme).

PAGE 44

36 Table 3.1: Cell Content of Ni 3 Sn structure of CeA1 3 [64). Atom Multiplicity Coordinates (Wyckoff notation) X y z Ce 2c 1/3 2/3 1/4 2/3 1/3 3/4 Al 6h 0.833 0.666 1/4 0.833 0 167 1/4 0.334 0.167 1/4 0.167 0.334 3/4 0.666 0.833 3/4 0.167 0.833 3/4 unit cell. Each Ce atom has 6 Al nearest neighbors at a distance dee-Al = 3.27 A, and 6 Ce nearest neighbors at a distance dc e -ce = 4.428 A [63). The central Ce atom is surrounded by six nearest neighbors (3 Al and 3 Ce atoms) above and six below the basal plane. It is important to point out that all nearest neighbors are located in the layers above and below the central Ce atoms and their distances are not along the c-axis direction, but rather at an angle. These off-axis neighboring distances might have some implications regarding the hybridization between Ce and Al atoms, as well as the effects of the RKKY interaction on the magnetic properties of CeAh ( see Chapter 7). 3.1.2 Specific Heat Early measureme~ts of the specific heat of CeAh below 10 K proved to be unreliable [65, 66) due to anomalies caused by the presence of the secondary phases. Later measurements by Brodale et al. [67] demonstrated a significant reduction of these anomalies. In their study, the low temperature specific heat showed a maxi mum around 0.4 K when plotted as C /T vs T. The value of the electronic specific heat coefficient, extrapolated from C /T vs T 2 is,= 1250 mJ /K 2 mol. This max imum in C /T has been the subject of intense controversy about the ground state of CeAh It was initially proposed that its origin is due to the formation of a Kondo

PAGE 45

3 7 lattice state in which the conduction electrons und e r go c oh e r e n t scatter i ng [ 68] Later experiments [69 70 71] suggested that th e m ax imum was du e t o eit h e r magnetic correlations or a possible antiferromagneti c ord e r in thi s c om p ound. The anomaly in C /T has also been studied at differ e n t pr ess ur es a nd m ag neti c fields Magnetic field measurements up to 4 T [68] s how e d t h at b o th t h e maximum and its temperature position decrease in field whil e th e r e is a n in c r ease of C /T values below 0.2 K (see Fig 3.3) Measurements abov e 1 Kand a t 23 T[72] indicated a decrease in C /T values below 4-5 K (more than 15 % at 1 K) and an increase in values above the same temperature (around 20 % n e ar 10 K). Th e s e results seem to indicate an initial increase of the electronic coeffi c ient with fi e ld followed by a marked decrease at higher fields. The pressure dependence of the specific heat as C /T vs T is shown in Fig. 3.3 [73] The specific heat is very sen sitive to pressure. C /T values at 0.4 K were found to decrease with pressure as pl/B. There is no sign of the specific heat anomaly at a pressure of 0.4 kbar. The coefficient is reduced from 1250 mJ /K 2 mol at atmospheric pressure to about 550 mJ /K 2 mol at 8.2 kbar. Values of C /T are essentially constant below 1 K for pressures around and above 2 kbar. An attempt was also made to measure specific heat on very small single crys tals of CeA1 3 [7 4]. The results proved to be sample-dependent. Some of the crystals showed peaks in the specific heat resembling antiferromagnetic phase transitions It remains to be understood whether there is any relationship between these peaks in the specific heat and the maximum observed in C /T for polycrystalline samples. 3.1.3 Magnetic Susceptibility A venel et al. [75] measured the magnetic susceptibility of polycrystalline CeAh down to 0.8 mK. The results show a broad maximum around 0.5 K resem bling the anomaly in C /T near 0.4 K (see Fig. 3.4). The su sce p t ibilit y be c ome s temperature independent below 40 mK (x(T = 0) 29 5 m e mu / mol ) c on s i ste n t

PAGE 46

2 1 J /. ... a 1.8 E Oo N A <>o 0 6 .... o MA LJ Ac. 1.2 =r I J 0 0.5 T (K) 1 I .8 ,----IJo._..'fl--. ----r-----,-------.--~--, .l), ..... rn 1 .4 <{ Q,) u QJ 0 E IO I....... 0 6 u .. Okbor fh r 11) 0 E 15 o 1 0 I....... u (C/Tlo4K= 179-0 85P 116 0 2 '------L---.-J..---''---....1.-. ---'-------' 0 2 0 5 2 T{K) 5 10 20 38 Figure 3.3: Magnetic field and pressure dependence of the specific heat of CeAiJ. Upper part: C /T vs T of CeAh in magnetic fields up to 4 T (0 T: circles, 2 T: diamonds, and 4 T: triangles) [68]. Lower part: Pressure dependence of C /T vs T for CeAh up to 8.2 kbar [73].

PAGE 47

39 45 0 ,--, :J ~ 0 E a> ,:::' 0 0 35 0 E E ~0.0 ...._ ;, E I >< (P I") 30 0 I 0 0 5 0 10 0 0 T (K) ..._ 25 0 >< .. 15 0 0 0 5 0 1 0 0 T (K) Figure 3.4: Magnetic susceptibility of CeAh below 10 K [75). The inset shows th e inverse susceptibility.

PAGE 48

40 with Fermi-liquid behavior. The inverse susceptibility follows Curie-Weiss law above 150 K with an effective magnetic moment close to that of a free Ce 3 + ion, eff = 2.54 8 and 8cw = -30 6 K. The susceptibility of single crystals above 4 K was also measured with the field parallel (x11) and perpendicular (x-1) to the c-axis [76]. The susceptibility along the c-axis XII is at least three times as large as x-1 around 4 K, indicating a large anisotropic magnetic behavior. 3.1.4 Transport Measurements Figure 3.5 shows the electrical resistivity of CeAh below 300 K. It can gener ally be described by a Kondo-like increase down to 50 K, a maximum around 35 K possibly signaling the crossover from single-impurity to Kondo-lattice behavior, and a sharp decrease below 10 K. At temperatures below 100 mK, the resistivity has the form of a Fermi-liquid with a coefficient A= 35 n cm/K 2 (see Fig. 3.5) No sign of a magnetic phase transition (i.e. kink in the resistivity curve) has been detected in electrical resistivity measurements around 0.4-0.5 K When pressure is applied, there is an increase in both the temperature and magnitude of the maxi mum [77]. In addition, the A coefficient decreases, and resistivity values above the temperature of the maximum are enhanced as pressure increases. The low temperature magnetoresistance of polycrystalline samples was found to change sign at a field of 2 T, becoming positive at lower fields [79, 80]. The results are shown in Fig. 3.6 . The resistivity values are dependent on the field direction with respect to the current. This anisotropic behavior increases with applied field and at low temperatures. The magnetoresistance at 4.2 K and field perpendicular to the current becomes less negative with increasing pressure for fields larger than 2 T [77]. In single-crystal measurements, the electrical resistivity in zero field along the basal plane is more than twice that along the c-axis [76, 81]. The field dependence of the A coefficient parallel to the c-axis shows a peak around

PAGE 49

,, Z40 ~) 220 zoo 100 ieo 140 IZO 100 80 IO 40 20 1 1 E 1.0 u c; :t 0 9 Q,, 0.8 ... ....... 0 100 ... .. .... .. C.AI, eltctficol mistiv1ty 200 T (lC) 0 7 ______ _,._ __ ___., ___ ..._ __ ....J 0 2 4 6 8 10 x ,o-, T2 ( K2 l 41 Figure 3.5: Transport measurements on CeAla. Upper part : Electrical resistivity below 300 K [78]. Lower part: p vs T 2 below 100 mK [20]

PAGE 50

42 2 T. The authors found this result to be in qualitative agreement with theoretical models describing weakly-antiferromagnetic metals. 3.1.5 Nuclear Magnetic Resonance Measurements on 27 Al nuclear magnetic resonance (NMR) on CeAh down to 0.3 K by Nakamura et al.[82] are part of a series of microscopic measurements arguing against the coherence interpretation of the anomalies in C /T and the mag netic susceptibility. The temperature dependence of the spin-lattice relaxation rate at 0.98 MHz ipcreases by one order of magnitude at the lowest temperatures in a nonlinear fashion. The relaxation rate reaches a maximum at 1.2 K. The authors attributed this maximum to the onset of antiferromagnetic order at this tempera ture. Later measurements by Wong and Clark [83] and Gavilano et al. [70] revealed not only the absence of a maximum in the relaxation rate at low temperature, but a Korringa-like (T 1 T = const.) behavior below 0.6 K as well. The reason for these discrepancies might be related to a large sensitivity of the ground state to lattice strains and sample preparation for NMR measurements. Powdered samples have grains with typical linear dimensions around 50 m. The nonuniform strains cre ated by preparing the powder can have a dramatic effect on the physical properties of CeAh below 1 K. The presence of secondary phases can also have an effect on the results, since it is more probable to find entire grains of either CeAh or Ce 3 Al 11 as proposed by Wong and Clark [83]. Gavilano et al. also measured the NMR spec tra of partially oriented powder ( c-axis along the direction of the applied field) at 6.968MHz, and observed two distinct components (Fig. 3.7). They concluded that these components correspond to two different regions of the sample being stud ied: the spectral lines seen in Fig. 3. 7 were attributed to a normal paramagnetic phase, while the broad structure was ascribed to a phase where static magnetic correlations take place. The Ce moments of this latter phase were estimated to be

PAGE 51

1. 0 1. 0 1.05 1.0 1.0 0.95 0.9 0.850 2 4 CeAt 3 ... i 6 B(T) Figure 3.6: Magnetoresistance of CeAh down to 100 mK [79]. 43

PAGE 52

(/) C: s .s 0 .r::. () w C 5.5 44 T = 3.1 K T = 1.4 K T =0.98 K 6.0 6.5 7.0 Fi~ld (kGauss) Figure 3.7: NMR spectra of partially oriented powder at 6.968 MHz for different temperatures [70].

PAGE 53

45 less than 0.05 8 The presence of magn et ic corre l ations in CeAh argues against a simple interpretation of its ground state in terms of a non-magnetic Fermi-liquid. 3.1.6 Muon Spin Rotation The only muon spin rotation (SR) experiments on pure CeAh avai l able to date are those of Barth et al. [69, 84]. The authors measured the time-dependent muon polarization on two polycrystalline samples, as seen in Fig 3.8 The muon polarization signal was described as the sum of several time-dependent components, two of which correspond to the response of muons from different magnetic envi ronments. The most significant finding was the detection of a spontaneous muon spin precession frequency in zero field below 0. 7 K from one of these components. This Larmor frequency, proportional to the local magnetic field has a very small temperature dependence below 0. 7 K. Its extrapolated value at T = 0 is just above 3 MHz which corresponds to an average local field of 220 G. In agreement with this estimate, the muon precession signal could not be observed at an external applied field of 750 G. Both the oscillating component and the fast relaxation of the muon polarization are commonly associated with spin-density-wave behavior [85]. The presence of the local field at the muon sites was interpreted as the development of short-range, quasistatic magnetic correlations in CeAh below 0. 7 K. As the temperature decreases these correlated moments, estimated to be around 0 8 develop some coherence in a spatially inhomogeneous manner. The appearance of this almost percolative effect was attributed to magnetic frustration. Electron paramagnetic resonance (EPR) measurements by Coles et al on GdAh (Ni 3 Sn structure) [86], also contributed to the development of this idea arguing that the magnetic behavior in CeAh might be mediated by frustrated antiferromagnetism in the triangular sublattice of the hexagonal a-b planes

PAGE 54

0--------------------0.05 -0.10 -0 15 -0.20 0 05 K ::, 0 0 ______ ..__ ___ ....._ ___ ....__ ___ ..i...,_ __ --,1 -0 05 C ~ -0 10 0 E: -0.15 o g_ -~.20 0.5 K Ot___ .._ ___ '___ ......_ ___ .,_ __ -005 -0.10 -0 .1 5 -0.20 IK 0 0.5 J.0 1 5 2.0 t m e ( tl,sec) 46 Figure 3 8: Muon polarization as a function of time in zero external field for T = 0.05 0.5 and 1 K [69].

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47 () J20 TK 80 40 ,-.. 6120 ,;; TK 80 40 0 ldl:m6~~~:t.=..:::t=:=i::::::=.::=.;t..::~~ -1S -JO -5 0 S 10 15 20 25 30 Energy transfer [me V] Figure 3.9: Magnetic contribution to the inelastic scattering function of CeA1 3 at T = 20 and 40 K [87). The solid line is a fit to a three-Lorentzian model. The dotted lines represent the individual fit components.

PAGE 56

48 3.1. 7 Neutron Scattering Inelastic neutron scattering is one of the most direct methods of determining electronic energies and crystal fields in metallic compounds. In CeAh the cerium ions occupy positions of low point symmetry. In hexagonal structures the Ce 3 + I J = ~) multiplet splits into three doublets under the influence of a crystalline electric field (CEF): f1 : I r 8 : I ~) and f 9 : I ~). In cerium heavy fermion compounds, the neutron scattering spectrum can be described in terms of two components: a quasielastic peak around zero energy transfer and a width of order TK at T ';::j 0 and an inelastic peak at an energy that coincides with the characteristic energy of crystal-field excitations. In addition to the quasielastic peak the most recent measurements [87) dis played a single inelastic peak at an energy Erv 6.4 me V for T = 20 K (Fig. 3. 9). With the help of previous single-crystal magnetic susceptibility data [76), the authors cal culated the crystal-field parameters for CeAh and determined the ground state to be f 9 : I ~) followed by f 8 : I ~) at 6 1 meV (T = 71 K) and f1 : I at 6.4 me V (T = 7 4 K) By comparing the parameters to those of other rare-earth trialuminides with Ni 3 Sn structure, they concluded that the hybridization of Ce 4f electrons with the conduction band is the dominant contribution to the CEF potential, as proposed by some theories of the Kondo effect in crystal fields [88). Thus, the hybridization is responsible for both Kondo and CEF energy scales. 3.1.8 Chemical Substitution Studies By far the most interesting doping studies on CeAh to date are those of La impurities on the Ce sites. Recent specific heat studies of Ce 1 _xLaxAh, performed after evidence for magnetic correlations was found for the pure compound [69, 84), added to the already existing controversy about the nature of the anomalies in CeAb. An enhancement of the anomaly in C /Twas found for 0 ::; x ::; 0.2 [71), and a corresponding peak appears in the specific heat, as seen in Fig. 3 10. The

PAGE 57

49 magnetic susceptibility also shows an enhancement in its co rr espond in g maximum, with a temperature around 2 5 K for x = 0 .2. A T 3 dependence of the specific heat below this maximum for the La-doped alloys led to the conclusion that the anomalies represented the development of an antiferromagnetic transition. Two reasons for this development were proposed. The first one is the application of a negative chemical pressure by the larger La atoms and a subsequent decrease in hybridization between f ions and conduction electrons. This effect is in accordance with the Kondo necklace model (see Chapter 2). The second possibility is the reduction of magnetic frustration in the basal-plane triangular lattice of Ce ions [86 89]. As the Ce ions are substituted by non-magnetic La atoms in the triangular sites, a number of the Ce moments are relieved from the frustration constraint and are free to interact with others. This explanation relies on the assumption that the in-plane interactions are much stronger than the interactions between two adjacent planes. More recent neutron scattering and SR studies on Ce 1 _xLaxAh [15 90] have shown that the temperature at which the maximum in the specific heat for x = 0.2 develops coincides with both the appearance of an inelastic peak in the neutron scattering function and the divergence of the SR relaxation rate. The divergence of the muon relaxation rate was interpreted as evidence for either short-range mag netic correlations, as found for pure CeAh [69, 84], or long-range magnetic order of small moments. Bragg scattering on powdered samples did not show evidence of long range order within the resolution of the measurement. The magnitude of the Ce moments was estimated as < 0.05 8 The position of the inelastic peak for x = 0.2 is weakly temperature-dependent, with an estimated energy of 0.54 me V at T = 0. It was argued that the magnetic correlations in this sample were too small to be responsible for the behavior of both the inelastic peak and the thermo dynamics below 2 K. In the search for an alternate explanation, the specific heat

PAGE 58

50 and the inelastic peak were described in terms of the anisotropic Kondo model ( discussed in Chapter 2) which shows a similar response function and a maximum in C /T for specific parameter values. This interpretation was not able to account for the magnetic behavior inferred from the SR results. Instead, the AKM proved to be useful in providing an explanation for the anomalies in terms of a single-ion mechanism rather than cooperative behavior. Numerical results for the specific heat of the AKM will be compared to specific heat measurements in magnetic field of La-doped CeA1 3 alloys in Chapter 6. Only one study reports doping of CeAh-based alloys on the Al ligand sites [61]. Corsepius et al. found that the alloys were single-phased for doping levels less than x = 0.1 and that substitution of Ga, Si and Ge contracts the lattice, while Sn expands it. All of the above elements have the same effect on the specific heat and the magnetic susceptibility. The anomaly in C /T for the pure compound is shifted to higher temperatures as much as 4.2 K for Ce(Al 0 9 Sn 0 1 )3 A maximum at a slightly higher temperature is also seen in the susceptibility between 0.1 and 70 kG. The maxima were attributed to the development of an antiferromagnetic phase transiton. All samples except those with Ga impurities exhibit discrepan cies between zero-field-cooled and field-cooled susceptibilities, and only those above x = 0.1 show a time-dependent maximum (spin-glass-like). The development of an apparent phase transition in the thermodynamic properties does not seem to be exclusively related to an isotropic volume change of the hexagonal lattice, since these features were seen in alloys with both smaller and larger lattice parameters than those of CeAh. Instead, the authors argued that the change in the tem perature position of the anomaly in C /T is related to the absolute-value change (increase or decrease) in the c/a ratio.

PAGE 59

Table 3.2: Cell Content of Cu 3 Au structure of CePb 3 [64] Atom Multiplicity Coordinates (Wyckoff notation) X y Ce la 0 0 Pb 3c 1/2 1/2 1/2 0 0 1/2 3.2 Properties of CePb 3 3.2.1 Crystal Structure z 0 0 1/2 1/2 51 The compound CePb 3 crystallizes in the face-centered cubic Cu 3 Au struc ture, Pearson symbol cP4, space group Pm3m, number 221. The Ce sites cor respond to the corners of the cube, while the Pb atoms occupy the face-centered positions. The structure forms directly from the melt at 1170C on the Ce-Pb phase diagram [91]. Unlike CeAb, there are no secondary phases that might af fect the physical properties and the formation of single crystals of this compound. The lattice constant is a = 4.876.002 A [92], corresponding to a lattice volume V = 115.93A 3 Figure 3.11 shows the Cu 3 Au unit cell of CePb 3 The cell contains one formula unit. The atomic coordinates with respect to the origin are given in units of a in Table 3.2. In an fee structure, the Ce atoms have 6 Ce nearest neighbors at a distance equal to the lattice constant, and 12 Pb nearest neighbors at a distance dee-Pb = a/ ../2 = 3.448 A. 3.2.2 Specific Heat The low-temperature specific heat, plotted as C /T vs T 2 is shown in Fig. 3.12. It has a peak around 1.1 K due to an antiferromagnetic transition. The magnitude of the peak is close to 3.5 J /K 2 mol, and the extrapolated electronic coefficient reaches a value around 1000 mJ /K 2 mol. The effect of high magnetic fields was

PAGE 60

52 I j I 4000 Ce La Al ...... 1-x X 3 0 e I) 3000 A e K-0. OS u y xO. t ., f ... e A ... x-0. 2 ..., 2000 ~-,. \ ,. ,. u "" # ... 1000 0 3 4 5 6 7 T (K) Figure 3.10: Specific heat of Ce 1 _xLa x Ah alloys (x = 0 05 0 1 and 0.2) [71]. Figure 3.11: Cubic Cu 3 Au structure of CePb 3

PAGE 61

4.0 1.5 3.0 1. N I 2.0 as 0 E h t1.0 5 s .... ....... --. .......... 40 10 Tz ( K2) 60 15 80 T2 20 53 Figure 3.12: Specific heat plotted as C /T vs T 2 of CePb 3 between 0.6 and 4 K. The inset shows C /T vs T 2 from 1.5 to 10 K [93).

PAGE 62

54 first studied by Fortune et al. [94]. Magnetic fields between 10 and 20T were found to suppress the antiferromagnetic state and reduce the electronic coefficient. Specific heat studies under pressure [95] revealed the existence of a pressure induced magnetic phase above 0. 7 GPa. Below the critical pressure the antiferro magnetic temperature TN is suppressed down to 0.6 K; above 0. 7 GPa, the temper ature of this pressure-induced type-II antiferromagnetic phase increases from 0.6 K to 1 Kat 1.3 GPa. Figure 3.13 illustrates the temperature-pressure phase diagram with TN decreasing up to 0.7 GPa and increasing at higher pressures. This behav ior is rather unusual since a continuous decrease of TN with pressure is expected for Kondo lattices especially when the Kondo temperature T K is about three times as large as the transition temperature, as in CePb 3 [96]. In addition contrary to other Ce Kondo lattices like CeCu 6 _xAUx (x > 0.1) [97], and CeRu 2 Ge 2 [45], no pressure-induced suppression of TN to zero was observed for this compound. 3.2.3 Sound Velocity Measurements The temperature dependence of elastic constants was determined from mea surements on a CePb 3 single crystal along the (10 0) and (110) directions [98]. Fig ure 3 14 illustrates the magnetic field dependence of the relative change in velocity of an elastic mode in the (110) direction at 10 MHz. Two phase boundaries (indi cated by arrows) can be distinguished at 0.38 K. The lower one signals the antifer romagnetic phase transition. The high~field boundary corresponds to an unknown phase, possibly a spin-flop state (98]. The exact nature of this field-induced phase remains to be determined by neutron diffraction experiments. Nevertheless, the discovery of this field-induced transition in the (110) direction motivated further investigation of the properties of CePb 3 single crystals in magnetic fields.

PAGE 63

55 1.2 CeP~ lo +-+ t.0 0 -++ -+.8 + + % .,_ .6 + .4 I I I .2 0 2 .6 .8 1D t2 t4 p (GPa) Figure 3.13: Thansition temperature-pressure phase diagram for CePb 3 up to 1.4GPa [95]; the graph shows specific heat measurements (crosses) neutron scat tering (circles), and transport measurements (triangles) The broken line indicates a crossover between two distinct magnetic phases ( see text)

PAGE 64

56 CePb 3 . I( 0 5 10 15 20 B (T) Figure 3.14: Magnetic field dependence of the relative change in sound velocity for the (c 11 c 12 )/2 elastic mode at 10 MHz [98].

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57 6Qr-----------------~ p 40 E u o .......... ~~2---,!,3__.___..4_..._ T(K) 100 200 T ( K) Figure 3.15: Magnetic contribution to the electrical resistivity of CePb 3 at H = l T below room temperature. The inset shows the resistivity betwee n 0.2 and 4 K at H = 0.93 T [93).

PAGE 66

58 3.2.4 Transport Measurements In order to m ea sure the electrical resistivity of CePb 3 it is important to measure in magnetic fields of order 1 T in order to suppress the superconducting transition due to the presence of Pb on the surface of the sample [93]. The reaction of CePb 3 with oxygen from air causes the separation of the two elements eventually followed by oxidation of Ce and Pb Figure 3.15 displays the magnetic resistivity between 0.2 and 4 K. It shows a logarithmic, Kondo-like increase from room tem perature down to 40 K, followed by two maxima and finally by a drop below 2 K The maximum around 20 K has been attributed to the decrease in Kondo scatter ing due to a depopulation of the excited crystal-field levels [99]. The maximum at 3.3 K is thought to be due to a coherence effect of the Kondo lattice. There is also a rapid change in slope around 1 K indicative of the antiferromagnetic phase transition as shown in the inset to the figure The pressure dependence of the magnetic resistivity was measured on a single crystal [99]. There is a shift of the maximum at 3.3 K toward higher temperatures. Only one broad maximum was detected for pressures above 11.5 kbar. This result is consistent with an increase of the Kondo temperature TK. The magnetore sistance was recently measured along the (110) crystallographic direction [100] Two field-induced anomalies were found for the magnetoresistance curves below 400 mK at 5 and 9.5 T, respectively (see Fig. 3.16). The resistivity increases up to 5 T decreasing sharply above the first transition, and becoming almost field independent after the second. A magnetic field-temperature phase diagram was constructed, in good agreement with previous sound velocity measurements. The angle dependence near the ( 11 0) direction was also measured in order to verify the orientational dependence of the field-induced phase above 5 T, detected by sound velocity measurements. A large increase in the magnetoresistance was observed as the field direction was rotated toward the ( 1 0 0) direction at which point the sharp

PAGE 67

59 40 ..-.. s 30 (.) -20 ::> CJ) I'll G.) 10 0 0 4 8 12 16 Magnetic Field (f) Figure 3.16: Magnetoresistance curves between 1 and 16 T for temperatures in the range 20 mK to 8 K. The magnetic field is along the (110) direction [100].

PAGE 68

60 drop at 5 T could not be detected. The low-temperature resistivity was found to be proportional to T 2 with a field-dependent A coefficient. At 5 T, A reaches a max imum, the range of T 2 dependence becomes smaller, and the resistivity acquires a linear term, all coinciding with the field-induced transition. This enhancement of A with field points to a corresponding enhancement of the specific heat coeffi cient,, as the ratio A/, 2 is expected to remain constant for heavy fermions [101]. At 10 T, there is a small bump in the A coefficient, indicating a transition to a ferromagnetically-polarized paramagnetic state [100]. 3.2.5 Magnetic Susceptibility Measurements of the magnetic susceptibility on a CePb 3 polycrystal below 4 K [102] revealed a maximum at 1.25 K, similar to that found for the specific heat at l.lK. Figure 3.17 shows the data measured at 2.6kG. This maximum is reminiscent of an antiferromagnetic phase transition, and coincides with the appearance of a maximum in the specific heat at 1.1 K. The estimated value of x(T = 0) is somewhere between 32 and 33 memu/mol. The inverse susceptibility follows a Curie-Weiss behavior, and gives a high temperature effective moment eff = 2.5 8 and a Curie-Weiss temperature 8cw = -25K. An investigation of the pressure dependence of the inverse susceptibility [99] found an increase of 8cw from Oto 15kbar, a trend consistent with an increase of TK. Recently, the ac susceptibility of a CePb 3 single crystal was measured as a function of crystallographic direction to verify the phase diagram and the field induced (presumably spinflop) phase transition [ 103]. Their phase diagrams along the (10 0) and (110) directions indicated that the range of the field-induced phase depends on the crystallographic direction. Between 20 and 600 mK, with H 11 (10 0), the range is about 1 T, while for H II (110), it is close to 5 T. The phase diagram determined from ac susceptibility data along (110) is in agreement with previous studies, as shown in Fig. 3.18.

PAGE 69

6 1 3.6 g 3.4 -... 3.2 N 0 ::: 3.0 H = 2.6 kG >< 1 2 3 T (K) Figure 3.17: Magnetic susceptibility of a CePb 3 polycrystal below 4 K at H = 2.6 kG [102].

PAGE 70

62 12 Paramagnetic State H//<110> 8 Spin-Flop phase E 6 4 Antifcrromagnetic State 2 o..._ __._ __ ...__ __._ ______ ~--~ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Temperature (K) Figure 3.18: Phase diagram (H T) for CePb 3 with the field along the (110) direction (Solid circles: ac susceptibility [103], open circles: sound velocity [98], and open triangles: magnetoresistance [100]).

PAGE 71

63 3.2.6 Neutron Scattering N e utron sc attering studie s a r e esse nti a l in t h e determination of the ordered mom e nt at low t e mp e ratures a nd th e c ry s t a l-fi e ld p a r a m ete r s of heavy-fermion systems The Cu 3 Au cubic structur e of CePb 3 provid es a hig h d egree of c r ysta l symmetry. In the cubic environment of Ce 3 + ions in CePb 3 the c r ysta lfie l d (CE F ) potential splits the IJ = ~) multiplet into a f 7 doublet a nd a r 8 qu a r tet [10 4 ] : lf1) =al~) bl =F ~) If s )= bl~)+aJ=F~) where a= 1 1 2 and b = (i) 1 1 2 ( 3.1) Th e magnetic scattering function of polycrystalline CePb 3 is shown in Fi g 3.19 which shows the inelastic, quasielastic and elastic peaks. A fit to th e scat t e ring function [105] determined that the ground state is the f 7 doublet. Th e CEF splitting between the doublet and the first excited state is around 72 K [106]. Bragg scattering studies on a single crystal led to the conclusion th a t th e m a gn e tic structure of CePb 3 is antiferromagnetic, and that the moments are aligned along the (10 0) direction [106]. The magnetism is incommensurate with a modula tion amplitude of 0.55 8 at 30 mK. A similar incommensurate stru c tur e h as a l s o been detected for CeAh [107], another cubic heavy-fermion compound V ett i e r e t al [106] concluded from a comparative study of Ce Kondo lattices that c ubi c c om pounds are more magnetic than those with a large crystal anisotrop y, lik e C e Ah CeCu 6 and CeCu 2 Si 2 This statement has important implic at ion s r ega rdin g a possible role of crystalline anisotropy in regulating the compe t i t i o n b etwee n t h e Kondo and RKKY energy scales.

PAGE 72

> a, E 4 ~30 ..,_ U) -.... .0 E (./) Ce Pb3 4K 0=.9A1 ;.:~ I \ \ I / \\ \\. ,/ '\\l J j \\. ,. ... ~1/ I \ Y: i ,. ''-:1:, / .... . -..... / ------. ,,,,,,,. 2 4 6 8 10 E [meV] 64 Figure 3.19: Magnetic neutron scattering function o f a CePb 3 polycrystal [105). The solid line is a fit to the data. The dashed line represents the determined quasielastic component, and the dash-dotted line corresponds to the inelastic com ponent.

PAGE 73

65 3.2. 7 Chemical Substitution Studies Alloying studies on the Ce sites of CePb 3 were first reported using La [96]. These studies are particularly important and have fundamental significance, because they constitute evidence of single-impurity effects in a concentrated heavy-fermion system. The specific heat, magnetic susceptibility, and electrical resistivity all scale with Ce concentration. Electrical resistivity measurements revealed that the crystal-field splitting is also unaffected by La doping. The electronic specific heat data for alloys with Lax = 0.4, 0.6, and 0 96 are shown in Fig. 3.20, along with the theoretical prediction for S = The Kondo temperature is constant throughout the series, implying a constant value of J. The transition temperature TN goes to zero near a La concentration x = 0.2. The suppression of magnetism as a result of a lattice expansion upon La substitution seems to indicate that the decrease in TRKKY with respect to TK is due to an increase in the average Ce-Ce distance rather than to an overall change in J. Indeed, Ce 1 _xLaxPb 3 is a unique system in the sense that TK and the coupling J seem to remain unaffected by La doping. While thermodynamic and transport properties of Ce 1 _xLaxPb 3 seem to be unaffected by the electronic environment surrounding the Ce 3 + ions, experiments on Ce 1 _xMxPb 3 (M = Y, Th) [109] confirmed that the single-impurity scaling observed by La doping on the Ce sites is the exception rather than the rule. Instead, a rather unusual behavior is observed upon either Y or Th doping. The magnetic susceptibility at 1.8 K increases with Y concentration. The Kondo susceptibility is inversely proportional to T K, so this result implies an unusual decrease of the Kondo temperature as the lattice contracts (increasing J). Substitution of Th on the Ce sites also contracts the lattice, and at the same time leads to magnetic-like anomalies in both specific heat and susceptibility for x = 0.3, 0.5. The differences in the outer electronic structure between Ce, Y, and Th seem to play an important role in the evolution of the ground state properties of Ce 1 x MxPb 3

PAGE 74

2.0r-----------------_ ,.s ., u .. u
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67 Chemical substitution studies were also performed on both f-ion and ligand sites of the CePb 3 structure. In Ce(Pb1-xMxh studies with M = Tl, In, and Sn [110, 111], the antiferromagnetic transition temperature decreased toward zero for a Sn concentration x = 0.4, and increased for both Tl and In. For the latter two dopants, there is a maximum towards the center of the TN x phase diagram. Substitution of Sn for Pb on the ligand sites suppresses TN and greatly increases the Kondo temperature [112, 113].

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CHAPTER 4 MOTIVATION This chapter begins with a discussion on the importance of the study of CeAla and CePb 3 followed by a presentation of the objectives of the current study. 4.1 Importance of CeAh and CePb 3 Both CeAla and CePb 3 are canonical well-documented heavy-fermion sys tems with values of the coefficient surpassing 1 J /K 2 mol crystal-field doublet ground states and a low temperature resistivity chara c teristic of Kondo lattices Studies on th e se compounds over the last 25 years made a substantial contribution to the standard interpretation of heavy-fermion systems based on the Kondo effect and Fermi-liquid theory. However deviations from this standard model have been observed in these and other compounds through the coexistence of mag netic order and heavy electrons the presence of unaccountable anomalies in the thermodynamic properties and non-Fermi-liquid effects. These are all topics of current interest yet they are among the least understood aspects of heavy-fermion physics. Any information obtained from the study of the above two compounds might be utilized in the development of new interpretations for the heavy-fermion state. The current work will concentrate on the coexistence of heavy fermions and magnetic order in CePb 3 the nature of the anomaly seen in the specific heat (plotted as C /T) of CeAla, and the heavy-fermion behavior of both compounds in magnetic fields. In 1975, specific heat and electrical resistivity measurements below 100 mK by Andres Graebner, and Ott led to the discovery of CeAla as the first heavy68

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69 fermion compound [20]. Despite its significance in the field of strongly-correlated electron systems, CeA1 3 is probably one of the least und ers tood among these com pounds. Ever since its discovery, it has been considered a canonical, nonmagnetic heavy-fermion system. Yet later experimental results (see Chapter 3) challenged its nonmagnetic status, and pointed to a possible magnetically-ordered ground state for CeAh. Whether the ground state in this compound is magnetic or not has been a long-standing debate, and remains an important topic in the study of heavy-fermion systems. The compound CePb 3 ranks among the most extensively studied magnetic Kondo lattices. The magnetic transition has little effect in reducing the large value of the electronic specific heat coefficient, 1000 mJ /K 2 mol. The electrical re sistivity has a large T 2 coefficient, A = 45 O cm/K 2 and the ratio A/, 2 is around 4 x 105 n cm K 2 mol 2 / J 2 When taking into account the relatively large value of for this compound the above suggests that the ground state is some superposi tion of ordered local moments and heavy electrons. Very little is known about the nature of the magnetic ground state of heavy-fermion materials. Measurements of thermodynamic properties of paramagnetic and magnetic states in this compound may be useful to understand the coexistence of magnetic order and heavy electrons. Another important characteristic of CePb 3 is the observation of single-ion scaling of thermodynamic and transport properties in a concentrated 4f system. The study of Ce 1 _xLaxPb 3 by Lin et al. [96] revealed that the normal state of alloys over the range (0 :S x < 1) can be described in terms of a single-ion picture (see Chapter 3). It is the only Ce heavy-fermion system to date exhibiting such behavior. The reason why such a concentrated system can exist with apparently noninteracting 4f sites remains unclear.

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70 4.2 Objectives 4.2.1 Magnetism and Heavy-Fermion Behavior in Ce Kondo Lattices The studies on CeAh and CePb 3 alloys presented in this dissertation are motivated by a fundamentally important topic in heavy-fermion research: the need for a full understanding of the interdependence between magnetic correlations and/ or magnetic order and the heavy-fermion state. The ground state of rare-earth intermetallics is generally described in terms of the competition between two energy scales, TK and TRKKv, discussed in Chapter 2. The former represents a single-ion effect due to the local Kondo interaction between conduction electrons and the f orbital. The latter portrays a collective effect due to indirect exchange interactions between ionic spins. The schematics of this delicate balance were shown in Fig. 2. 7. For TRKKv > TK, magnetic order occurs and the moments are unquenched at zero temperature. The size of the moments is close to that corresponding to the crystal field ground state. Concentrated Kondo systems falling into this category have relatively low values of ,, of order 100 mJ /K 2 mol ( e.g., CeCu 2 and CeAb [6]). Whenever TK >> TRKKY, the Kondo effect develops without magnetic order. This regime corresponds to most nonmagnetic Kondo lattices, with Kondo temperatures larger than 10 K. For TK 2: TRKKv, the formation of heavy electrons occurs, with, values in excess of several hundred mJ /K 2 mol. This is the least understood area of the Doniach phase diagram. The applicability of this model to heavy-fermion Kondo lattices, in particular to CeAh alloys, will be discussed as part of a study on the anomaly present in this system. Two empirical correlations have been postulated in order to distinguish between magnetic and nonmagnetic heavy-fermion ground states: the Wilson ratio R and the Kadowaki-Woods ratio. The experimental Wilson ratio R [5] is defined as 1r 2 k~xo/ ;ff, where Xo is the zero-temperature susceptibility and eff is the effective moment at room temperature. Values of Rare usually much larger for magnetically

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71 ordered than for nonmagnetic Kondo lattices [5]. eve rth e less th e ex p e rim enta l ratios for CeAh and CePb 3 are both around 0.7 a value within the rang e co rr e sponding to nonmagnetic heavy fermions. Thus this ratio does not seem to account for the magnetic order observed in CePb 3 as well as for a possible magnetic order in CeAh. In most heavy-fermion compounds, the empirical relation A/, 2 lies somewhat close to the Kadowaki-Woods ratio A/, 2 = 1 x 105 DcmK 2 mo1 2 /J 2 [101]. This ratio is about an order of magnitude larger than that corresponding to transition metal alloys. The magnetic field dependence of this relation has not been exten sively studied. The ratio A/, 2 has been observed to remain constant with field in nonmagnetic CeCu 5 9 Au 0 1 [114], the only published study of the field dependence of this ratio. In order to verify whether A/, 2 remains the same for both param agnetic and ordered states, it would be of interest to explore the field dependence of this ratio in a magnetically-ordered heavy-fermion system. Previous thermodynamic and transport measurements on Ce 0 6 Lao 4 Pb 3 [96] suggested a single-ion mechanism for the heavy-fermion behavior in this system A study of the specific heat in magnetic field of Ce 0 6 Lao 4 Pb 3 a nonmagnetic coun terpart of CePb 3 was conducted in this dissertation to search for further evidence of a single-ion Kondo origin for the heavy-fermion state in Ce-based systems. 4.2.2 Ground State of CeAh The experiments on CeAh alloys presented in this dissertation are motivated by the existing controversy about the ground state of CeA1 3 The nature of the anomalies in the thermodynamic properties of CeAh systems below 1 K is not well understood. It is a major topic of interest in the field of strongly-correlated electron systems. There are at least three competing interpretations for the origin of these anomalies. One explanation is that the weak maxima seen in C /T and in the magnetic susceptibility between 0.3 and 0.5 K is due to a reduction in the density

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72 of states caused by the formation of coherent states in the Kondo lattice (68). Another interpretation argues for an unconventional ground state in which heavy electrons coexist with either magnetic correlations or magnetic order. There is now enough evidence (61, 70, 69, 71) for the existence of magentic correlations below 1 K in CeAh through NMR and SR studies casting serious doubt on the so-called coherence interpretation (68). However, it is not clear at the present time whether the magnetic correlations are short-ranged, frustrated or whether they lead to long range order. The third and most recent interpretation suggests that the anisotropic Kondo model provides an alternative explanation to the ground state properties as driven by single-ion dynamics and dependent on the anisotropy of the Kondo interaction (15, 90). Under this point of view, the question remains of how to reconcile the presence of magnetic correlations in CeA1 3 with a single-ion Kondo description of its thermodynamic features.

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5.1.1 Synthesis CHAPTER 5 EXPERIMENTAL METHODS 5.1 Sample Preparation Alloys used in this dissertation were synthesized by melting its respective constituents in an Edmund-Buhler arc furnace under a high-purity argon atmo sphere. The arc-melting apparatus consisted of a stainless-steel vacuum chamber with a water-cooled copper crucible at the bottom and a hydraulic mechanism sup porting an electrode at the top. The tip of the electrode is made out of a tungsten alloy, and it is capable of carrying well over 100 A of current. Prior to melting each of the consituent elements was carefully cleaned to eliminate any oxide layer on the surface, and later weighed to an accuracy of 0.03 mg. Their molecular weights and stoichiometric ratios were used to calcu late the appropriate relative masses. The total mass of an average sample was about 500 mg and the diameter of a sample bead ranged between 0 5 and 1 cm. The Cu hearth on the arcmelter was thoroughly cleaned to avoid the presence of unwanted impurities during sample preparation. The element with the high est vapor pressure was placed on the Cu crucible below those with lower vapor pressures. This procedure minimizes direct contact between the Ar arc and the material with highest vapor pressure, therefore reducing its mass loss and mini mizing the discrepancy between predicted and actual stoichiometries for the alloy being synthesized. The chamber was then pumped and subsequently flushed with high-purity Ar. After this procedure was repeated three to four times the cham73

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7 4 Weighl Percenl Cerium 01020 30 40 50 60 70 eo 90 JOO 1600 I I I I I I ,1 I I t l460C 1400 I 1200 L u 0 V 1000 t s.. ::, .... ca 600 7gec s.. V 0.. E840 462 V 600 E400 (yCe) 25oc {Al) u Cl Cl 200 u u < .!> (II u Cl cs < < < u < 111c cs (pee 0 0 10 20 30 10 50 60 70 60 90 100 Al Alomic Percent Cer i um Ce Figur e 5 1 : Phase d i agram of Ce-Al [91].

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75 ber was filled to 0.5 atm of Ar gas. In order to avoid the unw anted presence of oxygen and water vapor, two measures were taken. First the high-purity Ar goes through a purifier before entering the arc-furnace. Second a zirconium bead is placed inside the furnace and melted before sample synthesis. Zirconium is known for its high absorbing capacity for oxygen. At the start of the melting process, a relatively low current was sent through the tungsten electrode. The arc was moved slowly towards the elements to avoid any thermal stresses and motion or splashing of material due to the arc pressure. During melting, enough time was allowed for the liquid components to mix via arc pressure. To ensure homogeneity, the above process was repeated several times and the sample bead was turned over after each melt. The mass loss during melting was obtained as a percentage difference (typically < 0.1 0.3%) between the total masses before and after sample synthesis. Alloys of CeAh Alloys of Ce 1 _xMxAh (M = La, Y) were synthesized using the purest avail able materials: cerium and lanthanum from Ames Laboratory, and Johnson Matthey (AESAR) aluminum (99.999% purity). The weighing of constituents required spe cial attention due to the sensitivity of the crystal structure of CeAh to small changes in the relative concentration of Ce and Al atoms. The synthesis of CeA1 3 alloys is always accompanied by the formation of a large amount of the secondary phases CeAh and Ce 3 Al 11 The presence of these unwanted phases is substantially reduced by proper annealing conditions. The cerium-aluminum phase diagram has been studied by several groups [91], its latest addition being CeAh [62]. It contains four other compounds: Ce 3 Al 11 CeAh, CeAl, and Ce 3 Al (see Fig. 5.1). Both CeAh and Ce 3 Al form directly from the liquid solution, CeAl and Ce 3 Al 11 form peritectically and CeA1 3 forms peritectoidally at 1135C. A peritectic reaction is one in which the compound

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76 melts incongruently [115), that is, the composition of the liquid just above the melting point has a different composition than the solid before melting. Only part of the solid forms a liquid solution, with the remaining part forming crystallites floating around in the liquid. As the temperature reaches the melting point, the mixture solidifies into a single phase. The peritectoid reaction in CeAh is similar to a peritectic reaction, except that the compound does not melt into a liquid crystallite mixture. Rather, it separates into a solid phase mixture of CeAh and ,B-Ce 3 Al 11 which in turn melts into CeA1 2 crystallites embedded in a liquid solution matrix. The transformation of a mixture of Ce-Al neighboring phases into the CeAh phase upon cooling has a marked effect on the way samples crystallize. The pres ence of secondary phases is the cause of many sample dependences of thermo dynamic and transport measurements. Polycrystals synthesized by arc melting consist of a mixture of CeAh with large amounts of CeA1 2 and Ce 3 Al 11 Anneal ing has been found to reduce the proportion of secondary phases to the point of becoming undetectable by conventional x-ray diffraction methods. Magnetic sus ceptibility measurements on annealed samples are an efficient way of detecting the above second phases, since CeAh is antiferromagnetic below 3.8 K, and Ce 3 Al 11 is ferromagnetic with transitions at 3.2 and 6.2 K [116]. Specific heat data has also been used successfully by some groups to detect irregularities at these tempera tures. Alloys of CePb 3 Lanthanum-doped CePb 3 alloys were made using Ames Laboratory Ce and La, and Johnson Matthey Pb with 99.9999% purity. Special care was also taken in the making of both CePb 3 and Ce 0 6 La 0 .4Pb 3 due to the large vapor pressure of lead. Therefore, Ce should be melted first, then Pb. Unfortunately, this procedure was not enough to significantly reduce Pb mass loss due to vapor pressure at

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77 0.5 atm of Ar gas. In order to compensate for this mass l oss an additional 3 % of the calculated mass for Pb was added to the constituents before the first melt. The mass loss for each bead after melting was mostly due to l ead, usually around 3 %. The sample was remelted in case the mass loss was less than the extra amo unt of Pb Correspondingly, more Pb was added in the event that the mass lo ss was greater than expected. After melting the sample, the stoichiometry was verified by recalculating the atomic percentages based on the final mass of the sample. CePb 3 -based alloys are generally free of any secondary phases except pure Pb which can precipitate in the surface as the alloys react with air. As a result the samples were kept in a vacuum container along with Drierite acting as a moisture absorber. 5 .1. 2 Annealing Annealing helps relieve stresses inside the samples not removed during crys tallization. It also reduces the amount of unwanted secondary phases in the final melt Typical annealing temperatures range between 2/3 and 3/4 of the melting point of the alloy. The final beads were broken into smaller pieces using a ceramic mortar instead of a metal crusher to avoid the presence of iron impurities in the samples. Part of each original bead was wrapped in a clean tantalum foil and placed inside a quartz tube. The tubes were pumped and flushed with Ar gas several times. Right before sealing the Ar pressure inside was reduced to 100 mtorr. The quartz tubes were then placed inside a Lindberg furnace and annealed according to a previously tested prescription. Alloys of Ce 1 _xLaxAh were annealed at 830C for two weeks while those of Ce 1 _x YxAh were annealed at 800C for two weeks, then 850C for five days. Both CePb 3 and Ce 0 6 La 0 4 Pb 3 were annealed at 800C for one week. In all cases, annealing started with the furnace already at annealing temperature. At

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78 the end of the prescribed annealing period, the samples were immediately removed from the furnace and left to cool down at ambient temperature. 5.2 Diffraction of X-Rays Measurements of x-ray diffraction were used as a means to verify whether the arc melting and annealing processes led to the formation of the desired crystal structure. From the diffraction pattern, it was also possible to determine the lattice parameters and the presence of secondary phases in the sample. The principle behind the diffraction of x-rays in crystals is based on Bragg's Law: .X = 2dsin0, (5.1) which for a first order (n = 1) spectrum relates the known Cu Ka wavelength to the diffraction angle 0 and the distance between lattice planes d. The lattice constants are then calculated from d and the intersection points of the lattice planes for the desired space group number, given in terms of the Miller indices (h kl). The experimental setup consisted of a Phillips APD 3720 diffractometer, an x-ray source with a water-cooled power supply, and a computer for data acquisition. The APD 3720 consists primarily of x-ray beam slits, the sample holder, and an electronic counter. Both the counter and the sample holder rotate about a horizontal axis so that the angle of rotation of the counter is always twice that of the holder. This latter angle corresponds to the angle of incidence/reflection from the sample plane 0. The x-ray beam is of known wavelength: a Cu Ka line with .X = 1.540562 A. Powder samples were ground out of annealed pieces from the original beads using a ceramic mortar. About 1 cm 2 of powder was then glued to a glass slide using a 7:1 amyl acetate collodion mixture. With the slide in place, the diffractometer power supply was set to 40 kV and 20 mA. The detector angular speed was set

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79 to 6 /min and its range to 5 :s; 20 :s; 120 The counting rate was set to 1000 counts/sec. All measurements were performed at room temperature. The angular positions of the resulting intensities were compared to the the oretical positions and reflection indices obtained from a structure-generating software. This procedure allows for identification of secondary-phase intensity lines larger than the background intensity ('"'-' 5% of maximum intensity line). For a cubic system (i.e. CePb 3 alloys), the indices for primary-phase lines are obtained from the following equation [117]: ).2 sin 2 0 = -(h 2 + k 2 + l 2 ). 4a 2 Similarly, for a hexagonal system ( CeA1 3 alloys), sin2 0 = ).2 [i (h2 + k2 + z2) + !:._] 4 3 a 2 c 2 (5.2) (5.3) The indices (h kl) and the angles 20 for the highest and narrowest intensity lines were entered as data points into a least-squares fitting program along with the wavelength and structure type. The room-temperature lattice parameters and their uncertainties were then obtained from a least-squares fit using one of the above two equations, depending on the structure type of the sample. 5.3 Magnetic Measurements All magnetization and magnetic susceptibility measurements were conducted using a Quantum Design Magnetic Property Measurement System (MPMS) SQUID magnetometer. The apparatus consisted of a liquid He dewar, the sample probe assembly, the electronic console with temperature and gas controllers the He gas handling system, and a Hewlett Packard computer. The probe assembly is inserted inside the dewar; it contains the sample space, thermometers, the sample heater an impedance controlling He flow, a superconducting magnet producing fields up to 5.5 T, and the sample transport mechanism. The temperature is regulat ed by the flow of He gas through the sample space and by the sample he ater. B e low

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80 approximately 4.2 K, the liquid-helium vapor inside a pot is pumped in order to reach temperatures down to 2 K. The technique used for magnetization measurements on the MPMS detects the change in flux induced by the sample under an applied field using a super conducting quantum interference device (SQUID) amplifier. The sample is first enclosed in a 0.5 cm-long plastic straw segment, which is slid into a drinking straw at the end of the support tube, serving as the sample holder. During each mea surement, the sample is moved upward along the axis of a series of pick-up coils connected to the SQUID. The SQUID voltage is read at different position intervals accross the scan length. This voltage is proportional to the change in flux detected by the coils, which in turn is proportional to the magnetization of the sample. The accuracy of magnetization measurements is generally around 3%, while the precision at a fixed temperature can be as low as 0.01 %. Magnetization curves as a function of magnetic field can also be obtained by measuring at the lowest temperature (2 K) and measuring at each field, sweeping the field from Oto 5 T. The magnetization (in emu/mol) is obtained by multiplying the signal by the molecular weight of the sample and dividing by its mass. The magnetic susceptibility x = M / H (in memu/mol) is calculated from the signal measured at a fixed field ( typically 1 kG), multiplied by the molecular weight of the alloy, and divided by its mass and the applied field. Each measurement sequence is fully automated, and uses a version of the MPMS software from Quantum Design. The convention used for units of magnetization and magnetic susceptibility in this dissertation follows from the literature on heavy-fermion systems (e.g., Refs. [5] and [6]).

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8 1 brass can pumping line block thermometer pms I .... :..---platform : -----:1 with sample Cu block /------: brass can Cu ring Figure 5.2: View of the cryostat used for zero-field specific heat measurements betwen 1 and 10 K.

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82 5.4 Specific Heat Measurements This section will discuss the necessary cryogenic and electrical equipment to measure specific heat of small samples ( < 100 mg) with large heat capacity, and the thermal relaxation method [118, 119, 120] used for this purpose. 5.4.1 Equipment Electronic The experimental setup for the measurement of specific heat in both zero and magnetic fields by the thermal relaxation method consisted of three cryostats, a liquid-He dewar, two Keithley 220 and a Keithley 224 programmable current sources a Keithley 195A, 196 digital multimeter for thermometer voltage measure ments an EG&G Model 124A lock-in amplifier for platform thermometer current detection a variable decade resistor and a resistance box with three internal resis tances. The resistance box is connected to the decade resistor in a Wheatstone bridge configuration. A more detailed explanation of the equipment is provided elsewhere [118, 119, 120, 121]. A Dell PC was used for data acquisition and anal ysis. The computer was interfaced to the digital equipment using an AT-TNT Plug and Play GPIB board from National Instruments. A 12-bit resolution Keith ley Metrabyte DAS-1402 A/D converter board interfaced the PC to the lock-in amplifier. The data acquisition was monitored using two PC-based programs for thermal conductance and specific heat measurements, respectively. The software was designed by the author using Lab VIEW version 5.1 for Windows 95 /98. Cryogenic The cryostats used for zero-field measurements are illustrated in Figs. 5.2 and 5.3. Figure 5.2 shows the probe used in the temperature range 1-10 K. The electrical connections are enclosed by a brass can attached to a taper joint by pumping on the enclosure. The cooldown procedure consisted of precooling in

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83 liquid nitrogen for about 15 to 60 minutes, insertion into a dewar and sub se qu e nt transfer of liquid He into the dewar, which reduces the temperature to 4.2 K. A temperature of 1 K was achieved by pumping the He vapor out of the dewar/prob e assembly for about an hour. Measurements in the range 0.4-2 K were conducted using the cryostat described in Fig. 5.3. After reaching a temperature of 4.2 K following the procedure above the 4 He pot was filled with liquid He from the bath by opening the needle valve and 3 He gas was transferred into the 3 He pot. The needle valve was then closed and the 4 He pot was pumped out to reach a temperature between 1 and 2 K Al though this temperature can be sustained for many hours, the 4 He pot can be easily refilled if necessary. In order to reach a temperature of 0.4 K the following method was used. A Cu container full of activated charcoal resides at the lower end of a rod inside the 3 He-gas enclosure. At 1 K, the 3 He gas condenses inside. As the charcoal container is lowered towards the 3 He pot, the condensed 3 He is attracted to the charcoal, which acts as an adsorption pump. Temperatures below 1 K could be achieved in 20 minutes and sustained up to several hours with this technique. Once the charcoal saturates with 3 He, it was warmed up to release the gas and the above process was repeated. Specific heat measurements in magnetic field were conducted in a specially designed dewar from Cryogenic Consultants Limited (CCL). The additional elec tronic equipment consisted of a GenRad 1689M RLC DigiBridge used to measure the capacitance of a thermometer used above 1 K, a CCL superconducting magnet and a magnet power supply. The magnet is made of two inner coil sections of niobium-tin wire and two outer coil sections of niobium-titanium wire. The cryo stat used below 1 K is the same as in Fig. 5.3, and the one used between 1-10 K is illustrated in Fig. 5.4. The main difference between them is the lack of a 3 He enclosure for the higher-temperature probe.

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needle valve / He4 pot pumping line heat sink C,U.UL.L...Ll.UJ.....I....L..I....I.IJI..LI, :.----He4 pot He3 pot I I platform : th l w1 samp e I I I Cu ring : brass can / ~pins 7~_,__--Cu block __ --r___ block thermometer I : '-------------brass can pumping line He3 pot pumping line 84 Figure 5.3 : View of the 3 He inner pot cryostat used m both zero and magnetic field specific heat measurements between 0.4 and 2 K.

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needle/ valve capillary brass can He4 pot pins platform : :::::--_,_ __ with sample I I Cu ring I I I I I I '-------------------brass can pumping line He4 pot pumping line Cu block block thermometer 85 Figure 5.4: View of the 4 He inner pot cryostat used for specific heat measurements in magnetic fields at temperatures between 2 and 10 K.

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86 All cryostats have a similar electronic design. They are equipped with radiation shields from top to bottom, and the wires are coupled to the He bath by a heat sink, as shown in Figs. 5.3, and 5.4. Additional wires are soldered from the heat sink to the Cu block, and wrapped around the 4 He pot to ensure thermal equi librium. The temperature of the block is regulated by a heater made of wrapped manganin wire. It is monitored by a Lake Shore calibrated Ge thermometer in the range 1-10 K, and by a Speer carbon resistor between 0.4 and 2 K. In mag netic fields, a Lake Shore capacitance thermometer was used above 1 K due to its negligible field dependence, and the Speer resistor was used from 0.4-2 K for its known magnetoresistance [122). All thermometers are linked to the block using thermally-conductive Wakefield grease. Sample Platform The sample resides at the bottom of the cryostat, attached to a sapphire platform by Wakefield grease. A flat surface at the bottom of the sample is impor tant in order to establish optimum thermal contact between platform and sample. The platform is thermally linked to a copper ring, as shown in Fig. 5.5. Two types of platforms were used in this study. Each platform has four wires soldered to silver pads attached to the ring by thermally-conductive Stycast. The two pairs of wires are connected to the platform heater and thermometer, respectively, using EpoTek H31LV silver epoxy. The platform heater is an evaporated layer of 7%Ti Cr alloy. For measurements between 1-10 K, the platform thermometer used was an elongated piece of doped Ge, and the platform wires were made of a Au-7%Cu alloy. A thin piece of Speer carbon resistor and Pt-10%Rh platform wires were used for measurements between 0.4 and 2 K.

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Stycast Wires : Au-7%Cu (T>lK) Pt-10%Rh (T<2K) 8 7 Solder: Cu-Sn-Cd (Au-7%Cu wires) Pb-Sn (Pt-10%Rh wires) Figure 5.5: Top view of the sample-platform/Cu-ring assembly at the bottom of the cryostat.

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88 5.4.2 Thermal Relaxation Method A thermal relaxation technique consists of calculating the time constant of the temperature decay of the sample linked to a heat bath by a small thermal resistance [118, 119, 120]. The electrical analog of the system is that of an RC circuit, where the time constant is proportional to the capacitance. When heat is applied to the platform-sample system by means of a small current (in A), the temperature increases from a base value T 0 by an amount !:J.T. When the current is turned off the system temperature T(t) decays exponentially to T 0 : (5.4) The time constant T 1 is proportional to the total heat capacity (sample plus plat form) ctotal: ctotal T1 = --, K, (5.5) where K, is the thermal conductance of the wires linking both platform and sample at T = T 0 + !:J. T, and the Cu ring at T = T 0 The time constant was obtained by measuring the time decay of the off-null voltage signal from a Wheatstone bridge using a lock-in amplifier. Two arms of the Wheatstone bridge consisted of a resistance box and the platform thermometer. By adjusting the resistance of the box it is possible to balance the bridge and obtain the platform thermometer resistance. The platform temperature is extracted from a previous calibration of the platform thermometer. The accuracy of the time constant measurement in the temperature range 0.4-10 K is 1-3%. The thermal conductance is given by p K, = ~T (5.6) Here, P = IV is the power applied to the platform heater. The above equations are valid under the assumption of an ideal thermal contact ( K, sa mple r-v oo) between sample and platform. In the event of a poor thermal contact between the sample

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8 9 and the sapphire ( K sa mpl e rv K ) th e temp e rature d eca y ca n ge n era ll y b e d esc ri bed as the sum of two exponenti a ls (5. 7 ) where A and B are measurem e nt parameters and T 2 is th e tim e c on s t a nt b et w ee n sample and platform temperatures. The total heat capacity ca n b e ca lcul ate d from T 1 T 2 and K. The thermal conductance is measured separately b y a ppl y in g a current to the platform heater calculating the power P = IV and calcul a tin g Do T as a result of the power applied to the heater. The accuracy of this m eas ur e m e nt between 0.4-10 K is 5% The sample heat capacity is calculated by s ubtra c ting the heat capacity of the addenda (sapphire platform wires silver epoxy pl a tform thermometer and thermal grease) from the total heat capacity. Finally th e s p ec ific heat is obtained by multiplying by the molecular weight and dividing by th e sa mpl e mass 5.5 Experimental Probes In order to accomplish the objectives discussed in the previous chapter two mechanisms for the study of thermodynamic properties were used in this disser tation: alloying and magnetic fields. Alloying is a powerful tool that allows for changes in the electronic structure, the lattice constants, and the properties of a system. Magnetic fields allow to probe the energy scales relevant to heavy-fermion systems at low temperatures and test their thermodynamic properties against th oretical predictions. The two main types of doping on heavy-fermion compounds are Kondo-hole and ligand-site doping. The first one consists of replacing the magnetic ion by a nonmagnetic counterpart (e.g. La or Y instead of Ce) In this m e thod t her e i s a reduction of the number of magnetic moments in the sample and some disord e r in their electronic environment. In addition the lattice structur e c h a ng es s i g nifi ca n t l y

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90 due to an atomic size difference between the f ion and the dopant ion. Doping with La usually leads to a lattice volume expansion, while Y substitution corresponds to the application of a positive chemical pressure. Ligand-site doping consists of substituting the ligand atoms of one species by another. The main effect here is a dramatic change in the electronic environment of the magnetic ions, changing the value of the local exchange constants. Maximum atomic disorder is introduced using this method, which could complicate the analysis of properties. It is of current interest to investigate the extent to which each method of doping affects the electronic properties. The measurement of thermodynamic properties as a function of applied mag netic field is an important, though not often implemented tool in the study of heavy fermions. The relevant energy scales, both single-site and cooperative, are small enough that magnetic fields easily accessible in a laboratory can help determine their overall magnitude and their role in determining physical properties. The mag netic behavior of heavy-fermion compounds ranges from short-range correlations to non-Fermi-liquid behavior to long-range antiferromagnetic order. Magnetic fields are useful in understanding the different types of magnetic behavior through a comparative study of changes in the density of states, the entropy, the specific heat, and the magnetic characteristic temperature. Various theoretical models, including the single-impurity Kondo description, have different predictions for the magnetic field response of thermodynamic properties. Therefore, the use of mag netic fields as an external parameter is a convenient way of testing the applicability of these models. Specific heat measurements in magnetic field on CePb 3 and CeAb alloys will be presented in this dissertation in order to study the trends followed by parameters relevant to both Kondo and magnetic degrees of freedom in these systems.

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91 5.5.1 Experiments on CeAh A doping study of the lattice parameters specific heat and magn et ic sus ceptibility of Ce 1 _xMxAh alloys has been conducted, with M = La concentrations 0 ::; x ::; 1, and M = Y concentrations 0 ::; x ::; 0.2. The evolution of the lat tice parameters and their ratio c/ a with La/Y concentration x was investigated to determine how the relative variation of a with respect to c and changes in the lattice volume are related to trends in the thermodynamic properties. In addition, the specific heat, the anomaly in C /T, the magnetic susceptibility, and the Wilson ratio expressed as x/, of Ce 1 _xLaxAh were studied over the whole concentration range to search for evidence for a magnetic origin of the anomaly in this system by comparing the concentration dependence of T K and the temperature Tm of the anomaly in C /T, with their dependence on the parameter J based on Doniach's Kondo necklace model. The coupling J is proportional to the hybridization which is expected to decrease with La concentration ( expansion of the lattice). The specific heat of Ce 0 8 La 0 2 Ab and Ce 0 3 La 0 7 Ab was measured in magnetic fields up to 14 T to compare to the predictions of the anisotropic Kondo model [15 36, 37) and to search for clues regarding the magnetic character of the ground state in these alloys. The measured field dependence will allow to determine a connection between the maxima in C /T and those of the AKM. The specific heat data of Y-doped samples will be compared to data as a function of pressure for CeAb to distinguish between the effects of chemical and hydrostatic pressure on the anomaly in C /T. Additional Ceo.s(La1-x Yx)o. 2 Ab samples with x = 0.09, 0.4 were also pre pared for specific heat and magnetic susceptibility studies. In this system yttrium doping of Ceo 8 Lao 2 Ab was conducted to create a similar hybridization environ ment to that of CeAb by reducing the lattice volume to that of the undoped compound. Thermodynamic measurements will allow to test the magnetic inter

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92 pretation of the anomaly in C /T by assuming a constant coupling J yet reducing TRKKv by increasing the Ce-Ce distance with respect to CeA1 3 5.5.2 Experiments on CePb 3 In CePb 3 the increase in the A coefficient of the electrical resistivity along (110) points to a possible enhancement of the heavy-fermion state in magnetic fields based on the proportionality between A and A study of the specific heat of a CePb 3 polycrystal in magnetic fields will be presented in order to describe the changes of the Fermi-liquid parameters and A/, 2 as a function of mag netic field. The phase diagram obtained from these measurements will be com pared to previous magnetoresistance results along (110) to search for evidence of the field-induced transition detected by previous sound velocity and magnetoresis tance measurements and for possible non-Fermi-liquid effects. The data should be helpful in understanding the effects of a magnetic transition on the nature of the heavy-fermion state. Results from measurements of the heat capacity of Ce 0 6 La 0 .4Pb 3 in magnetic fields up to 14 T will also be discussed in order to investigate further the single impurity nature of the paramagnetic heavy-fermion state of CePb 3 The electronic contribution to the specific heat below 10 K will be compared to predictions for the S = single-impurity Kondo model in magnetic fields. The above measurements on CePb 3 and Ce 0 6 La,o.4Pb 3 allow for an analysis of the electronic coefficient, and the Kondo state in both nonmagnetic and magnetic heavy-fermion systems.

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CHAPTER 6 STRUCTURAL A D THERMODYNAMIC PROPERTIES OF CeA1 3 ALLOYS 6.1 Lattice Parameter Study of CeAh Alloys Samples for x-ray diffraction were prepared according to the procedure des c ribed in the previous chapter. All data were taken at room temperature. The diffrac tion pattern for a CeAh sample is shown in the upper half of Fig. 6.1. The data shown are normalized to the intensity of the largest peak (2 0 1) and compared to the calculated intensities for CeA1 3 The residuals are shown in the lower half of Fig. 6.1. The average background intensity per degree is about 5% of the maxi mum intensity corresponding to the (201) peak. Both positive and negative values larger than 5% correspond to the subtraction of theoretical peaks from experimen tal data. A comparison between the residual plot and calculated intensities for the secondary phases CeAh and Ce 3 Al 11 was conducted in order to detect peaks associated with these phases. After a careful analysis, no diffraction lines from any of these two phases could be distinguished from the background data. As mentioned in section 5.2, this does not rule out the presence of a smaller ( <5% of maximum intensity) amount of secondary phases, which could have an effect on other sample properties The lattice parameters obtained from the diffraction pattern were a = 6.543 0.003 A and c = 4.611 0.004 A with a lattice volume V = 170.97 0.16A 3 and a c/a ratio of 0.7047 0.0007. All of these values are within one uncertainty of the original values published by Buschow et al. [62], and those of Corse pi us et al. [ 61]. 93

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0.6 0.5 0.4 .... 0.3 --0.2 >, 0.1 Cl) C 0.0 Q) C 0.4 'U Q) 0.3 -~ co 0.2 E '0 0.1 z 0.0 -0.1 -0.2 CeAl 3 polycrystal (annealed, 800C, 2 weeks) 10 20 30 40 50 60 70 80 90 100 110 120 20 94 Figure 6.1: Diffraction pattern of an annealed CeAh polycrystal (data taken at room temperature). Top: Experimental intensities of CeAh, along with the calcu lated intensities for a Ni 3 Sn structure using the lattice parameters of Ref. [61]. The two largest intensities, around 20 = 25 and 37, correspond to (101) and (201) reflections, respectively. Bottom: Difference between calculated and experimental normalized intensities ( see text).

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95 1800 1600 1400 LaA1 3 1200 Cl) .::= 1000 C: :::J .c 800 Ceo_sLao_sA13 co 600 400 200 CeA1 3 0 10 20 30 40 50 60 70 80 90 100 110 120 20 Figure 6.2: Room-temperature x-ray diffraction patterns for annealed Ce 1 x La x Ah alloys (x = 0 0.5 and 1).

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96 6.1.1 Lanthanum Doping: Ce1-xLaxAh The chemical substitution of Ce by La atoms in the hexagonal Ni 3 Sn struc ture is possible because of their similar electronic structure and atomic radii. Sub stitution of La for the smaller Ce atoms leads to a lattice expansion. Furthermore, the present study revealed that properly annealed Ce 1 _xLaxAh alloys crystallize in the Ni 3 Sn strucure across the entire concentration range (0 x l). This result indicates that the Ce and La atoms are present in solid solution, and that no ternary phases were found. The x-ray diffraction patterns for Ce 1 _xLaxAh (x = 0, 0.5, and 1) are shown in Fig. 6.2. All three data sets exhibit the same pattern (hexagonal Ni 3 Sn). The diffraction peaks shift to lower 20 values with increasing La concentration. According to Bragg's Law, a shift to lower angles implies an increase of the interplane distance d, and also suggests an expansion of the lattice. The lattice parameters for Ce 1 _xLaxAh are shown as a function of La con centration x in Fig. 6.3. The error bars for these and all other lattice parameter data were extracted from the least-squares fits to crystallographic reflections for each sample. The volume increase as a function of La doping is anisotropic. The a parameter increases with x, while c remains essentially constant. The a parameter experiences a larger increase ( almost 10 times larger) than the c parameter. The increase in lattice volume V is therefore mostly due to the increase in a vs x. Fig ure 6.4 illustrates the linear dependence of V with La doping. Due to the larger rate of expansion of a, the c/a ratio decreases (by about 1.6%) between x = 0 and x = 1. This linear decrease as a function of x can be seen in Fig. 6.5. Thus, the effects of La doping on the Ce sites of the hexagonal structure of CeAh are an expansion of the basal plane and a decrease in the c/ a ratio. This ratio moves further away from the ideal close-packed ratio (0.816) due to a rapid increase in a with respect to c for c/ a < 1. This anisotropic volume change could have a significant effect on the electronic environment of the Ce f ions and the exchange

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97 6 680 6 660 I 6 640 I I I 6 620 I < I ......,.. 6 600 I I l::J 6 580 I 6 560 I 6 540 ..... 4 640 4 630 t t < 4 620 II I I l t I 1 ......... 4 6 1 0 4 600 4 590 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 La concentration (x) F i gur e 6 3 : L a tti ce p ara m eters a a nd c as a funct i on of L a concentration x for Ce 1 -x L ax Ah ( 0 :S x < 1 ).

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98 0.0 0.2 0.4 0.6 0.8 1.0 La concentration (x) Figure 6.4: Lattice volume Vas a function of La concentration x for Ce 1 _xLaxAh (0 x 1). The solid line is a least-squares fit to the data.

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99 0.706 0.704 0.702 0.700 0.698 0 696 0.694 0.692 0.0 0.2 0.4 0.6 0.8 1.0 La concentration (x) Figure 6.5: Ratio c/ a as a function of La concentration x for Ce 1 _x La x Ah (0 :S x :S 1). The solid line is a least-squares fit to the data.

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100 constants in the c axis and the hexagonal plane. In fact, it has been argued that in Ce 1 _xLaxA1 3 alloys, the magnetic anisotropy due to a c/ a ratio with c < a leads to an anisotropic Kondo scenario [15, 36, 37]. This aspect will be discussed later in the chapter. The above room-temperature lattice parameter data, especially the values of c/ a, can be interpreted along with results for the low temperature properties of doped CeAh alloys if both a(x) and c(x) show a small-enough temperature dependence. At the present time there are no published results on the temperature dependence of the lattice parameters for CeAh. Nevertheless, the temperature dependence of the thermal expansion coefficient was measured by Kagayama and Oomi [123] on a polycrystalline sample down to 6 K. These values represent an average over all crystallographic directions. A rough estimate of the strain ~l / l between 6 and 300 K, extracted by integrating the thermal expansion coefficient a.(T) of Ref. [123], corresponds to a decrease of the order of 0.1 % in the lattice parameters. This value is 3-4 times smaller than the average increase in volume caused by a change in La concentration equal to 0.1 (see Fig. 6.4). The increase in V is mostly due to the increase in a upon La doping (Fig. 6.3). Since the increase of a between x = 0 and x = l ( 2%) is larger than the average decrease with temperature suggested by ~l/l between 300 and 6 K, a change in the trends observed in Figs. 6.3, 6.4, and 6.5 is not expected at low temperatures. 6.1.2 Yttrium Doping: Ce1-x YxAl3 The substitution of Y for Ce atoms in the hexagonal Ni 3 Sn structure of CeAh induces a positive chemical lattice pressure due to the smaller atomic radius of Y. Doping studies with Y can be used along with pressure studies on pure CeAh [124] to compare the effects of both methods on the lattice parameters a and c. Samples of YAh have been reported to crystallize in the Ni 3 Sn structure [125], which allows

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101 I I I I I I 6 5506.5006 .4 50 I I I I I 4 620 4 610 f ! I -\j 4.600 0 0 0.1 0.2 0 3 0 .4 0 5 Y concentration (x) F i gure 6 .6: L attice p a r a m ete r s a a nd c as a function of Y concentration x for Ce1 x Y x A h a llo ys (x = 0 0 0 2, 0 0 5, 0 1 0 2, and 0.5) T he x = 0.5 value was obtaine d from C S. J e e a nd G. R S tewa r t ( u npub li shed).

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102 174.0----------------------~ 172.0 170 0 I > 168 0 I 166 0 164.0 ~---........ ---........ ---------------0.0 0.1 0.2 0.3 0.4 0.5 Y concentration (x) Figure 6.7: Lattice volume V as a function of Y concentration x for Ce 1 _x YxAh alloys (x = 0 0 02 0.05 0.1 0 : 2, and 0.5). The x = 0 5 value was obtained from C S. Jee and G. R. Stewart (unpublished)

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0.715 ----------------------~ 0.7100.705 I I I~ I 0. 700 ----,--------,------,-------,------,--------,0.0 0.1 0.2 0.3 0 4 0.5 Y concentration (x) 10 3 Figure 6.8: The ratio c/ a as a function of Y concentration x for Ce 1 x Y x A1 3 alloy s (x = 0 0.02, 0.05, 0.1, 0.2, and 0.5). The x = 0.5 value was obtained from C. S. Jee and G. R. Stewart (unpublished).

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104 for the possibility of obtaining solid-solution Ce 1 _x Y xAh alloys between x = 0 and X = 1. However, YAh undergoes a phase transformation to a rhombohedral, BaPb 3 type structure around 644 C [91]. Studies by D. M. Bailey [125] and R. L. Snyder [126] confirmed that the low-temperature hexagonal structure ocurrs in furnace-cooled needle-shaped crystals, and that attempts to obtain the Ni 3 Sn struc ture from a bulk sample were unsuccessful, even after some annealing below the transformation temperature. Moreover, there have been reports of a third, cubic structure associated with this compound [62]. Due to the shortcomings in prepar ing pure YAh, the annealing procedures for Y-rich Ce 1 _x YxA1 3 alloys might prove to be fairly complex. Diffraction patterns for Y concentrations up to x = 0.1 did not reveal the presence of secondary phases. On the other hand, patterns corresponding to x = 0.2 and particularly x = 0.5 (C. S. Jee and G. R. Stewart, unpublished) showed some broadening of Bragg peaks when compared to data from La doped samples for the same concentrations. In addition, these two concentrations revealed the presence of extra reflections of low intensity that could not be identified with either the hexagonal or rhombohedral variation of YAh. These results point toward difficulties in obtaining single-phase hexagonal Ce 1 _x Y xAh alloys for x > 0.2. As Fig. 6.6 illustrates, a large decrease in both a and c was observed up to x = 0.5. A plot of lattice volume V vs x indicates the expected compression of the lattice with Y doping (see Fig. 6.7). There is a significant increase in the c/a ratio for the Y-doped samples, as a consequence of a larger compression rate in the basal plane (Fig. 6.8). This increase inc/a is much larger than the decrease observed with La doping. As a result, both Y and La studies have confirmed that the a parameter is the most sensitive to alloying on the Ce sites.

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105 A comparison of the change in lattice parameters as a function of Y con centration with previous pressure studies on CeAh lattice constants [124] seemed appropriate since doping with Y atoms contracts the lattice, therefore applying an effective chemical pressure on the alloy. It is also important because of a suggestion that the thermodynamic properties of these alloys, in particular the anomaly in C /T, are dependent on values of c/ a, and therefore on the anisotropy of the exchange constants along the c axis and in the a-b plane of the Ni 3 Sn struc ture [61]. The difference between alloying and the application of hydrostatic pres sure is influenced by the degree of disorder, the changes in the electronic structure, and the reduction in the number of Ce f ions introduced by alloying. Kagayama and Oomi [124] found an anisotropic change in a and c in their high-pressure lattice constant measurements of CeAh. At 17 GPa, the lattice volume change V /Vo with respect to the pure compound corresponded to a 20% decrease, and the ratios a/ a 0 and c/ c 0 were 9% and 4 %, respectively. The c/ a ratio increased with applied pres sure by as much as 5% at 17 GPa. No pressure-induced transitions were observed. Kagayama and Oomi established a relation between pressure and lattice vol ume change from a least-squares fit of their data to a first-order Murnaghan's equation of state [124]: (6.1) where B 0 is the bulk modulus at ambient pressure, and B~ its rate of change with pressure, 8P Bo = a In V P=O 8B Bo= 8P l. P=O (6.2)

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106 Table 6.1 : Fractional changes (in%) in the lattice parameters, the change inc/a, and their corresponding chemical pressures (in GPa) Pv, Pa, Pc, and Pc/a for Y concentrations x = 0.02, 0.05, 0.1, 0.2, and 1 (see text for details). The x = 0.5 and x = l values were obtained from C. S. Jee and G. R. Stewart (unpublished) and Van Vucht et al. [62], respectively. The pressure data correspond to lattice parameter changes at room temperature. Y x I V/Vo a/ao c/co c/a I Pv Pa Pc Pc/a 0.02 0.0016 0.015 0.01 0.705(0) 8.58 X 104 0.02 0.03 0.32 0.05 0.16 0.085 0.026 0.705(4) 0.09 0.11 0.08 0.45 0.1 0.44 0.208 0.052 0.706 0.24 0.27 0.16 0.69 0.2 1.06 0.482 0.108 0.708 0.58 0.64 0.34 1.22 0.5 3.5 1.55 0.3 0.714 2.01 2.14 0.97 3.46 1.0 8.9 4.0 0.7 0.730 5.58 6.08 2.35 10.13 This treatment was extended heuristically to find similar relations between pressure and the lattice constants a and c. The data for a/ a 0 and c/ c 0 as a function of pressure are in good agreement with the following equations [124]: where P. = (!::) [ (:~t -1], Pc=(!:) [(j( 0 -1], 8P BiO = a ln i P=O B' __ 8Bi l iO 8P 3' P=O (6.3) (6.4) the index i corresponding to either a or c. The c/ a ratio was fitted to the following equation, in fair agreement with the data: (6.5) where = 0.24.

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107 A relation b etwee n pressure and Y concentration ( corresponding to chemical pressure) was obtained in this dissertation combining the above results with the concentration dependence of the lattice paramet ers. Fir st, the fractional changes V/V 0 a/a 0 c/ eo with respect to published values for CeA1 3 [61], and the c/a ratio were plotted for Y concentrations between x = 0 and pure YA1 3 (Van Vucht et al. [62]). The data were fitted to a square polynomial to determin e an approximate concentration dependence over the range 0 x l. The following equations were obtained: V/Vo = l.00 0.05x 0.04x 2 a/ao = 1.00 0.02x 0.02x 2 c/ c 0 = 1.000 0.005x 0.002x 2 c/ a = 0. 705 + 0.012x + 0.013x 2 (6.6) A square polynomial, rather than a linear fit was used because the increase in c/ a as a function of doping does not imply an isotropic lattice volume change, described by Vegard s Law and characteristic of cubic alloys. When compared to data for YAb (x = 1), the results for x < 0.2 follow a different slope with respect to values for CeAb (x = 0). The above equations allow for a consistent determination of the fractional changes in V, a, and c and the change in c/a with x. Values from the fit were substituted into their respective Murnaghan equations above to determine a chem ical pressure associated with the fractional change for a given Y concentration. In this manner, each concentration is associated with a change in volume V /V 0 and a corresponding chemical pressure Pv. The same argument applies to all other parameters. The fractional changes in the lattice parameters for all concentrations investigated, along with their associated chemical pressures are given in Table 6.1. The most striking fact is that Y doping induces a much sma ll er chemical pressure along the c-axis than along the hexagonal plane compared to the app li cat ion of

PAGE 116

108 hydrostatic pressure. Therefore, the anisotropic character of the change in lattice parameters is stronger as a function of Y concentration than as a function of pres sure. A pressure concentration diagram is illustrated in Fig 6.9. It can be seen from the graph that the parameter most strongly affected by doping is the c/ a ratio. This result might have strong implications as far as the role of anisotropy in determining the ground state properties of this system, as mentioned later in the chapter along with specific heat studies of Y-doped samples. 6.1.3 Mixed Doping: Ceo.s(La1-x Yx)o 2Ah The two main effects associated with alloying on the Ce sites are a reduction in the number of magnetic ions, resulting in an increase of the effective distance between them, and a change in the average /-ion to ligand-atom hybridization. The former has a direct influence on the strength of RKKY interactions, while the latter affects the local Kondo coupling constants. The present alloying study on Ce 0 8 La 0 2 Al 3 combines both Y and La on the Ce sites to keep the average hybridization constant with respect to CeAh, while reducing the Ce concentration. Assuming that the hybridization is dependent only on the value of the lattice constants, this study may help distinguish between the effects of changes in the concentration of magnetic impurities and changes in their electronic environment. In Ce 0 8 (La 1 _x Yx)o 2 Ah, it was found that yttrium doping on the Ce/La sites induces a compression of the lattice . As shown in Fig. 6.11, the change in volume is linear in Y concentration, and is mainly due to a decrease in the a parameter (Fig. 6.10). Therefore, there is an overall increase of the c/a ratio with x (Fig. 6.12). The lattice parameters for x = 0.4 are within the error bars of those of CeA1 3 Thus, this experiment demonstrates that by chemically substituting a certain proportion of Y and La atoms on the Ce sites it is possible to obtain the same lattice parameters as in the undoped compound.

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11 10 9 8 7 6 a. 5 (!J a. 4 3 2 0 0.0 -P V ---0--p Q --6---p C P c/a 0 2 0.4 0.6 Y concentration (x) 109 ,, 0 0.8 1.0 Figure 6.9: Chemical pressures Pv, Pa, Pc, and Pc/a as a function of Y concentra tion x for Ce 1 _x YxAh alloys (x = 0 0.02, 0.05, 0.1, 0.2, 0.5, and 1 ; see text for details). The lattice parameters for x = 0.5 and x = l were obtained from C. S. Jee and G. R. Stewart (unpublished) and Van Vucht et al. [62], respectively. Th e lines are guides to the eye.

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110 6 580 I I 6 570 c<( 6 560 6 550 6 540 I 4 625 4 620 I 1 4 615 I 4 610 4 605 4 600 0 0 0 1 0.2 0 3 0 4 Y concentration (x) Figure 6.10: Lattice parameters a and c as a function of Y concentration x for Ceo s(La1~ Yx)o 2Ah (x = 0 0.09 and 0.4) The open circles indicate the corre sponding y-axis values for CeAh

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111 173.0 172.5 ~172.0 > 171.5 171.0 0.0 0.1 0.2 0.3 0.4 Y concentration (x) Figure 6.11: Lattice volume V as a function of Y concentration x for Ce 0 8 (La 1 _x Yx)o 2 Ah (x = 0, 0.09, and 0.4). The open circle indicates the cor responding y-axis value for CeAh. The solid line is a least-squares fit to the data.

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112 0.706 0.705 0.704 0.703 0.702 0.701 0.0 0.1 0.2 0.3 0.4 Y concentration (x) Figure 6.12: Ratio c/a as a function of Y concentration x for Ce 0 8 (La 1 _x Yx)o 2Ah (x = 0, 0.09, and 0.4). The open circle indicates the corresponding y-axis value for CeAh. The solid line is a least-squares fit to the data.

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11 3 6.1.4 Summary Chemical substitution of La in CeAh caus es an exp a n s ion of th e l att i ce an d a decrease in c/a while Y doping on both Ceo s(La1 -x Y x )o 2 Al 3 a nd C e1 -x Y x Al 3 alloys results in a contraction of the lattice and an incr e as e in c/ a. Th e ov era ll changes in the structure are more drastic for Y than for La substitu t ion F or example, the change in V between Ce 0 8 Y 0_ 2 Ah and pure CeAh is more th a n tw i ce as large as that using the same amount of La. In addition the corre s pondin g decrease in c/ a caused by La is less than half the increase in c/ a from Y doping A comparison of Ce 1 _x YxAh data to the pressure dependence of V a and c for CeAh revealed that both alloying and pressure affect the a paramet e r mor e than c, yet the difference in the rates of reduction for a and c is largest in th e case of alloying. Therefore, c is more affected by hydrostatic pressure th a n b y chemical substitution. The presence of Y in the Ce sites induces an a nisotropi c lattice contraction that could have a significant effect in the electronic environm e n t surrounding the Ce f ions. Another comparison can be made between f-ion and ligand-doping latti ce parameter results. A previous study by Corsepius et al. [61] determined that substitution of Ga Si and Ge on the Al sites causes a net contraction of the lattice, while doping with Sn expands the lattice. In this case the relative changes between a and c were found to depend on the choice of dopant. For example both Si and Ge affect a more than c, while Ga and Sn affect c more than a. Th e r e for e, ligand-site doping seems to affect both a and c more than Kondo-hole ( La Y) doping of the Ce sites which mainly affects the a parameter.

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40-------------------~ 35 30 0 E Q) 25 ::J E Q) E ..._ 20 ?-< 15 0 5 10 T(K) x=O o x=0.1 x=0.2 V x=0.3 x=0.4 15 20 114 Figure 6.13: Low temperature magnetic susceptibility X vs T for Ce 1 -xLa x Ah alloys, 0 ::S x < 0.4 (H = 1 kG).

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70-------------------------, . 60_ 500 E Q) (.) 40'"3 E Q) -S, 3020. x=0.5 o x=0.6 A x=Q.7 v x=0.8 x=0.9 10-+-------------....-,-.....-.....-.....-.....-.....,-.....-.....-.....-.....-.....,-.....-.....-.....-.....-.....,--1 0 5 10 15 20 T(K) 115 Figure 6 14: Low temperature m a gn e ti c s usc e ptibilit y x v s T for C e 1 x L ax A h alloys 0.5 < x 0 9 (H = 1 kG)

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6.2 Thermodynamic Measurements of Ce 1 _xLaxAh Alloys 6.2.1 Magnetic Susceptibility 116 The magnetic susceptibility of Ce 1 -xLaxAh alloys was measured between 2 and 300 K, and was normalized per Ce mole by first subtracting the susceptibility of LaAh, then dividing by the Ce concentration. Figure 6.13 shows the low temper ature susceptibility of samples with La concentrations 0 :S x :S 0.4. The anomaly in the susceptibility, which occurs around 0.5 K in CeAh, is visible at 2.5 K for x = 0.2 and 0.3, while a shoulder can be detected at the same temperature for x = 0.4. Measurements performed on x = 0.2 found no discrepancy between zero field-cooled and field-cooled measurements at temperatures around the anomaly. Values for the susceptibility at 2 K increase from about 29 memu/Ce mol for x = 0 to almost 37 memu/Cemol for x = 0.4. The susceptibility for higher La concen trations (0.5 :S x :S 0.9) is shown in Fig. 6.14. The rate of increase of x values at 2 K is larger than for x :S 0.4, from 40 memu/Ce mol for x = 0.5 to about 66 memu/Cemol for x = 0.9, as illustrated in Fig. 6.14. This enhancement of low-temperature susceptibility values might be an indication of an enhancement of the zero-temperature susceptibility Xo between x = 0 and x = 0.9, consistent with a decrease of the Kondo temperature TK (see Chapter 2). It is not certain from these measurements that similar anomalies are present for other concentrations at temperatures below 2 K. An upturn in the susceptibility does not always lead to a phase transition; it could also indicate an increase in magnetic correlations without leading to a maximum in x vs T. Nevertheless, despite the apparent non monotonic dependence of the temperature of this anomaly with La concentration, the continuous increase of susceptibility values at 2 K with x suggests a decrease of TK, as seen in Fig. 6.15. .. The inverse susceptibility data of various Ce 1 _xLaxAh alloys are shown in Fig. 6.16. The temperature dependence of x followed a Curie-Weiss form above

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117 70 65600 E 55Q,) () 50:::J E Q,) 45E 40N II I.........,. 353025 I I I I I 0.0 0.2 0 4 0.6 0.8 1 0 La concentration (x) Figure 6.15 : Low temperature susceptibility x (T = 2 K) vs La concentrat ion x for Ce1-xLaxAh, 0 < X < 0.9 (H = l kG).

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118 Table 6 2: Magnetic susceptibility parameters for Ce 1 _xLaxA1 3 alloys 0 X < 0.9. Lax Xo (2 K) (memu/Ce mol) eff (s) 8cw (K) 0 28.9 2.53 29 0.1 31.7 2.57 33 0.2 30.9 2.52 29 0.3 33.5 2.54 25 0.4 36.8 2.59 25 0.5 40.3 2.53 23 0.6 43.8 2.58 24 0.7 51.5 2.44 11 0.8 57.9 2.53 18 0.9 65.6 150 K, with the exception of x = 0.9. The calculated effective moments were around the Hund's rule value eff = 2.54 8 for the 4f 1 configuration of Ce 3 +. Table 6.2 shows the variation in the susceptibility at 2 K, the high-temperature effective moment, and the magnitude of the Curie-Weiss temperature 8cw with La concentration. Values of the effective moment range between 2.44 8 and 2.59 8 per Ce ion, with most of them around 2.54 8 The random errors in eff might be due to its extraction over a short tem perature range (100 K T < 300 K) for this system, in particular the narrow range between 300 K and the excited crystal-field levels ("' 70 K). Nonetheless these measurements point to a stable trivalent configuration of the Ce ions at higher temperatures. The extracted values of 8cw are negative, consistent with both antiferromagnetic RKKY interactions between the Ce ions and the Kondo effect. The calculated 8cw shows a trend towards decreasing values with x. This decrease is usually associated with the decrease of T K in Kondo alloys, where 8cwCXTK [32, 127].

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450 400 350 300 :::J E (1) 250 0 E 200 (1) u :>-< 150 T""" 100 50 0 0 50 100 150 200 T(K) x=O o x=0.2 'v x=0.4 x=0.6 x=0.8 250 119 300 Figure 6.16: Inverse susceptibility vs temperature for Ce 1 _xLaxAh, x = 0 0.2 0.4 0.6, and 0.8.

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1 2 0 5000 4500 t " 4000 ro 3500 to 0 3000 ~"o E 'v .t 'v Q) 2500 16 (.) V~ i i 2000 -, E X=O O (.) 1500 'v X=0 1 1000 X=0 2 0 X=0.3 500 X=0.4 0 0 2 3 4 5 6 7 8 9 10 11 T{K) F igure 6 1 7: Sp eci fi c h eat vs temperat u re o f Ce 1 _x L ax Ah a llo ys, 0 ::; x ::; 0 .4. D ata bel o w 1 K for C e A h is fr om Andraka et al. [ 71 )

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121 4000 3500 .. 3000 ,. A .... 0 2500 0 0 E Q) O 'YO 0 2000 A 0 o A
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122 6.2.2 Specific Heat The specific heat curves of Ce 1 _xLaxA1 3 alloys are shown in Figs 6.17 and 6.18. The specific heat of LaAh was subtracted from the data to account for the phonon contribution. It is represented by the following formula between 0.35 and 20 K [128]: C(T) = 4.95T + o.1213T 3 + 4.13 x 104 T 5 3.88 x 101 T 1 (6.7) Substitution by La induces the development of a maximum in C vs Tat a temper ature TM, as was previously seen for low concentration levels (x < 0.2) [71]. This temperature reaches a maximum around 2.3-2.4 K for x = 0.3, and it is reduced to 2 K for x = 0.4. The magnitude of this anomaly initially increases with increasing La concentration. It achieves a value around 4750mJ/K Cemol for x = 0.2, before decreasing to 3600 mJ /K Ce mol for x = 0.4. The increases in both TM and the magnitude of the maximum in C support the idea of Andraka et al. [71] that this anomaly evolves smoothly as a function of doping from the weak maximum seen in C /T of CeAh at 0.4 K. Both TM and the magnitude of the maximum continue decreasing at higher La concentrations. The lowest temperature TM detected within the range of measurement was about 0. 7 K for x = 0.8. The anomaly for this concentration has a magnitude of 2250 mJ /K Ce mol. Values of the specific heat for the more dilute x = 0.9 seem to saturate below 0.4 K, suggesting the presence of a broad maximum at lower temperatures for this concentration. Figure 6.19 shows the specific heat as C /T vs T per mole of Ce for 0 :::; x :::; 0.4. The temperature of the anomaly in C /T, Tm, shifts continuously towards higher values with La doping for x < 0.3. The maximum increases in magnitude ("-'2200mJ/K 2 Cemol for x = 0.2), and Tm reaches a maximum value of 2.3K at x = 0.3, similar to that of TM from the specific heat data. Values of C /T at 0.4 K decrease significantly compared to that of CeA1 3 while those above 4 K

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2400 2200 2000 1800 -;1600 E Q) 1400 () (\J 1200 -:, 1000 E -t:: 800 () 600 400 200 0 2 3 4 5 T(K) X=O.O 0 X=0.1 'v 6 X=0.2 X=0.3 X=0.4 7 123 8 9 10 Figure 6.19: Specific heat plotted as C/T vs T for Ce 1 x La x Ah alloys 0 :S x :S 0.4 Data below 1 K for CeAh is from Andraka et al [71]

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1 24 4000 i 3500 T 3000 X=0.5 0 E 2500 0 X=0.6 Q) (.) A X=0.7 C\I 2000 X=0.8 -, T X=0.9 .S 1500 t:: (.) 1000 500 0 0 1 2 3 4 5 6 7 8 9 10 T(K) Figure 6 20 : Specific heat plott e d as C /T vs T for Ce 1 x La x Ah allo y s 0 5 ::; x ::; 0 9.

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1 25 appear to be less dependent on La c on ce ntr a tion It i s po ss ibl e th a t th e m e r g in g o f th e curves points to a characteristic temp e ratur e for th e d eve lopm e nt of m ag n et i c correlations. At higher concentrations the temp e ratur e T m d ec rea ses, followin g the trend of TM. The magnitude of the anomaly in C /T momentaril y d ec r eases between x = 0.3 and x = 0.4 but increases dramatically for larger values of x, as shown in Fig. 6.20. The entropy is redistributed to lower temperatures with v a lu es of C /T at 0.4 K increasing to more than six times that of x = 0.2 for x = 0 9 The largest maximum detected above 0.4 K has a value of 3900 mJ /K 2 Ce mol and corresponds to x = 0.8. If x = 0.9 has a similar maximum in C /T its magnitude could easily surpass 4 J /K 2 Ce mol due to a very large slope in C /T vs T below 1 K In fact, recent SR studies on Ce 1 x LaxAh alloys [15] found that the divergence of the muon damping rate signaling the presence of magnetic correlations o cc urs around the same temperature as th e anomaly in C /T for at least x = 0.2 Th e damping rate for x = 0.9 diverges around 0 1 K so it is likely that this sampl e exhibits an anomaly in C /T near this temperature. The electronic specific heat coefficient, was extracted for Ce 1 _xLaxAh alloy s from a linear fit of the data below Tm in C /T vs T 2 form, where I corresponds to the intercept. The main sources of error are the relatively large values of C /Tat the lowest temperature (0.4 K) and the uncertainty in the true form of the temperature dependence of this quantity down to T = 0. Brodale et al. determined that C / T is linear in temperature between 0.06 Kand 0.25 K for CeA1 3 [67]. The calculat e d values of, in this section assume C /Tex T 2 down to T = 0. Other sour c e s of error include experimental and regression uncertainties. Figure 6 21 di s pl ays t h e evolution of as a function of La concentration The value of 1250 mJ / K 2 mol for pure CeAb decreases to a minimum of 520 mJ /K 2 Ce mol for x = 0.2. A v e r y l a r ge increase in the electronic coefficient is th e n observ e d for x 0 3 with r eac hin g 3400 mJ /K 2 Ce mol for x = 0.8. Thi s minimum in th e v s x c urv e m ig h t i n di cate

PAGE 134

126 the competition of two effects in the determination of the ground state properties of the system. Another result possibly indicating the competition between two contributions to the ground state properties is the change of the temperature of the anomaly in C /T with x, shown in Fig. 6.22. Data for x = 0.01 and x = 0.05 was obtained from the previous low-level doping study of Andraka et al. [71]. A rapid increase in Tm can be seen for x:::; 0.2. What was previously unknown is that a maximum in Tm around 2.3 K is reached at x = 0.3, followed by an almost linear decrease all the way to x = 0.8. This behavior is similar to that observed for the antiferromag netic anomalies in the specific heat of Ce 1 _x ThxCu 2 Si 2 [129], where the associated temperature position reaches a maximum value also at x = 0.3. An extrapolation of the Ce 1 _xLaxAh data to higher concentrations gives a value of Tm near 0.1 K for x = 0.9. The maximum in the data is asymmetric, due to a sudden increase in Tm values at lower La concentrations. Clearly, this is a sign of two competing interactions taking place in Ce 1 _xLaxAb. Finally, the Wilson ratio R = 218.7x/(,;ff) [5] was calculated for La concen trations up to x = 0.8 using the susceptibility values at 2 K (Fig. 6.15), the extrap olated values from the C /T data, and the high-temperature effective moment eff = 2.54 8 Figure 6.23 illustrates the trend of R vs x, which is very similar to that of Tm vs x. The ratio rises sharply from x = 0 to x = 0.2. The maximum at x = 0.2 is then followed by a slower decrease up to x = 0.8. The highest values of both R and Tm are in the range 0. 2 :::; x :::; 0 .4. When com pared to the Wilson ratio of other magnetic heavy-fermion systems (e.g., R(U 2 Zn 17 )=0.79, R(UCd 11 )=1.55l.82 [5]), the large values of R (1.8-2.2) for Ce 1 _xLaxAh within this doping range suggest an increase in the magnetic character of this system.

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127 3500I 30002500Cel-xLa x A13 I 0 E 2000Q.) (.) C\J ::::c::: 1500 ...., E 1: ?1000 ][ ][ I 5000 I I I I I I I I I 0 0 0 1 0.2 0.3 0 4 0.5 0.6 0.7 0.8 0.9 La concentration (x) F igure 6.2 1 : El ectro ni c s p eci fi c heat coefficient vs La concentration x for Ce1-x L ax A h

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1 28 2 5 0 0 2 0 0 () 0 E 1.5 0 0 '......... 0 0 -E ..... 1. 0 0 0 0 5 0 0 0.0 0 1 0 2 0.3 0.4 0 5 0 6 0 7 0 8 0 9 La concentration (x) Figur e 6 .22: T emperature of t he m ax imum i n C /T ( T m) vs L a c on ce n trat io n x fo r Ce 1 x L ax Ah D a t a for x = 0 01 0.05 w as obt a ined from Andr a ka e t al. [71]

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1 29 2.2 2.0 1.8 1.6 a: 0 1.4 cu 'C 1.2 0 !:!!. 1.0 0.8 0.6 0.4 I I I I I 0.0 0.2 0.4 0.6 0.8 La concentration (x) Figure 6.23: Wilson ratio R [5] vs La concentration x for Ce 1 _xLa x A1 3 0 :S x :S 0.8.

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130 6.2.3 Discussion The behavior of lattice parameters and thermodynamic properties of the Ce 1 _xLaxA1 3 system are very similar to those found by La substitution of another heavy-fermion Kondo lattice CeCu2Si2. The properties of Ce 1 _xLaxCu 2 Si 2 alloys seem to be consistent with Doniach's Kondo necklace model [130, 40]. Ce 1 _xLaxAh alloys have a hexagonal structure with c < a, while La-doped CeCu 2 Si 2 alloys have a tetragonal structure with c > a. When comparing the change in lattice parame ters between the two systems, it was found in both cases that the a parameter is the most affected by La substitution. The change in lattice volume is mostly due to the change in a, and the c/ a ratio decreases linearly by a similar amount across the whole series: 1.2% for Ce1-xLaxCu2Si2 [130] and 1.5% for Ce1-xLaxAh. The electronic specific heat coefficient of Ce 1 _xLaxAh alloys has a minimum around x = 0.2. A similar nonmonotonic dependence of the electronic coefficient with La doping was also found in CeCu 2 2 Si 2 [130]. Studies in which Ce is substituted by La revealed that has a minimum at a La concentration x = 0.5, and achieves a value close to that of pure CeCu 2 2 Si 2 at x = 0.9. Magnetic susceptibility values around 2 K for this system also have a minimum for x = 0.5. The observed similar trends for the changes in, and low-temperature susceptibility values point to a common origin of their behavior as a function of La concentration. The non-single-ion-like changes in upon dilution with La in the above systems are of general interest in the study of strongly-correlated electron sys tems. The increase in, with La concentration observed in dilute samples can be explained by a decrease in the Kondo temperature T K and in the hybridization between 4f and conduction electrons. On the other hand, the observed increase of this coefficient with decreasing La concentration could be interpreted in two different ways. The first interpretation attributes the change to the development

PAGE 139

131 of a paramagnetic heavy-fermion state. Th e sec ond e xpl a n at ion is b ase d on t h e suppression of magnetic order with increasing C e con ce n t r at ion The development of the heavy-fermion state from a c oll ect ion of nonint e acting Kondo scatterers is one of the major unresolved issu e s in h e avy-fermion physics. This problem is linked to the Kondo exhaustion paradox [131]. In such a concentrated system at low temperatures ther e are not e nough conduction electrons within a narrow band around the Fermi level ( rv kaTK) to individually compensate all of the impurity spins at the lowest temperatures. Yet each electron is involved in the simultaneous screening of many local moments. This state devel ops at a characteristic lattice temperature lower than the single-impurity Kondo temperature TK. The decrease in TK with the development of the heavy-fermion state has been experimentally observed in U l-xMxBe 13 [132] (M = nonmagnetic dopant) and Ce 1 _xLaxCu 2 2 Si 2 [130] From these observations it is possible that the behavior of"( in Ce-rich Ce 1 _xLaxAh alloys can also be explained in terms of the formation of a coherent Kondo lattice state. However assuming that the maximum in C /T is indicative of a magnetic phase transition, the electronic coefficient in Ce 1 _xLaxA1 3 extracted from C /T at the lowest temperatures, does not correspond to the heavy-fermion paramagnetic state but to an antiferromagnetic ( or spin-glass) state The phase transition leads to a decrease in the value of the electronic specific heat coefficient. Therefor e, it is quite unreliable to extract a measure of the lattice Kondo temperature from t he inverse of the electronic coefficient of magnetic heavy-fermion alloys. In order to estimate the concentration dependence of a characteristic lattice Kondo temp e ra ture for the Ce 1 -xLaxAh alloys studied, values of TK were extracted instead using the magnetic entropy Sm(T 0 ), defined as S (T,) = {To Cm(T) dT m O lo T ( 6 .8)

PAGE 140

132 where C m (T) /T is th e s p ec ifi c heat contribution per Ce mole aft e r subtra c ting the phonon contribution (L a Ah) and T 0 > Tm, the characteristi c magnetic tran sition temperature In C e heavy-fermion compounds, the magnetic entropy at low temperatures includes contributions from the Kondo effect as well as mag netic interactions while at T oo it reaches the value R ln 2 for a mole of S = magnetic moments. At a temperature T 0 sufficiently larger than the magnetic ordering temperature magnetic interactions represent only a minor contribution to the specific heat [133 134], and the entropy Sm(T 0 ) is essentially the differ ence between Rln 2 and that removed by the Kondo effect at T 0 In the range T 0 :=; T < oo the entropy removed is a function of TK only so that Sm(T 2: T 0 ) provides a good measure of T K. All C /T vs T curves between x = 0 and x = 0.8 were numerically integrated up to T 0 = 3 K This temperature is above all Tm values between x = 0 and x = 0.8. Values of TK were extracted by comparing the results for Sm(3 K) with the Bethe Ansatz solution for the S = Kondo entropy curve [30]. Calculating the entropies at values of T 0 < 5v K was found to have little effect on the values of TK determined from the curves. In addition the contributions and concentration dependences of higher crystal-field levels at this temperature were assumed to be negligible. The calculated entropies at 3 K and values of the Kondo temperature are shown in Table 6 3. As the La content increases in Ce 1 _xLaxAh Sm(3 K) increases which implies a decrease in TK A characteristic temperature Ce concentration phase diagram, shown in Fig. 6.24, was constructed using the calculated values of TK for (0::; x ::; 0.8) and assuming that the maxima in C /T at Tm are indicative of a magnetic transition. The resulting diagram is similar to that of the Kondo-necklace model shown in Fig. 2.7 [42 43]. Yet, it is important to keep in mind that changes in both TK and Tm with Ce concentration might not only reflect the effect of reducing J, but also

PAGE 141

1 33 4 0 3 5 3 0 T K ...... 2.5 E 2 0 .... T I;: m I1. 5 . 1 0 0.5 0 0 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0.9 1.0 1 .1 Ce concentration (1-x) F ig ur e 6 24: Ph ase diag r am illu strat ing bot h t h e te m perature of t h e anomaly in C /T T m and t h e calcu l ated Kon d o te m pe r ature T K (see text) as a function of Ce co n ce n trat io n. T he li nes are g u i d es t o t h e eye

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134 T a ble 6.3: Values of th e m ag n e tic entropy Sm (in units of Rln 2) (T = 3 K)/TK the Kondo temperature TK and TK normalized to that of CeAh (TK ,..__,4 K [6]) for Ce1-xLa x Ah alloys. Lax Sm(3 K) (Rln 2) (T = 3K)/TK TK(K) TK/TfeAl 3 0 0.586 0.749 4.0 1.00 0.1 0.624 0.884 3.4 0.85 0.2 0.652 1.008 3.0 0.74 0 3 0 636 0.933 3.2 0.80 0.4 0 660 1.071 2.8 0 70 0.5 0 704 1.319 2.3 0.57 0.6 0.735 1.541 2.0 0.49 0.7 0.813 2 650 1.1 0.28 0.8 0.826 2.901 1.0 0.26 the effect due to an increase in the average distance between Ce 4f moments. This Doniach-like diagram positions CeAh at the end of the magnetic temperature curve in the region corresponding to TK > TRKKY The description of CeA1 3 in terms of the Doniach model places it in the proximity of a critical point at Tm = 0 consistent with current views on heavy-fermion systems [135, 136 137, 138] 6.3 Thermodynamic Measurements on Ce 1 _x Y xAh Alloys 6.3.1 Magnetic Susceptibility The magnetic susceptibility of Ce 1 _x Y xAh alloys was measured between 1.8 and 400 K at a field H = 5 kG. Figure 6.25 shows data for x = 0, 0.02, 0.05, 0 : 1, and 0.2 per Ce mole below 20 K. The main consequence of Y doping is a decrease in the magnitude of the susceptibility at this temperature range The magnetic susceptibility at 1.8 K x(T = 1.8 K), is reduced by about 40% for x = 0.2 from the value of pure CeAh. A decrease in low-temperature susceptibility values with compression of the lattice is usually associated with an increase of the Kondo temperature T K since the zero temperature susceptibility is inversely proportional to T K The inverse susceptibility as a function of temperature is

PAGE 143

135 30 x =0 a 0 x=0 02 C A x=0 05 25 QQ x=0 .1 ~AA QC 0 x=0 2 E 'v A 'v AA Q) 'v A e (..) 20 "" A 0 :::::s A E A 0 Q) A 0 A 2 E " -15 i " 10 0 2 4 6 8 10 12 1 4 16 18 20 T(K) F igure 6.25: Magnet i c susceptibi l ity vs temperature of Ce 1 x Y xAh a ll oys 1.8 ::; T :::; 2 0 K H = 5k G

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136 600-.-------------------------, 500I 400::J E Q) ::::::: 0 300g g E X=0 Q) (.) .!~ X=0.02 -200,, X=0.05 T"" V X=0.1 100 X=0.2 0 I I . I I I 0 100 200 300 400 T(K) Figure 6 26 : Inverse magnetic susceptibility vs temperature of Ce 1 _x Y x Ah alloys 1.8::; T::; 400K H = 5kG

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1 3 7 Table 6.4: Magnetic susceptibility paramet e rs for C e 1 _x Y x Ab a ll oys, 0 ::; x::; 0. 2 Y x X o (2 K) (memu/Ce mol) e ff a ) G cw (K ) 0 28.89 2.53 29 0.02 28.56 2 58 41 0 05 25.19 2.60 4 1 0 1 23.61 2 57 40 0 2 17.49 2.60 55 illustrated in Fig. 6.26. Data for x = 0.2 are noticeably higher th a n th e r es t especially below 150 K. All concentrations show linear behavior following a Curie Weiss law above 100 K. The Curie-Weiss parameters were extra c ted from a least squares fit of the data above 100 K (see Table 6.4). The calculated values for the high temperature effective moment eff are in the vicinity of the Ce 3 + fre e -ion value eff = 2.54 8 The negative Curie-Weiss temperature G cw in c reases with x, which is also consistent with an increase of the Kondo temperature TK. 6.3.2 Specific Heat The specific heat of Ce 1 _x Y xAb alloys (0 ::; x < 0 2) plotted as C /T vs T per mole of Ce, is shown in Fig. 6.27. The temperature of the anomaly Tm is slightly larger for x = 0.02 than for CeAb. It remains around 0.6 K between x = 0.02 and x = 0.1, and increases toward 1 K for x = 0.2. At the same time, the magnitude of the anomaly decreases gradually, from about 1650 mJ /K 2 Ce mol for x = 0 to 540 mJ /K 2 Ce mol for x = 0.2. Values of C /T a round 0.4 K just below Tm, decrease monotonically within this range of concentration from above 1600 mJ /K 2 Ce mol to 420 mJ /K 2 Ce mol. This trend in C / T valu es indi ca tes a decrease in values of the electronic coefficient at T = 0. V a lu es of c ould not be extracted from the C /T curves with reasonable a c c ur acy du e t o t he s m a ll difference between 0.4 K, the lowest temperature of th e m eas ur eme n t, a nd T m. A larger temperature range and number of data points is n ee d e d t o d etermine, fr o m

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1 38 1600 Ce 1 _xYxA1 3 1400 I -;1200 lX=0 E 0 X=0.02 Q) X=0 05 (.) 1000 C\I 6. X=0.1 :::s:::: 'Y X=0.2 ---:, E 800 t: 6. Li~ (.) 600 f""'Y'Y-y 'Y 'Y 'Y 400 'Y 'Y 'Y 'Y 'Y 'Y ~
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139 a linear fit of C /T vs T 2 below Tm In addition, the area under the C /T c urv es up to 7 K, equal to the entropy Sm (To rv 7 K) clearly decreases with Y concentration. Both the apparent decrease in I and the decrease in Sm (To rv 7 K) with x point to an increase of the Kondo temperature. A decrease in the Kondo entropy, which i s the dominant contribution to Sm, is consistent with a decrease of (To= 7 K)/TK [30], as previously discussed in the context of Ce 1 _xLaxAh alloys. 6.3.3 Discussion Both specific heat and magnetic susceptibility results for O :::; x :::; 0.2 point towards an increase in the hybridization between Ce and Al atoms, and therefore to an enhancement of the Kondo effect, with increasing Y concentration. The increase of TK is manifested in the increase of 8cw, in the reduction of the magnetic entropy Sm around 7 K, and in the decrease in x and C /T values at the lowest measured temperatures. The specific heat data can be compared in this regard with previous results for the heat capacity as a function of pressure of CeA1 3 (see Fig. 3.3) [67]. According to the comparison between Y doping and pressure dependence of the lattice parameters of Ce 1 _x YxA1 3 and CeAh, respectively, presented earlier an Y doping level of x = O. l induces a change in the lattice volume corresponding to a chemical pressure Pv of 2.4 kbar (0.24 GPa). This sample shows an anomaly at 0.46K, with C(0.4K)/T=860mJ/K 2 Cemol. A similar pressure (2.2kbar) was applied on CeAh by Brodale et al. [67], suppressing the anomaly in C /T and reducing both C ( 0.4 K) /T and the extrapolated I to 838 mJ /K 2 Ce mol. It is inter esting that the values of C(0.4 K)/T are the same within uncertainty in both cases, while the anomaly only appears in the Y doped sample. Also interesting is that values of C /T above the temperature of the anomaly Tm are more strongly reduced by Y substitution. The main differences between the application of chemical and hydrostatic pressures are a reduction in the number of Ce moments and a much slower decrease of the c lattice parameter with Y doping. Since the anomaly is still

PAGE 148

140 present despite a reduction in Ce concentration its rapid suppression in the case of CeAh may be related to a stronger reduction of the c parameter with pressure. The almost constant value of Tm for Y concentrations between x = 0 and x = 0.2, when compared to its rapid suppression between ambient pressure and 2.2 kbar in CeAh cannot be reconciled in terms of Doniach's Kondo necklace model, and lacks a complete explanation. However, these results seem to indicate that interactions between the hexagonal planes strongly affect the magnetism in this system. In fact, magnetic susceptibility measurements in single crystals [76] revealed a large magnetic anisotropy, with x below 40 K being larger along the c direction. The decrease in c is larger with pressure than as a function of Y con centration, significantly reducing the distance between hexagonal planes, increas ing the hybridization between Ce and Al atoms in adjacent planes, and therefore suppressing magnetic order. A similar argument has been proposed for the hexag onal heavy-fermion compounds CePd 2 Ah [139, 140] and CeCu 5 [141, 142] based on annealing, pressure, and doping studies on the Ce sites. In these two com pounds, the intra plane hybridization is larger than that between planes ( J J_ >> J11), while the opposite is true of CeAh, according to previous susceptibility and neu tron scattering studies [76, 87]. Despite this difference, the strength of magnetic interactions in both cases seems to be dependent on the hybridization between hexagonal planes. On the other hand, the lack of a suppression of Tm with Y doping appears to be consistent with recent ligand-site doping measurements on CeAh by Corsepius et al. [61], where both an expansion and contraction of the lattice were found to enhance the anomaly in C /T. The authors argued that the absolute-value change in c/ a was responsible for the development of this maximum. This ratio is related to the hybridization angles between Ce and Al atoms. Assuming that c/ a in CeAh roughly corresponds to the angle with optimum screening of f moments,

PAGE 149

1 4 1 any vari a tion in c/ a will disturb the s c r ee nin g a n d w ill g i ve rise to l arge r moments. The int e ra c tions between these moment s th e n in creases a ll ow i ng the deve l opment of magnetic anomalies in the specific h e at. 6.4 Thermodynamic Measurements on Ce 0 8 (La 1 _x Y x ) o 2 Al 3 Alloys 6.4.1 Magnetic Susceptibility In order to explore further the magneti c n a tur e of the C /T anom a l y in Ce 1 _xLaxAh alloys an yttrium doping study was c ondu c ted on Ce 0 8 Lao 2 Ah. Th e motivation was to determine the effect of keeping the lattice volume at a value close to that of CeA1 3 while keeping the numb e r of Ce moments at a const a nt but reduced value, and to search for changes in properties due to intersite intera c tions. The lattice parameters for an Y concentration x = 0.4 are a= 6.542.002 A and c = 4.616 0.004 A both within error bars of those of pure CeAh. Figur e 6.28 shows the magnetic susceptibility per Ce mole of C e 0 8 (La 1 _x Y x )o 2 Ah alloys for Y concentrations x = 0 0.09 and 0.4 along with data for CeAh up to 20 K The maximum seen for x = 0 appears to shift towards lower temperatures (below 2 K) and the susceptibility values above the anomaly (> 3 K) decrease with increasing Y concentration. There is also a small increase of x (2 K) between x = 0 and x = 0.09 (see Table 6.5). This increase might be due to the observed decrease in the temperature position of the maximum which will be discussed in the following section. Values of x (2 K) for x = 0.4 and for CeAh are very similar ( differ b y 2%). It seems that the similarity between the two values is coincidental sin ce data for x = 0.4 show a larger decrease between 2 and 10 K than that of the pur e compound. The inverse susceptibility of Ce 0 8 (La 1 x Y x )o 2 Ah ( x = 0 0.09 and 0 .4) is illustrated in Fig. 6.29. The data follow a Curi e -Weiss law a bov e 150 K a nd the calculated high-temperature effective mom e n ts a r e clo se t o th e C e 3 + value

PAGE 150

35-,----------------30 25 Q) u ::, 20 E 15 CeAl 3 x=O D. x=0.09 x=0.4 10-+........................................................................................ .......-.......-.......-.......-.......-----.--.-..,.........., 0 2 4 6 8 10 12 14 16 18 20 T(K) 142 Figure 6.28: Low temperature magnetic susceptibility x vs T for Ceo a(La1x Yx)o 2Ah alloys = 0 0.09, and 0.4 (H =1 kG). Data for CeAh ar~ shown for comparison.

PAGE 151

450 400 350 ,.._ 300 ::J E Q) 250 0 E 200 Q) () -150 T""" 100 50 0 0 50 100 150 200 T(K) CeAl 3 x=O x=0.09 x=0.4 250 1 43 300 Figure 6.29: Inverse susceptibility vs temperature for Ce 0 8 (La 1 _x Y x)o. 2 Ah alloys x = 0 0 09 and 0.4 (H =l kG). Data for CeAh are shown for comparison

PAGE 152

144 Table 6.5: Magn et ic susceptibility parameters for Ce 0 8 (La 1 _x Yx)o 2 Al 3 alloys x = 0, 0 09 and 0.4 Data for CeAla are shown for comparison. Lax X (2 K) (memu/Ce mol) e ff 8 ) 0cw (K) 0 30.9 2.52 29 0 09 0.4 CeAla 32.5 28.4 28.9 2.57 2.60 2.53 32 40 29 eff = 2.54 8 The parameters obtained from a linear fit of 1/x vs T above 150 K are shown in Table 6.5. The negative Curie-Weiss temperature 0cw increases with Y concentration Yttrium doping contracts the crystalline lattice, increasing the coupling between conduction and f electrons in the Kondo necklace model and therefore increasing T K. It should be noted that CeAla has the same lattice volume as x = 0.4, and consequently a similar average hybridization. Yet the larger value of 0cw obtained for x = 0.4 seems to indicate a higher TK for this sample. 6.4.2 Specific Heat Figure 6.30 shows the specific heat as C/T vs T for Ceo s(La 1 _xYx)o 2Ala (x = 0, 0.09 0.4). Data for CeAla is also shown for comparison. The behavior of C /T with Y concentration is somewhat analogous to that of Ce 1 _xLaxAla alloys between x = 0 and x = 0.2 with decreasing La content The anomaly at 2.1 K is attenuated in magnitude and its temperature reduced with Y concentration. Yet, the C /T curve for x = 0.4 does not have a maximum down to the lowest temper ature measured (0.4 K). Values of C /T at this temperature increase dramatically, approaching that of CeAla at x = 0.4. The inset to the figure indicates that the specific heat at x = 0.4 shows no sign of the anomaly, as in pure CeAla. The entropy between 0.4 and 4 K ( area under the C /T vs T curves) clearly decreases from x = 0 to x = 0.4. A crossing of the C /T curves for the Y-doped samples can be observed around 4 K upon closer inspection of the data. Values of this quantity

PAGE 153

145 above 4 K are highest for x = 0.4 whi c h seems to indicate that the lost entropy i s recovered at temperatures much larg e r than 10 K. Based on the similarities between their latti ce parameters, it is assumed that both CeA1 3 and Ce 0 8 (La 0 6 Y 0 4 ) 0 2 Ah also have a similar Kondo temperature. An estimate of TK for the alloy with x = 0.4 can be obtained using the proce dure described earlier for La-doped alloys, then compared to TK = 4 K for CeA1 3 The entropy Sm(3 K) was obtained by fitting the data below 3 K to a power law and analytically integrating this function using the fit coefficients. A pow e r-l aw behavior assumes a divergent value for ,. Therefore, the area calculated would correspond to an upper-limit value of Sm(3 K) and a lower-limit value of TK The value obtained was TK = 4.4 K, slightly larger than TK for CeAh. This result is consistent with the larger value of 8cw obtained from the inverse susceptibility of Ce 0 8 (Lao 6 Y 0 .4) 0 2 Al 3 and suggests that this alloy has a larger Kondo temperature than the undoped compound A larger Kondo temperature for x = 0.4 despite having the same values of a and c as CeAh indicates that the average coupling J may not be exclusively dependent upon changes in the lattice constants Alloying of Ce 0 8 La 0 2 Ah with Y introduces random microstresses m the lattice which could change the average hybridization and suppress the specific heat anomaly. In order to investigate whether the suppression of this anomaly is indeed due to lattice stress, the specific heat of a pressed pellet made out of Ce 0 8 Lao 2 Ah powder was measured down to 1 K. Grinding of a sample into powder causes microscopic tensile and compressive stresses that can simulate effects asso ciated with alloying and can also contribute to changes in the physical properties of a system with a pressure-sensitive ground state. Data for C /T on Ce 0 8 Lao 2 A l 3 bulk and pellet samples are shown in Fig. 6.31. The effects of grinding the sam ple are a broadening and an attenuation of the magnitude of the anomaly. The broadening of the anomaly indicates that simultaneous tension and compression

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2400 2200 2000 1800 01600 E a> 1400 (.) C\I~ 1200 E 1000 -C: 800 (.) 600 400 200 0 I\ X=O 0 X = 0.09 A X = 0.4 CeAl 3 5000-,--------~ ~1:_:: : j 4000 i~ ., 3000 0 1 2000 f i"'! ., .-1,-I; t ~& O 1000 I :...._ o o ... o Q 0 2 4 6 8 10 A T(K) & ~ ~., ~ If) tr~ 4>" 2 3 4 5 6 7 8 9 10 T(K) 146 Figure 6.30: Specific heat plotted as C /T vs T for Ceo 8(La1-x Yx)o.2Ah (x = 0, 0.09 and 0.4) The specific heat of CeAh in C /T form is also shown for comparison ( data below 1 K for CeAh by Andraka et al [71]). The inset shows C vs T for x = 0 0.09 and 0.4

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147 of the lattice can be found at the microscopic level leading to a pos s ibl e di str ibu tion of temperatures Tm The temperature of the maximum is slightly incr eased by about 0.2-0.3 K. Subsequent annealing of the pellet at 600C for 24 hours partially restores the shape of the anomaly for the bulk sample. Therefore the anomaly does not seem to be related to random stresses due to alloying. Rather the reduction of such stresses by annealing was found to enhance the size of the anomaly. Previous specific heat measurements have also been conducted on pellets of isostructural UPt 3 [143), CeAh (B. Andraka and R. Pietri, unpublished), and Ce(Al 0 97 Ga 0 03 )J [61]. An increase in temperature of the related anomaly in C was found in the latter two cases. In particular, when comparing the pellet data on Fig. 6.31 with measurements on a pressed pellet of CeA1 3 it is found that C /T values at 0.4 K for the pellet are significantly lower than those of bulk CeAh, while the corresponding values for Ce 0 8 La 0 2 Ah for both bulk and pellet samples remain essentially the same. This comparison suggests that values of for the more magnetic state of Lax = 0.2 are less sensitive to random lattice stresses than those of CeAh, which has both a lower Tm and a higher TK. 6.4.3 Discussion Doping of Yon the Ce/La sites of Ce 0 8 La 0 2 Ah was found to be successful in restoring the lattice parameters corresponding to CeAh, as reported at the beginning of the chapter. The effect of reducing the number of Ce impurities while keeping the same lattice parameters as in the pure compound has been observed in both specific heat and susceptibility. The anomaly was suppressed towards lower temperatures by attempting to keep the hybridization constant ( assuming J depends on a, c only) while increasing the distance between Ce atoms, therefore decreasing the RKKY interaction ( see end of section). There seems to be an overall increase in both C /T and x values at the lowest temperatures (T 0) The C / T

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1800 1600 1400 1200 0 E C\J 1000 ..., E 800 -t: 600 (.) 400 200 0 0 .. .. .... !!:A A A A -A I 'A fl A 2 3 4 bulk pellet pellet (annealed) ~. ~~ .a 18 5 T(K) 6 7 8 9 148 10 Figure 6.31: Specific heat plotted as C /T vs T for Ce 0 8 Lao 2 Al 3 bulk, pressed pellet, and post-annealed pellet samples.

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149 anomaly visible in CeAh at 0.4 K either completely di sa pp ears or sh if ts towards lower temperatures for an Y concentration x = 0.4. It seems that the intersite magnetic correlations, which depend on the overall number of Ce moments, play a crucial role in determining the strength of the energy scale giving rise to the anomaly in CeAh. A uniform rise in C /T at the lowest measured temperatures is a signature commonly associated with non-Fermi-liquid behavior [12], where C /T is either a logarithmic function of the temperature as in the Kondo disorder model [50 49], or obeys a power law Tv as in quantum critical (v = 0.5) [53, 55] and Griffiths phase (0 2 v 2-1) [58, 59] models. Specific heat results for x = 0.4 show no sign of a maximum in C /T down to 0.4 K, suggesting the presence of non-Fermi-liquid effects. In order to verify whether the temperature dependence of C /T for this alloy is consistent with any of the predictions from the above models the data were plotted in semilog and log-log forms and as C /T vs T 1 1 2 The data for C /T did not follow linear behavior on both semilog and T 1 1 2 forms. It rather roughly followed a power-law dependence in the limited temperature range of 0.4-1. 7 K with an exponent close to -0.5 (see Fig. 6.32). The magnetic susceptibility was also plotted in log-log form, with the data following linear behavior up to 30 K as shown in Fig. 6.33. A fit of the data to a power-law dependence yielded an exponent of -0.33. In the Griffiths phase model [58] the specific heat is related to the magneti c susceptibility by a power law: er) ex x(T) ex r-1+>., (6.9) where the parameter .\ < 1 can be determined by a best fit through the dat a. A value of .\ = 1 indicates Fermi-liquid behavior. The corresponding parameters

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150 obt a ined from fits to C/T (0.4-l.7K) and X data shown in Figs. 6.32 and 6.33 respe c tively are A c = 0 54 and A x = 0.67. The above valu e s for ).. are fairly close to each other indicating a possible rela tion between C /T and X A similar analysis has been performed for two canonical non-Fermi-liquid systems: UCu 4 Pd (Ac = 0.71; Ax = 0.72) and U 0 6 Th 0 .4Pd 2 Ah (Ac = 0.84; Ax = 0.63) [59]. The former is a disordered ligand system with a cubic structure [144]; the latter a Kondo hole system with a hexagonal structure [145]. It is worth noting that the difference !Ac Ax! is larger in the hexagonal alloy, and may be due to anisotropy in its magnetic properties. The authors attributed this larger discrepancy to the polycrystalline nature of the sample so that the measured susceptibility represents the average over different crystalline directions and expected better agreement on single crystalline measurements. The differ ence of 0.21 observed for U 0 6 Th 0 .4Pd 2 Ah is larger than that of polycrystalline Ce 0 8 (La 0 6 Y 0 .4) 0 2 Ah (!Ac A x l = 0.13) indicating that a Griffiths phase model may describe the observed dependence in C /T and x down to 0.4 K provided that C /T follows a power law down to temperatures much lower than 0.38 K. The validity of this description also depends on whether the alloy in question reproduces the physical scenario required for the formation of a Griffiths phase [58, 59]: magnetic anisotropy, disorder due to alloying and the competition between Kondo and RKKY energy scales. The alloy Ce 0 8 (Lao 6 Y o.4) 0 2 Ah seems to fulfill all of these requirements, since a strong magnetic anisotropy has been deduced from neutron scattering data [87] and magnetic susceptibility studies on single crystals [76]. Yet, measurements at lower temperatures ( especially for C /T) are necessary in order to verify this interpretation. The alloying procedure described in this section potentially demonstrates a novel method of inducing non-Fermi-liquid effects in antiferromagnetic Kondo lattices. The standard method consists of using alloying pressure, or magnetic

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--0 1250 E Q) u N -, E t::: u C/T oc T 1 +'" Ac= 0.54 1 T(K) 1 5 1 ..... 10 Figure 6.32: Log-log plot of C/T vs T for Ce 0 8 (La 0 6 Y 0 .4) 0 2 Ah The solid line i s a fit of the data below l. 7 K to the power-law equation shown in the graph.

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0 E :5 10 E (l) E --1 X OCT -1+)., A = 0.67 X 10 T(K) .. 100 152 Figure 6.33: Log-log plot of x vs T for Ce 0 8 (Lao. 6 Y 0 .4) 0 2 Ah at H = l kG. The solid line is a fit of the data below 30 K to the power-law equation shown in the graph.

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153 fields as external parameters to significantly change the coupling J in order to drive Tm to zero. This novel method uses a llo ying on the impurit y s it e, but with a combination of dopants that keeps the l attice parameters fairly constant with respect to the pure compound. Assuming J depends only on the value of a and c changes in this quantity are minimized by using atoms with both smaller/larger atomic radii than that off ions. At the same time, the reduction in the number off ions increases the average distance R between them. The latter causes a decrease in the RKKY temperature (TRKKv ex J 2 / R 3 see Chapter 2) with respect to the Kondo temperature thus driving the system through a quantum critical point. In this manner, non-Fermi-liquid effects might be observed by only changing the distance between impurities without significantly affecting the value of J 6.5 Heat Capacity of Ce 0 8 Lao 2 Ah and Ce 0 3 Lao 7 Ah in Magnetic Fields As mentioned previously, recent neutron scattering and SR studies by Gore mychkin et al. [15] on Ce 0 8 Lao. 2 Ah revealed the absence of magnetic Bragg peaks and estimated the upper limit of any possible ordered moment to be 0.05 8 The response function deduced from time-of-flight measurements changes from a quasi elastic form to an inelastic form around 3 K below which features develop in the specific heat and the magnetic susceptibility. This result [15] was attributed to weakly dissipative dynamics consistent with the anisotropic Kondo model (AKM) [35]. . Data from SR experiments showed Lorentzian damping, with a temperature dependent damping rate. The temperature at which the damping rate starts to diverge coincides with the temperature Tm of the maxima in C /T for x = 0 .2 0. 7, and 0.9 samples, as previously described. The divergence was attributed to the development of static magnetic correlations indicating the possibility of mag netic order of small moments as seen in URu 2 Si 2 [146]. In order to investigate further the applicability of the AKM to both CeAh and Ce 0 8 Lao 2 Al 3 the effect of

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154 magnetic fields up to 14 Ton the linear coefficient 'Y and on the temperatures TM and Tm of the maxima in C and C /T, respectively, was studied by specific heat measurements. Magnetic field measurements were also performed on Ce 0 3 La 0 7 Ah to study the effects on a more dilute 4f system. 6.5.1 Results Figure 6.34 shows the specific heat of Ce 0 8 La 0 2 Ah in fields of 0, 5, 10, and 14 T. The phonon contribution was subtracted using the specific heat of LaAh [128], and the remainder has been normalized to a mole of Ce. Data plot ted as C /T vs T can be seen in Fig. 6.35. The main effect of the field is a strong reduction in the magnitude of the anomalies in C and C /T, but probably the most striking fact is the very weak field dependence of the temperature posi tion of the anomalies. A pronounced peak in C located at TM 2.3 K for H = 0 is replaced by a shoulder near 2.1 K for H = 14 T. The peak in C /T also shifts slowly with field, with Tm decreasing from 2.1 Kat OT to 1.7K at 14 T (see Fig. 6.36). The difference between TM and Tm grows with applied field. A difference of the same order has been observed in zero field for Ce 1 _xLaxAh alloys with x < 0.2, where TM-Tm grows with decreasing La concentration x [71]. In this respect, an increase in the magnetic field has a similar effect to a decrease in x. Another important result is an increase with field of C /T values at tem peratures below 1 K, suggesting a partial restoration of the heavy-fermion state present in pure CeAh. The large nuclear moments of 27 Al and 139 1a (n = 3.64 and 2. 76 N, respectively) contribute in part to the enhancement of C /T at the lowest temperatures and the largest fields. In fact, the 14-tesla C /T data display a low-temperature tail which is due in part to a nuclear hyperfine contribution Cn/T = NAnH 2 /3kBT 3 (e.g., see Ref. [147]). The combined hyperfine contribu tion from 27 Al and 139 La at 0.4 K and H = 14 T is around 25 mJ /K 2 mol (per total mole). None of the curves at lower fields show a similar upturn. The linear specific

PAGE 163

1 55 5000 4500 ,. H =OT 0 H = 5T 4000 "v H =10T 3500 H = 14T 0 3000 0 E 0 00 0 Q) 0 "v () 2500 0 "v 0 t ~-!7~ Oio~ 0 0 0 0 0 -, 2000 E ""' _... () 1500 0 1 000 500 0 0 2 3 4 5 6 7 8 T(K) Figure 6.34: S peci fi c h e~t vs tem p erature for Ce 0 8 La 0 2 Ah at H = 0 5 10 and 1 4 T

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2500....---------------------~ 2000 -0 E 1500 Q.) (.) C\J ::::c::'. E 1000 --1:::: (.) 500H=OT o H=S T H=10 T H=14 T 0 -----,---,---.---,-----,-...-----,------,-----,---0 1 2 3 4 5 6 7 8 T(K) 156 Figure 6.35: Specific heat plotted &s C /T vs T for Ce 0 8 La 0 2 Ah at H = 0, 5, 10, and 14 T.

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157 heat coefficient was extracted from a linear fit to C /T vs T 2 below 1 K exc pt for the data at 14 T, where, was determined from the slope of CT 2 vs T 3 below 1 K. As illustrated in Fig. 6.36 , seems to saturate above H 10 T. The error bars for were calculated by taking into account the effect of both experimental and linear regression uncertainties. y The specific heat of Ce 0 3 La 0 7 Ah, plotted as C /T vs T is shown in Fig. 6.37. In this sample the magnitude of the peak is strongly attenuated at H = 6 T and it completely disappears at larger fields. The temperature of the maximum Tm is reduced by about 0.2 K in a 6 T field, a relatively larger rate than for x = 0.2. A similar trend has been observed in the field dependence of the anomaly of pure CeA1 3 [68] where was found to increase slightly and the anomaly was found to disappear at fields of order 5 T. In contrast to the data for x = 0.2 C /T values at 0.4 K for this sample with a lower Tm are significantly reduced from about 2400 mJ /K 2 Ce mol at H = 0 to almost 1000 mJ /K 2 Ce mol at 14 T. The small rise in C /T values below 0.6 K for the 10 and 14 T data may be described in terms of a Schottky contribution from the 27 Al nuclei. The observed reduction of C(0.4K)/T with field points to a possible decrease of, in magnetic field. All C/T curves seem to cross above 1.5 K, suggesting that the entropy associated with the maximum shifts toward higher temperatures. Finally, a shallow maximum appears around 1 K for H = 10 T, and at 1.3 K for H = 14 T. A possible explanation for this feature will be provided in Chapter 7. 6.5.2 Discussion The magnetic-field specific heat for x = 0.2 was analyzed in terms of the anisotropic Kondo model (AKM) for a single magnetic impurity. The data was compared to numerical results for the specific heat of the AKM. The model, previously introduced in Chapter 2, assumes an anisotropic exchange interaction JzS zSz + JJ_(Sxsx + Sysy) between the impurity spin S and the net conduction

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2 2 2 1 2 0 g E 1 9 I1.8 1 7 1 6 800 O 700 E Q) () Ni:!: 600 ..., ,s 500 i. ...... .... i0 ... ' .. 2 .... ... .. ............... -1 I 4 6 158 I 1 8 10 12 14 H(T) Figure 6.36: Temperature of the maximum in C/T, Tm vs H and vs H for Ce 0 8 La 0 2 Ah, where Tm is the temperature of the maximum in C /T. The dotted lines are guides to the eye.

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159 3500 H=OT 3000 0 H=6T H=10T .. H=14T 0 2500 E Q) CJ 0 0 O N 2000 00 0 0 0 0 """') 0 E 0 t: 1500 0 CJ I) 0
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160 electron spin s at the impurity site. The AKM has been proposed as a description for the thermodynamic properties of both Ce 0 8 La 0 2 Al 3 and CeAh. A strong de pendence on field orientation in the magnetic susceptibility of some CeAh single crystals [76) suggests anisotropic behavior corresponding to lz >> J 1> 0, with the magnetic z direction along the crystallographic c axis. Assuming that the cou plings Jz and J 1are dependent only on the values of a and c, the above scenario corresponds to c < a (c/a < 1; recall c/a = 0.705 for CeAh). The AKM is known to be equivalent to a number of other models in the limit of low energies. For more than a decade, a mapping [148) of the spin-boson model with Ohmic dissipation onto the AKM has been used [35, 36, 37) to deduce physical properties of dissipative two-level systems [34) from numerical calcula tions originally performed for the AKM. These studies have shown that under certain conditions, the impurity contribution to the zero-field heat capacity of the AKM exhibits a peak in both C and C /T, resembling the anomalies described in Figs. 6.34 and 6.35. The temperature of the peak in C /Tis given by Tm = a* R/,, where R is the gas constant and a* is a function of (}olz (see Chapter 2). The value a* = ,T ml R = 0.13 for Ce 0 8 La 0 2 Ah in zero field is in agreement with the estimate of Ref. [15). It was calculated from the observed peak position Tm = 2.1 K and the linearly extrapolated = 520 J /K 2 Ce mol. Both a* and Tm were used as inputs for a numerical renormalization-group calculation [149) of the specific heat of the AKM. Figure 6.38 shows the predicted behavior of C /T with applied magnetic field along the z axis, under the assumption that the impurity and the conduction electrons have g factors gi = 9e = 2 [149). The numerical data show three main trends with increasing field. First, the anomaly in C /T becomes broader and lower. Second, there is a marked shift of the maximum toward higher temperatures. Third, C /T decreases significantly at temperatures below the zero-field value of Tm. The effect in, is greater than that

PAGE 169

0 E Q) (.) -, E t::: (.) 1000 800 600 400 200 H a 0 T 0.130 ----5 T 1 0 T 15 T 20 T --25T 0.118 0.084 0.066 0.049 0.037 0 ............... ~......., ........ ---.__. ___ ....,.... ....... __ .......,,......,._ ........ ___ ....,.... _____ .......,,......,.__,.. ............... -4 0 2 4 6 8 T(K) 10 12 14 161 Figure 6.38: Numerical solutions of C /T vs T for the anisotropic Kondo mod e l in various magnetic fields H [149], with model parameters chosen so that a* = 0.130 for H = 0 ( see text for details).

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162 Table 6.6: Values of the specific heat coefficient , the peak temperature Tm and a* = ,Tm/ R (where R is the gas constant) for Ce 0 8 La 0 2 Ah in different magnetic fields H. H(T) (mJ/K 2 Cemol) Tm(K) a* 0 520 30 2.13 0.05 0.133 0.008 5 640 30 1.86 0.05 0.143 0.008 10 690 40 1.75 0.05 0.145 0.009 14 700 40 1.70 0.05 0.143 0.009 in the peak position, so that a* ( H) = 1 ( H)T m ( H) / R decreases monotonically with increasing magnetic field, as shown in the legend of Fig. 6.38. It is important to keep in mind that these numerical results are applicable only to single-crystal Ce 0 8 La 0 2 Ah, with a magnetic field along the c axis. The justification for comparing to the polycrystalline data assumes a basal-plane g factor 9i = 0 for the Ising-like crystal-field ground state of Ce 3 + in CeA1 3 [87]. The specific heat data for the polycrystal then constitutes a weighted average of single-crystal results over fields H 0 [149]. Both the shift of Tm to higher temperatures and the decrease in low temper ature C /T values are in stark contrast with experiment. The temperature Tm is weakly depressed in Ce 0 8 Lao. 2 Ah, while C /T increase slightly below 1 K. Moreover, these two trends keep a* relatively constant up to a field of 14 T (see Table 6.6), which goes against the prediction of the AKM. The specific heat data of Ce 0 3 Lao 7 Ah also do not seem to follow the pre dicted field dependence of C /T for the AKM. The suppression of the maximum in this sample towards lower temperatures from H = 0 to H = 6 Tis in disagreement with Fig. 6.38, and tends to rule out a description solely in terms of the AKM. On the other hand, there is a significant decrease in the electronic coefficient, a trend which is at least in qualitative agreement with the model. This behavior is quite different from that observed in Ce 0 8 La 0 2 Ab.

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1 63 The preceding comparisons qu est ion t h e re l ia bili ty o f th e A KM as a sole description of Ce 1 _xLaxAh alloys in m a gn et i c fi e ld s Th e l ac k of a d escr i tion exclusively in terms of this model m ay b e du e to th e n e gl ect o f m agnet i c correlations around the temperature of th e maximum as identifi e d in r ece nt SR studies [15] The presence of magnetic corr e l a tions c ould point tow a rd s lon g range order of small moments, as seen in URu 2 Si 2 [146] This latter compound h as a n ordered moment eff = 0.04 0.01 8 In addition the peak associated with i ts T N does not broaden in magnetic fields and the Neel temperature TN follows a pow e law field dependence ITN(0) TN(H)I ex Hv where v = 2. Another explana t ion might be that the magnetic correlations are shortranged, and therefore not ea s ily detected by neutron diffraction. Nevertheless the above results support a th e or et ical scenario based on smallmoment magnetism instead of on the AKM. The extremely low rate of reduction of the temperature position of t h e anomaly in the specific heat of Ce 0 8 La 0 2 Ah with field remains to be understood The temperature Tm follows a field dependence with an exponent v < 1 ( s ee Fig. 6.36), and the anomaly broadens significantly between 0 and 14 T indicating a different behavior than the one expected for long range order of small moments in heavy fermions according to studies on URu 2 Si 2 In addition both TM and Tm are depressed in an applied field at a much lower rate than is the Neel tem perature in antiferromagnetic, Ce-based heavy-fermion systems. For example in CeCu 5 2 Ag 0 8 TN is reduced from 0.7 K to OK in a field of about 2.5 T [150]. On the other hand, magnetic fields have a stronger effect on both the magnitude a nd the temperature of the anomaly in Ce 0 3 La 0 7 Ah than for x = 0.2. An estim a te of the exact rate of change of Tm with field in this sample proved to be r a th e r difficult, since its maximum broadens significantly between H = 0 and 6 T a nd i ts temperature position is very close to the low temperature limit of the d ata

PAGE 172

164 Finally values of C /T at the lowest measured temperatures (0.4 K) showed different behavior in Ce 0 8 La 0 2 Ah and Ce 0 3 La 0 7 Ah for the range of fields studied. These results suggest that the electronic coefficient I for x = 0.2 has a different field dependence than that for x = 0. 7. The magnetic field dependence of I in heavy fermion antiferromagnets has not been thoroughly studied in the past. Both an increase and a decrease in field have been reported in different compounds. Of particular interest are systems which show an initial increase in I followed by a decrease at high fields ( e.g. CePb 3 see Chapter 7). Non-Fermi-liquid behavior has been observed in some alloys at fields corresponding to a maximum in this coefficient. The variation of I with applied field depends on the relative strength of the energy scales TK and TRKKY with respect to the Zeeman energy H. Small values of I in antiferromagnetic heavy fermions are due to changes in the excitation spectrum with respect to the nonmagnetic Fermi liquid. The application of a magnetic field leads to both a suppression of antiferromagnetic order, which favors an increase in 1 and a Zeeman splitting of the Kondo resonance, which favors a reduction of 1 The relative magnitude of these two effects with respect to H determines the observed trend in I vs H. In particular, if TK << TRKKY, as in Ce 0 3 La 0 7 Ah, the smaller Kondo temperature leads to a large decrease in field, enough to overwhelm the expected increase due to suppression of magnetic order. On the other hand, if TK,...., TN, as in Ce 0 8 La 0 2 Ah, the increase in I due to the suppression of magnetic order is larger than the decrease from the suppression of the Kondo effect at low fields, so that an initial increase, followed by a decrease of the electronic coefficient at high fields ( of order 20 T), is expected.

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CHAPTER 7 MAGNETIC FIELD STUDY OF CePb 3 ALLOYS The goal of this chapter is to address the subjects discussed in Chapter 4 through the study of CePb 3 alloys in magnetic fields. An investigation of the mag netic state of CePb 3 would help describe the role of magnetic order in the formation of the heavy-fermion state through the evolution of the Fermi-liquid parameters A and,. Also, specific heat measurements of nonmagnetic Ce 0 6 La 0 .4Pb 3 would pro vide insight into the single-ion properties in magnetic fields. The chapter starts with results on the specific heat of CePb 3 in magnetic fields. The magnetic field dependence of the specific heat of Ce 0 6 La 0 .4Pb 3 will then be compared to the pre dictions of existing single-impurity models to further explore the feasibility of such a description on a concentrated system. 7 .1 Specific Heat of CePb 3 in Magnetic Fields The CePb 3 polycrystal used for specific heat measurements was synthezised by arc-melting following the procedure described in Chapter 5. No additional sec ondary phases were found by x-ray diffraction. Special care was taken to minimize exposure of the sample to air before x-ray diffraction measurements. Contact with oxygen in air causes Pb tends to segregate on the surface. This segregation has been detected from the formation of time-dependent diffraction peaks corresponding to the structure of Pb [151]. The calculated lattice parameter was a= 4.868.001 A in agreement with previously published values [92]. Magnetic susceptibility and specific heat data in zero field were also consistent with previous results 165

PAGE 174

166 The specific heat data below 2 K in magnetic fields from 0 to 14 T are shown as C /T vs T in Fig. 7.1. The specific heat of LaPb 3 mostly due to the lattice, was not subtracted from the CePb 3 data since its contribution is negligible over this temperature range. The antiferromagnetic peak is suppressed up to a field of 6 T, with TN reduced from 1.1 K to around 0. 7 K. There is no clear sign of the transition for fields above 7 T. The rate of suppression of TN decreases significantly between 5 and 6 T, so the absence of a maximum for 7 T implies that it is strongly attenuated at these fields, rather than shifted towards lower temperatures. The field-induced transition, which is strongest in the (110) direction, [98, 100, 103] could not be detected on this polycrystal measurement. A broad shoulder above 1 K was found on the 10 and 14 T data. It is apparently unrelated to the field induced transition and shifts to higher temperatures with applied field. A similar structure was detected at 16.1 T by Fortune et al. [94]. A possible origin of this feature will be discussed at the end of the chapter. An H T phase diagram can be constructed using the temperature of the maximum in C /T, as illustrated in Fig. 7.2. The corresponding temperature of the maximum in C vs T is slightly larger for H =I0, the difference between them increasing with field. Figure 7.2 also compares the phase diagram from spe cific heat measurements with that obtained from the magnetoresistance along the (110) direction on a single crystal [100]. The dashed line represents the first-order transition between an incommensurate antiferromagnetic (AF) phase and the field induced so-called 'spin-flop' (SF) phase. At higher fields, the field-induced phase gives way to a ferromagnetically-polarized paramagnetic (PM) phase at low tem peratures. The error bars on the data points represent the estimated uncertainty in the determination of the temperature of the maxima at different fields, increasing with the width of the peak. As the figure illustrates, measurements on a poly crystal differ from those taken along (110) since the former constitute an average

PAGE 175

3500 3000 :::::2500 0 E C\I 2000 E t:: (.) 1500 1000 . .. t::.t::. .6 6 la 6 6 ...... ,. ... ,.JY., 6 Lflre ,.. ... 6 .... ~. D D + ,,.. /5. liJD Do D +_. e H=OT H=4T t::.. H=5T ,.. H=6T H=7T o H=8T o H=10T H=14T D 'Y~ e Q:>oo O 00 o o o o oCb 01~"~ o ~ 0.4 0.6 0.8 1.0 1 2 1.4 1.6 1.8 2.0 T(K) 167 Figure 7.1: Specific heat plotted as C /T vs T for CePb 3 below 2 K in magnetic fields H = 0 4, 5, 6, 7, 8, 10, and 14 T.

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168 ov e r a ll crystallographic dir e ctions. Since th e field-induced transition is strongly d e t e cted only along (110) its transition temperature could not be found on these measurements. The field dependence of the electronic specific heat coefficient is shown in Fig 7.3 Values of, were determined from a linear fit to C /T vs T 2 data below the maximum for H 6T and from the values of C/T at 0.4K for H > 7T. Above this field C /T values do not vary appreciably below 0.8 K. The error bars were extracted from the propagation of both regression and experimental uncertainties. Data for 10 and 14 T both exhibit a small tail below 0.5 K. The temperature depen dence of this feature can be described by the nuclear Schottky contribution from Pb Cn/T ex y3 This contribution is still smaller than the uncertainty in the measurement at high fields ( rv 10%). The electronic coefficient initially increases with field reaching a maximum of 1770 mJ /K 2 mol at 6 T. The small decrease obtained for at 1 T is within the uncertainty of the results. The maximum in vs H coincides with the attenuation of the antiferromagnetic transition as seen in Fig. 7 1. The coefficient then decreases for higher fields, with a value around 600 mJ/K 2 mol at 14 T. The trend followed by the field dependence of is very similar to that of the square coefficient of the resistivity A in magnetic fields obtained from mag netoresistance measurements along (110) [100]. As seen in Fig. 7.4 A follows an initial increase with applied field, reaching a maximum at 5 T instead of 6 T as in vs H. This discrepancy might be due to differences between single-crystal and polycrystalline measurements. The obtained specific heat coefficients repre sent averages over all crystallographic directions. As the field is rotated 10 away from (110), the maximum in A becomes less pronounced and its field position slightly increases, consistent with an attenuation of the AF-SF transition. There is also a small maximum in A vs H observed at 10 T. A similar maximum could

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1 6 9 10 9 PM 8 7 SF 6 I5 foj ----I ----4 -foj ..... ..... ...... foj 3 2 AF ~ 0 4-----------------------------.,..Cl.l...._--1 0 0 0.2 0.4 0 6 0.8 1. 0 1. 2 T(K) Fi g ur e 7.2: Ph ase di agram ( H -T ) fo r Ce P b 3 T he data points are obtained from the temperature o f t h e maxim u m in C / T vs T. The solid and dashed lines follow the phase d i agram obta in ed fr om single crystal magnetoresistance measurements a l o n g t h e ( 1 1 0 ) directi o n [ 100]

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170 2000 1 800 I 1 600 I I I -1400 0 I I E C\J~ 1200 I I I J E I I I -;: 1 000 800 I I I 600 0 2 4 6 8 10 12 14 H(T) F igure 7.3: Magnetic fi eld dependence of the electronic spec i fic h eat coefficient of po l ycrystalline Ce P b 3

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171 not be deduced from the determination of I at different fields. The two maxima in the field dependence of the A coefficient coincide with the AF-SF (5 T) and SF-PM (10 T) phase transitions detected in the magnetoresistance curves below 150 mK. The preceding discussion assumes that the increase in A with field is due to the proximity to a spin-flop transition In fact, the sharpness of the maximum in A vs H along (110) is consistent with the appearance of a phase transition However a field-induced spin-flop phase has not yet been confirmed by neutron scattering experiments. The maximum in I vs H can also be related to the competition between relevant energy scales in heavy-fermion antiferromagnets (see Ch a pter 6, section 6.5.2). At small fields compared to TK the antiferromagnetic and Kondo entropies redistribute in such a way to enhance the values of 1 At high er fields, the antiferromagnetic state is suppressed and the electronic coefficient de c rease s due to Zeeman splitting of the Kondo resonance. The A coefficients obtained from magnetoresistance data along (110) were used to obtain the field dependence of the ratio A/ 1 2 A plot of A/ 1 2 vs His shown in Fig. 7.5. The dotted line corresponds to the average value for heavy-fermion systems obtained by Kadowaki and Woods [101], A/ 1 2 =1 x105 f2cmK 2 mo1 2 /J 2 This value has been postulated as a universal value for nonmagnetic heavy-fermion materials. The figure reveals that A/ 1 2 is nearly constant for fields H > 6 T and that these values are only slightly higher than the Kadowaki-Woods ratio. A similar result was obtained for CeCu 5 9 Au 0 1 [114] This alloy exhibits non Fermi-liquid behavior in zero field, but for H =/= 0 the ratio A/ 1 2 is c onstant and close to the postulated universal value. Figure 7.5 also shows a significant increase of A/ 1 2 in the antiferromagnetic state ( H < 6 T) with a value around 4.6 X 105 n cm K 2 mol 2 / J 2 at 1 T. The enhancement of A/ 1 2 in CePb 3 for H < 6 T is comparable to values reported for systems in which heavy electrons coexist with magnetic order (see

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172 60 10 from (110) 0 ____________ __a _____ ....__. 0 5 10 15 Magnetic Field (T) Figure 7.4: Magnetic field dependence of the sqare coefficient of the resistivity A, with the field along (110) and 10 away from (110) [100].

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5.0 N--. 4.0 N":2. 0 E 3.0 E 0 a LO 2.0 'o T"'"" N?< 1.0 0.0 ------.-......-----,,--......-----,,--------.,-----..----..-----..-----r--0 2 4 6 8 10 12 14 H(T} 173 Figure 7.5: Magnetic field dependence of A/, 2 Values of A were extracted from previous magnetoresistance studies [100].

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174 Table 7.1: Valu e s of Aj,y2 for several magnetically ordered 4f heavy-fermion com pounds (TN of ord e r 1 K). Compound CeA1 2 CeAuAh CePd 2 In YbPdBi 5 X 105 [153] 10 X 105 [154] 3 X 105 [155] 30 X 105 [156] Table 7.1). A model based on antiferromagnetic spin fluctuations [152] predicts a constant A/, 2 ratio except in the vicinity of a magnetic instability (TN = 0) where it diverges. Magnetic correlations clearly have a strong effect on this ratio It is important to point out that if the zero-field were to be calculated from the Kondo temperature T K = 3.3 K [96] (, = 1700 mJ /K 2 mol) as proposed by current models [108], the corresponding A/, 2 ratio for H = 0 would not be consistent with experiment (A/, 2 = 1.6 x 105 n cm K 2 mol 2 / J 2 ) but would be close to the postu lated value by Kadowaki and Woods. From this comparison it can be concluded that the electronic specific heat coefficient exhibits a larger field dependence in the antiferromagnetic phase ( H :::; 6 T) than the A coefficient of the resistivity. As a consequence, the proportionality relations between and T K and between A and 2 fail to apply in this region. Finally, no field-induced non-Fermi liquid properties were observed in the specific heat of polycrystalline CePb 3 N on-F~rmi-liquid effects triggered by the suppression of TN towards zero have been reported, for example, in CeCu 4 8 Ag1.2 at 3 T [157]. Theoretical models based on quantum phase transitions attribute non-Fermi liquid behavior to critical fluctuations corresponding to TN 0 [12]. Thermodynamic signatures of magnetic order in the specific heat disappear long before TN reaches zero under the influence of an external field so that the system may not reach the quantum critical point.

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17 5 7.2 Single-Ion Kondo Behavior of Ce 0 6 La 0 .4 Pb 3 in Magnetic Fields A previous study on Ce 1 x La x Pb 3 (96] d e monstr a t e d that th e th e rmod y n a mi c and transport properties of this system show single-impurity scaling in z e ro a ppli e d magnetic field with a Kondo temperature TK = 3 3 K. This is a uniqu e b e h a vior among concentrated Kondo systems. In the search for understanding th e Kondo effect in Ce-based heavy-fermion systems it would be useful to study the s p e cifi c heat of a nonmagnetic analog to CePb 3 Ce 0 6 La 0 .4Pb 3 in order to compare to the numerical solutions for the S = Kondo model in magnetic field, as well a s to describe the behavior of the electronic specific heat coefficient with applied field. Data for the field dependence of the electronic specific heat and the coefficient 1 for this alloy will be presented in this section. 7.2.1 Results The specific heat was measured between 0.4 and 10 K in magnetic fields up to 14 T. The electronic contribution was obtained using the following proce dure: A cubic (lattice) term was obtained by using the zero-field specific heat data of Ce 0 6 La 0 .4Pb 3 from Lin et al. [96], and subtracting their electronic contri bution from the total specific heat. The resulting coefficient is equal to 5.24 0.03 mJ /K 4 mol. This cubic function was then subtracted from the measured spe cific heat, and the difference was divided by the Ce concentration. The electronic specific heat C of Ce 0 6 La 0 .4Pb 3 at fields between 0 and 14 T is illustrated in Fig. 7.6. Numerical renormalization group (NRG) solution s for different ratios of gisH/ksTK (provided by K Ingersent, to be publish e d) ar e also shown for comparison. The parameter 9 i corresponds to the g-factor of the impurity, and was chosen to be equal to one. The error bars take into a cc ount the uncertainty in the measurement as well as a temperature-depend e nt t e rm du e to the subtraction of the large lattice contribution. Around 10 K th e e l ect roni c specific heat is "' 10% of the sample specifi c h ea t h e n ce th e l a r ge e rror at t hi s

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176 2400 2200 --g i BH I kBTK = 0 -----9 ; BH I kBT K = 1.7 2000 g i BH I kBTK = 2 7 -g l BH I kBTK = 3.4 1800 --g i BH I kBTK = 4.4 0 1600 E Q) 1400 (.) 1200 -, 1000 E -(.) 800 H=O
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1 77 temperatur e. The zero-field data are s om e wh at diff e r e n t fr om those of Lin et a l The maximum in 6-C is about 6% low e r than in th e pr ev i o u s s tud y. Al so, t h e zero fi e ld dat a ar e described by the S = Kondo sp ec ifi c h eat c ur ve w i t h T K = 2 3 K, instead of the previously obtained value of 3 3 K [96] The low-temperature specific heat is suppr e s se d in a m a gn e ti c fi e ld as seen in Fig. 7 6. The maximum becomes larger and narrow e r a nd it s po s ition s hif ts t ow ard higher temperatures. Assuming that the Kondo t e mp e rature TK = 2 3 K a nd t h e impurity g-factor 9i = 1, the numerical solutions for g i aH/kaTK = 1.7 2 7 3 .4, and 4.4 correspond to magnetic fields H = 5.8 9 3 11 7 and 15.1 T r e sp ec tiv e l y. These curves resemble the temperature dependence of the experimental d ata a t H = 5, 8 10 and 14T. The specific heat was also plotted as 6-C/T b e tween 0.4 and l0K (Fig 7 7) in order to extract a value of the electronic coeffici e nt 1 at each field. This qu a ntit y shows a significant discrepancy between the dat a and the available NRG s olutions at the lowest temperatures. The adjustment of parameters like g i aH and T K could lead to a better agreement between theory and experiment. The closest matches found between the NRG solution and the data were for H = 0 and at 14T using the curve for giaH/kaTK = 4.4. The experimental results show a significant decrease of low-temperature val ues of 6-C /T, pointing to an expected decrease of 1 with field. But the most striking result is the appearance of broad maxima for fields larger than 5 T These anomalies become more distinct with increasing magnetic field The temper a ture position of each maximum Tm shifts toward higher temperatures between 5 and 14 T Also within the same field range the decrease in 6-C /T values below T m a t each field is accompanied by an increase in such values a bove this t e mp e ratur e up to 10 K.

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2500 2000 0 E 8 1500 (\J -, _s 1000 I::: () .4Pb 3 for H = 0 5 8 10 and 14 T. The lines correspond to NRG solutions of the S = Kondo model for various ratios g i sH / k 8 T K (R. Pietri K. Ingersent and B. Andraka to be published). The estimated Kondo temperature is TK = 2 3 K

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179 In order to rule out the possibility that the maxima in ~ C /T might be due to extraneous phases the specific heat was also measured on a second Ce 0 6 La 0 4 Pb 3 sample from a different batch as well as on a Ce 0 55 La 0 .4 5 Pb 3 samp l e. Plots of ~C /T vs T at all of the above fields confirmed the presence of anomalies for both La x = 0.4 and x = 0.45. Both the magnitude and the temperature position of these maxima at each field did not vary appreciably between the three samples studied A more likely explanation is that the maxima are an intrinsic feature of the electronic specific heat. A comparison of the data with NRG solutions for ~C/T at various ratios giaH/kaTK led to the conclusion that the maxima seem to be a previously unidentified characteristic of the S = Kondo specific heat in magnetic fields. As revealed in Fig 7. 7, the data are in qualitative agreement with the numerical solutions, which show maxima at similar temperatures. The NRG solutions also show a similar decrease in low-temperature values of ~C /T 7.2.2 Discussion In a Kondo-impurity system, the zero-field ~C /T increases monotonically with decreasing temperature. However at significantly larger fields the appear ance of a maximum in this quantity is expected based on the following argument. It is well known that in the limit H >> k 8 T K where is the magnetic moment in the direction of H, the Kondo effect is suppressed and the single-ion specific heat takes the shape of the free-spin Schottky anomaly due to the Zeeman splitting of the lowest-lying crystal-field level. The Schottky specific heat for a two-level system has the following form [158]: C -R(j__) 2 go exp(5/T) Sch T 91 [1 + (go/ 91) exp( 5 /T) ]2 (7.1) where R is the gas constant, 5 is the energy separation between the two levels in degrees Kelvin (5 = 2H/k 0 ) and g 0 and g 1 are the degen erac i es of the lowest and

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180 Table 7.2: Valu e s of th e spe c ific heat coefficient = i:l.C(T 0.4 K)/T and the temperatures of th e maxima in i:l.C and i:l.C/T (TM and Tm respectively) for Ce 0 6 La 0 .4Pb 3 in different magnetic fields H; also shown are TM and Tm values for NRG solutions at different ratios gisH/ksTK (R Pietri, K. Ingersent and B Andraka to be published). H(T) ,(mJ/K 2 Cemol) TM(K) 0 5 8 10 14 2290 180 1740 120 1150 70 850 50 560 50 1.6 0.1 1.9 0.1 0.50 0.03 2 5 0.2 0.84 0.03 3.0 0 2 1.06 0 10 4.2 0.2 1.65 0.10 0 1.7 2.7 3.4 4 4 1.56 1.98 2.55 2.99 3 68 0.30 0.05 0 80 0 03 1.18 0 03 1.76 0.04 highest levels respectively. For the r 7 doublet in Ce 3 +, g 0 / g 1 = l. The Schottky specific heat Cs c h has a peak at a temperature TM proportional to the splitting 8. The quantity Cs c h/T also has a peak at a temperature Tm
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1 8 1 2600 2400 2200 2000 1800 0 E 1600 Q) () 1400 C\J 1200 -:, .S 1000 ?800 600 400 200 0 2 4 6 8 10 12 14 H(T} Figur e 7 8: El ectro ni c s p ec i fic h eat c o e ffi cie n t, vs H for Ce 0 6 L 3.o.4Pb 3 Error bars acc oun t fo r ex p e rim e n ta l u ncertai n t i es. Th e fi t to t h e data corresponds to Eq. 7.4 ( s ho wn a bo ve).

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182 r(H) 2 = r(o) 2 + 2 H 2 (7 2) wh e r e f(O) ex TK ex 1/,(0) a nd th e magnetic moment of the impurity = z = g i 8 s with s = 1/2. Therefore ,(H) = ,(0) J1 + (H/ksTK) 2 (7.3) with 1 (0) being the electronic coefficient in zero field. This description is based on the field dependence of the electronic specific heat of the resonant level model by Schotte and Schotte [160). Even though this model agrees with the exact solutions of the S = Kondo model in zero field (Bethe Ansatz NRG) [161], there are significant discrepancies between the magnetic field solutions of the resonant level model and the S = Kondo model. The extrapolated values of, from NRG solutions follow a somewhat different magnetic field dependence ( courtesy of K. Ingersent to be published): ( H) = ,(O) 1 + (H/ksTK) 2 (7.4) A fit to the data is shown in Fig 7.8. The ordered moment for the crystal-field r 7 doublet ground state of CePb 3 is equal to 0.71 8 [106). This moment corresponds to a g-factor gi = 1 ; [162). Remarkably the field dependence of the maximum in the specific heat and its temperature position seem to be described fairly well by the NRG solutions with ratios gi 8 H/ksTK using an impurity g-factor gi = l. The NRG curves in Figs. 7.6 and 7.7 correspond to a moment= gi 8 s = 0.5 8 somewhat smaller than the expected value of 0. 71 8 The generation of numerical solutions using gi = 1 ; and values of H closer to the experimental values may lead to better agreement between the model and the specific heat data. Another estimate for can be extracted from a fit of Eq. 7.4 to the data on Fig. 7.8. Using a value of TK = 2.3 K and the electronic coefficient ,(0) = 2460 mJ /K 2 Ce mol extrapolated from the zero-field NRG solution the best fit

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1 83 giv e s = 0.46 0.02 8 a smaller but c omp arab l e va lu e to t h at obtained from the NRG solutions The discrepancy b e tw ee n th e ex p ecte d m oment and t h e va l ue obt a in e d from the fit might be due to two fa c tor s Fir s t th e un certa in ty i n t h e measurement of = ~C(0.4 K)/T. Second th e small e r v a lu e of indi cates a weaker field dependence of, especi a lly at high fi e lds which m ay b e du e to th e neglect of the contribution to the specific heat from the low es t Z ee m a ns plit l e v e l of the excited r 8 crystal-field state. The present study confirmed that the specific heat of C e 0 6 L a 0 .4 Pb 3 follows the field dependence predicted by the S = Kondo model [26 30] with its maxi mum shifting toward higher temperatures and its magnitude approaching that of a free-spin Schottky anomaly at high fields. This is the first direct evidence of Kondo behavior in the specific heat of a concentrated system in magnetic fields. Similar studies have been conducted in dilute systems, like Ce x La 1 x Ah [163] (S = and Ce x La 1 _xB 6 [162] (S = ~). The agreement of the present data with the theory is comparable to that of previous studies This study also revealed that the weak maxima observed in ~C /T for H 2 5 T may be due to single impurity effects rather than to some exotic cooperative phe nomena. The maxima can also be observed in the low-temperature C /T data of CePb 3 at 10 and 14 T (see Fig. 7.1), and in previous measurements at 16 and 20 T [94]. These features are also evident in C /T data of Ce 0 3 La 0 7 Ah at 10 and 14 T (Fig. 6.37 Chapter 6). The appearance of a maximum in ~C /Tat large fields suggests a careful reevaluation of field-induced transitions reported in other heavy fermion systems, in particular the so-called B-phase of CeCu 2 Si 2 [164 165 166]. This compound exhibits a line of transitions above 7 T between the param a netic region and the unidentified B-phase [165]. The transitions are c h a r acte ized by weak maxima in C /T [164 166] that shift toward high e r t e mp e r at ur es with increasing magnetic field.

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CHAPTER 8 CONCLUSION This chapter summarizes the results of thermodynamic measurements on CeAh-based and CePb 3 -based alloys as a function of doping concentration, tem perature, and magnetic field, and discusses possible interpretations of the data. New ideas for experiments on each compound are then addressed in order to stim ulate further the ongoing interest in both CeAh and CePb 3 8.1 Summary The determination of the lattice parameters a, c, V, and c/a from x-ray diffraction studies of Ce 1 _xMxAh alloys (M=La, Y) helped establish the nature of the chemical pressure effect induced by Y doping (x :S 0.5) and La doping (0 :S x < 1), in agreement with previous studies [71, 89]. Substitution of La on the Ce sites expands, while Y contracts the hexagonal lattice. For both Y and La substitutions, the c parameter is less affected than a, especially with La, so that most of the volume change occurs in the a-b plane. A temperature-concentration phase diagram, depicting TK and Tm, was con structed for Ce 1 _xLaxAh. Specific heat and magnetic susceptibility measurements as a function of La doping are consistent with a Kondo necklace picture [42, 43], assuming that the maxima in the specific heat and in C /T are associated with a magnetic phase transition. The temperature location of the transition, whose precursor exists in the pure compound, has a nonmonotonic concentration depen dence. A maximum in the concentration dependence of the temperature Tm is observed at x 0.3. This maximum is not only suppressed by changes in the cou184

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1 85 pling J but also by a r e duction in th e ov e r a ll c on ce ntration of m ag n et i c impur i ti es ( dilution effect). The Kondo t e mp e ratur e e xtra c t e d from t h e m agnet i c entropy above Tm decreases with La con c entration. Th e s e ch a ng es a r e co n s i s t e n t w i t h a continuous decrease of the coupling J between the 4f moment and th e co ndu ct i on electrons A decrease in J is in turn rel a ted to an expansion of the unitce ll vo lu me and therefore of the average distance between Ce and Al atoms The specific heat and lattice parameters of Ce 1 x Y x A1 3 were comp a r e d t o those of CeAh as a function of pressure. Substitution of Y led to more ani s otropi c changes in a and c while hydrostatic pressure caused a stronger reduction in both c and the size of the anomaly in C /T. These results imply that th e c h a r ac t e istic energy of magnetic interactions TRKKY is more sensitive to the hybridiza t ion between hexagonal planes than that in the a-b plane. A similar int e rpr e t a tion was also suggested by alloying and pressure studies on hexagonal Kondo l a tti ces CePd 2 Ah and CeCu 5 In addition the lack of a reduction of Tm with Y doping up to x = 0 2 is consistent with a previous study [61] attributing th e dev e lop ment of the anomaly at this temperature to an angular dependence of the !-lig a nd hybridization related to the absolute-value change in c/ a The lattice parameters of the alloy Ce 0 8 (Lao 6 Y o.4) 0 2 Ah are identical to those of CeAh within uncertainty. This similarity allowed for a study of thermodynami c properties on a CeAh-like system with a net reduction in the overall number of C e moments (increase in R c ec e) yet assuming an average hybridization equiv a l e n t t o that of the undoped compound Specific heat measurements on the abov e allo y did not show an anomaly in C /T down to 0.4 K. Alloying on the Ce site s u s ing bo t h Y and La dopants was found to drive the transition temperature to b e low 0 .4 K by increasing the distance between Ce atoms, therefore reducing T RKKY Thi s r es ul t i s an indication that the concentration of impurities and their int e r s i te i nteractions are also important for the development of this maximum

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186 Both C /T (between at least 0 38 and 1.7 K) and x vs T for Ce 0 8 (La 0 6 Y 0 4 ) 0 2 Ah follow a power law at low temperatures with an exponent that can be related to a model based on a Griffiths phase [58 59). This model provides a common physical description for the non-Fermi-liquid effects seen in many heavy-fermion systems like UCu4Pd [144] and Th 1 _x UxPd 2 Ah [145). In this respect, the alloying proce dure described above represents a novel method of tuning antiferromagnetic Kondo lattices through their quantum critical point. Measurements of x vs T and C /T vs T in Ce 0 8 (La 0 6 Y 0.4) 0 2 Ah and similar alloys at lower temperatures are needed in order to verify the above temperature dependence over more than one decade. Results for the specific heat of La-doped alloys in magnetic fields revealed considerable discrepancies between trends of the data and the predictions of the anisotropic Kondo model [36, 37). The temperature Tm of the anomaly in the alloy Ce 0 8 La 0 2 Ah decreased slowly and the electronic coefficient I increased slightly with applied field, while the model predicts a large decrease in I and a shift of Tm toward higher temperatures [37, 149). The increase in I with field in this alloy is consistent with the suppression of magnetic order. Thus, a single-impurity anisotropic Kondo description cannot be applied to Ce 1 _xLaxAh alloys. The specific heat measurements on polycrystalline CePb 3 in magnetic fields up to 14 T were motivated by the unusual behavior of the field dependence of the A coefficient in the resistivity found for a single crystal [100]. The electronic coefficient I has a maximum around 6 T, and its field dependence is similar to that of A. The ratio A/ 1 2 postulated as a universal value for heavy-fermion sytems, is approximately constant in the paramagnetic state ( H > 6 T), while it is enhanced and field-dependent in the magnetic regime ( H < 6 T). This is the first comprehensive study of this ratio on a heavy-fermion system as a function of a wide range of magnetic fields. The behavior of A/ 1 2 in the paramagnetic and magnetic

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1 8 7 regions seem to be in agreement with previou s d a t a on m ag n et i c Ce -b ase d h eavy fermions Specific heat data of the heavy-fermion alloy C e 0 6 L a 0 .4 Pb 3 in m a gn e ti c fi e ld s up to 14 T showed that the electronic specific heat can be d e s c rib e d in t e rms of the S = Kondo model in magnetic fields [30], with a Kondo temperature TK = 2 3 K This result complements previous zero-field studies [96] which support a s ingle ion description for Ce 1 _xLaxPb 3 alloys. In fact the current specific heat study in magnetic fields provides further evidence that the mechanism responsible for heavy-fermion behavior is particularly of a single-impurity Kondo nature. This study also led to the discovery of previously unknown magnetic-field induced anomalies in C /T below 2 K for Ce 0 6 La 0 4 Pb 3 A direct comparison of ~C /T results with NRG solutions indicate that the anomalies appear to be an intrinsic feature of the theoretical solutions for the S = Kondo model. Moreover a comparison of the data to C/T data for CePb 3 and Ce 0 3 La 0 7 Ah (Figs. 7.1 and 6.37 respectively) at H = 10 T and 14 T revealed that the anomalies are also present in other Ce heavy-fermion compounds. 8.1.1 Ideas for Future Work Without a doubt, there is still a great deal of experimental work to be done on CeAh and its related alloys. Although the nature of the anomaly in CeAh could be attributed to magnetic correlations, the physical circumstances that lead to its formation are still elusive. In order to investigate further the magnetic character of the anomaly in CeAh, an extensive SR study of Ce 1 _xLaxAh alloys would be desirable. Muon spin relaxation measurements probe the local magnetic structure and are able to detect local magnetic fields at different interstitial sites which would better help determine the effective moment of Ce atoms in thes e a llo y s Future measurements in the millikelvin range would aid in the d e t e rmina t ion of Ce local moments at low temperatures

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188 It is of utmost importance to develop proper techniques to synthesize high quality single crystals of CeAb that are large enough for measurements to be performed with reasonable accuracy. The orientational dependence of thermo dynamic and transport properties is currently a topic of interest in the study of Ce-based Kondo lattices (e.g., CeCu 5 [141] and CePd 2 Ab [139]). In addition, uni axial pressure studies on single crystals of CeAb are essential to understand its magnetic behavior. At the present time, the synthesis of single crystals of CeAb is an arduous task, but a necessary one for a compound that appears to have a strong anisotropy in its physical properties. Single crystals are also essential to understand the directional dependence of physical properties in CePb 3 A field-induced spin flop transition along (110) has been inferred in CePb 3 from features in the magnetoresistance, magnetic sus ceptibility, and the elastic constants, but its nature has not yet been determined. Neutron diffraction measurements on single crystals in magnetic field could help determine the magnetic structure and the effective moment of this field-induced phase. Specific heat measurements along (10 0) and (110) at millikelvin tempera tures and magnetic fields up to 15 T would be useful in understanding the orienta tional and temperature dependences of this phase. These experiments would also help search for signatures of field-induced non-Fermi-liquid behavior, suggested by magnetoresistance measurements along (110). Finally, an analysis of the field dependence of the magnetization in Ce 0 6 Lao. 4 Pb 3 may be used to verify the agree ment of the data with the predictions of the S = Kondo model.

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REFERENCES [1] A J S c hofield Contemporary Physics 40 : 95 1999. [2] D. K. K. Lee and A J. Schofield. Phil Trans. R. Soc Land A 358 : 111 2000. [3] G. R. Stewart Rev. Mod. Phys. 73, 2001. [4] Z. Fisk H. R Ott, T. M. Rice and J. L. Smith Nature 320:124 19 8 6 [5] G. R. Stewart. Rev Mod. Phys., 56:755 1984. [6] N. Grewe and F. Steglich. Heavy fermions. In Handbook on th e Phys ic s and Chemistry of Rare Earths volume 14 page 343 Amsterdam 1991. Els e vier Science. Edited by K. A. Gschneidner Jr. and L. Eyring. [7] H. R. Ott. Progress in Low Temperatur e Physics volum e 11 p a g e 215. Elsevier Amsterdam 1987. [8] P A. Lee T. M. Rice J. W. Serene L J. Sham and J. W. Wilkin s. Com ments Condens. Matter Phys., 12:99, 1986. [9] C. Kittel. Introduction to Solid State Physics. John Wiley & Sons In c., New York, 1986. [10] N. W. Ashcroft and N. D. Mermin. Solid State Physics. W. B. Saunders Co., Philadelphia 1976. [11] B. Andraka R. Pietri, S. G. Thomas G. R Stewart E.-W Scheidt and T. Schreiner. Eur. Phys. J. B, 12:55 1999. See also references therein. [12] J Phys.: Condens. Matter, 8, 1996. Proceedings of the Conference of Non Fermi-liquid Behavior in Metals, Santa Barbara, CA June 17-21 1996 [13] P. Gegenwart, F. Kromer, M. Lang, G. Sparn C. Geibel and F. St e gli c h Phys. Rev. Lett., 82:1293 1999. [14] J. S. Kim J. Alwood S. A. Getty F. Sharifi and G. R. Stew a rt Phys R ev. B 62:6986 2000. [15] E. A. Goremychkin R. Osborn B. D. Rainford a nd A. P Mur a ni Ph ys. Rev. Lett ., 84:2211 2000. [16] L. D. Landau. Sov. Phys -JETP 3 : 920 1957 189

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190 [17] A. Ron. Theory of fermi liquids. In The Helium Liquids: Proceedings of the 15th Scottish Universities Summer School in Physics, 1974, page 211. [18] L. D. Landau and E. M. Lifshitz. Statistical Physics, volume 2. Pergamon Press, Oxford, New York 1980. [19] G. Baym and C. Pethick. Landau Fermi-Liquid Theory: Concepts and Applications. John Wiley & Sons, Inc., New York, 1991. [20] K. Andres, J. E. Graebner, and H. R. Ott. Phys. Rev. Lett, 35:1779, 1975. [21] Kei Yosida. Theory of Magnetism. Springer-Verlag, Berlin, Heidelberg, Ger many, 1996. [22) P. W. Anderson. Phys. Rev., 124:41, 1961. [23] J. A. Mydosh. Spin Glasses: An Experimental Introduction. Taylor & Francis, Bristol, PA, 1993. [24] J. R. Schrieffer and P. A. Wolff. Phys. Rev., 149:491, 1966. [25] Jun Kondo. Prag. Theor. Phys., 32:37, 1964. [26] N. Andrei K. Furuya, and J. H. Lowenstein. Rev. Mod. Phys., 55:331, 1983. [27] N. Andrei. Phys. Rev. Lett., 45:379, 1980. [28) P. B. Wiegmann. JETP Lett., 31:364, 1980. [29] P. Schlottmann. Phys. Rep., 181:1, 1989. [30] P. D. Sacramento and P. Schlottmann. Phys. Rev. B, 40:431, 1989. [31] P. W. Anderson and G. Yuval. Phys. Rev. Lett., 23:89, 1969. [32] A. M. Tsvelick and P. B. Wiegmann. Adv. Phys., 32:453, 1983. [33] H. Shiba. Prag. Theor. Phys., 43:601, 1970. [34) A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger. Rev. Mod. Phys., 59:1, 1987. [35) T. A. Costi and C. Kieffer. Phys. Rev. Lett., 76:1683, 1996. [36] T. A. Costi. Phys. Rev. Lett., 80:1038, 1998. [37] T. A. Costi and G. Zarand. Phys. Rev. B, 59:12398, 1999. [38] F. Guinea, V. Hakim, and A. Muramatsu. Phys. Rev. B, 32:4410, 1985. [39] N. B. Brandt and V. V. Moshchalkov. Adv. Phys., 33:373, 1984.

PAGE 199

191 [40] F. G. Aliev N. B. Brandt V V. Moshchalkov, and S. M. Chudinov J. Low Temp. Phys., 57:61 1984. [41] N. B. Brandt and V. V Moschalkov Sov. Phys. Uspekhi 29:725, 1986 [42] S. Doniach. Valence Fluctuations and Related Narrow Band Phenomena page 169. Plenum Press, New York New York 1977. [43] S. Doniach. Physica B 91:231 1977. [44] J. R. Iglesias, C. Lacroix, and B. Coqblin. Phys. Rev. B 56:11820, 1997 [45] S. Siillow, M. C. Aronson B. D. Rainford and P. Haen. Phys Rev Lett. 82:2963, 1999. [46) D. L. Cox. Phys. Rev. Lett., 59:1240 1987. [47) P. Schlottmann and P. D. Sacramento Adv. Phys. 42:641 1993. [48) F. G. Aliev, S. Vieira, R. Villar and V. V. Moshchalkov J. Phys. : Condens Matter, 8:9807, 1996. [49) 0. 0. Bernal, D. E. MacLaughlin H. G. Lukefahr, and B. Andraka Phys Rev. Lett., 75:2023, 1995. [50] V. Dobrosavljevic, T. R. Kirkpatrick and G. Kotliar. Phys. Rev. Lett. 69:1113, 1992. [51) E. Miranda, V. Dobrosavljevic, and G. Kotliar. J. Phys.: Condens. Matter 8:9871, 1996. [52) J. A. Hertz. Phys. Rev. B, 14:1165, 1976. [53) A. J. Millis. Phys. Rev. B, 48:7183, 1993. [54) A. M. Tsvelik and M. Reizer. Phys. Rev. B, 48:9887, 1993. [55) T. Moriya and T. Takimoto. J. Phys. Soc. Jpn ., 64:960 1995. [56) S. L. Sondhi, S. M Girvin, J. P. Carini and D. Shahar. Rev. Mod. Phys. 69:315, 1997. [57) F. Steglich, B. Buschinger P. Gegenwart, M. Lohmann R. Helfrich C Lang hammer, P. Hellmann, L. Donnevert S. Thomas A. Link C. Geibel M. Lang, G. Sparn, and W. Assmus. J. Phys.: Condens. Matter, 8:9909 1996. [58) A. H. Castro Neto, G. Castilla and B. A. Jones. Phys. R ev. Lett. 81:3531 1998.

PAGE 200

192 [59] M. C de Andrade R Chau, R. P. Dickey, N. R. Dilley, E. J. Freeman, D. A. Gajewski, M. B. Maple, R. Movshovich, A. H. Castro Neto, G. Castilla, and B. A. Jones. Phys. Rev. Lett., 81:5620, 1998. [60] R. B. Griffiths. Phys. Rev. Lett., 23:17, 1969. [61] S. Corsepius, M. Lenkewitz, and G. R. Stewart. J. Alloys Comp., 259:29, 1997. [62] J. H. N. Van Vucht and K. H.J. Buschow. J. Less-Comm. Met., 10:98, 1965. [63] K. H. Mader and W. M. Swift. J. Phys. Chem. Solids, 29:1759, 1968. [64) J. L. C. Daams, P. Villars, and J. H. N. Van Vucht. Atlas of Crystal Structure Types for Intermetallic Phases. ASM International, Materials Park, OH, 1991. [65] J. V. Mahoney, V. U.S. Rao, W. E. Wallace, R. S. Craig, and N. G. Nereson. Phys. Rev. B, 9:154, 1974. [66] M. H. van Maaren, K. H. J. Buschow, and H. J. van Daal. Solid State Commun., 9:1981, 1971. [67] G. E. Brodale, R. A. Fisher, N. E. Phillips, and J. Flouquet. Phys. Rev. Lett., 56:390, 1986. [68) C. D. Bredl, S. Horn, F. Steglich, B. Luthi, and R. M. Martin. Phys. Rev. Lett., 52:1982, 1984. [69] S. Barth, H. R. Ott, F. N. Gygax, B. Hitti, E. Lippelt, A. Schenck, C. Baines, B. van den Brandt, T. Konter, and S. Mango. Phys. Rev. Lett., 59:2991, 1987. [70) J. L. Gavilano, J. Hunziker, and H. R. Ott. Phys. Rev. B, 52:R 13106, 1995. [71) B. Andraka, C. S. Jee, and G. R. Stewart. Phys. Rev. B, 52:9462, 1995. [72) B. Andraka, G. Fraunberger, J. S. Kim, C. Quitmann, and G. R. Stewart. Phys. Rev. B, 39:6420, 1989. (73) G. E. Brodale, R. A. Fisher, N. E. Phillips, J. Flouquet, and C. Marcenat. J. Magn. Magn. Mater., 54-57:419, 1986. (74) G. Lapertot, R. Calemczuk, C. Marcenat, J. Y. Henry, J. X. Boucherle, J. Flouquet, J. Hammann, R. Cibin, J. Cors, D. Jaccard, and J. Sierro. Physica B, 186-188:454, 1993. [75) 0. Avenel, J. S. Xia, B. Andraka, C. S. Jee, M-F. Xu, Y. J. Qian, T. Lang, P. L. Moyland, W. Ni, P. J. C. Signore, E. D. Adams, G. G. Ihas, M. W. Meisel, G. R. Stewart, N. S. Sullivan, and Y. Takano. Phys. Rev. B, 45:5695, 1992.

PAGE 201

193 [76] D. Jaccard R. Cibin, A. Bezinge J Sierro K Matho a nd J Flouqu et. J. Magn. Magn. Mater. 7677 : 255, 1988. [77] G. Oomi and T. Kagayama. J. Phys. Soc. Jpn ., 65 : 2732 1996 [78] H. R Ott, 0. Marti, and F. Hulliger. Solid State Commun. 49:1129 1984. [79] U. Rauchschwalbe, F. Steglich, A. de Visser, and J. J. M. Franse. J. Magn. Magn. Mater 63-64:347, 1987. [80] G. Remenyi, A. Briggs, J. Flouquet, 0. Laborde, and F Lapierre. J. Magn Magn. Mater., 31-34:407, 1983. [81] D. Jaccard, R. Cibin, and J. Sierro. Helv. Phys. Acta 61:530 1988. [82] H. Nakamura, Y. Kitaoka, K. Asayama, and J. Flouquet. J. Phys. Soc. Jpn. 57:2644, 1988. [83] W. H. Wong and W. G. Clark. J. Magn. Magn. Mater. 108:175, 1992. (84] S. Barth, H. R. Ott, F. N. Gygax, B. Hitti, E. Lippelt A. Schenck, and C. Baines. Phys. Rev. B, 39: 11695, 1989. [85] A. Schenck and F. N. Gygax. Handbook of Magnetic Materials, volume 9 page 151. Elsevier, North Holland, Amsterdam, 1995. [86] B. R. Coles, S. Oseroff, and Z. Fisk. J. Phys. F, 17:1169, 1987. [87] E. A. Goremychkin, R. Osborn, and I. L. Sashin. J. Appl. Phys., 85:6046, 1999. [88] P. M. Levy and S. Zhang. Phys. Rev. Lett., 62:78, 1989. (89] R. Pietri and B. Andraka. Physica B, 230-232:535, 1997. [90] R. Osborn, E. A. Goremychkin, B. D. Rainford, I. L. Sashin, and A. P. Murani. J. Appl. Phys., 87:5131, 2000. . (91] K. A. Gschneidner, Jr., and F. W. Calderwood. Binary Alloy Phase Diagrams, volume 1, p. 134, Second Edition. ASM International, Materials Park OH, 1990. [92] F. Canepa, G. A. Costa, and G. L. Olcese. Solid State Commun., 45:725, 1983. [93] C. L. Lin, J. Teter, J. E. Crow, T. Mihalisin J. Brooks A. I. Abou-Aly and G. R. Stewart. Phys. Rev. Lett, 54:2541, 1985. (94] N. A. Fortune, G. M. Schmiedeshoff, J. S. Brooks, C. L. Lin J. E. Crow T. W. Mihalisin, and G. R. Stewart. Jpn. J. Appl. Phys (Suppl.) 26-3 : 541 1987.

PAGE 202

194 [95] T. Kirsch, A. Eichler, P. Morin, and U. Welp. Z. Phys. B, 86:83, 1992. [96] C. L. Lin, A. Wallash J E. Crow, T. Mihalisin, and P. Schlottmann. Phys. Rev. Lett., 58:1232 1987. [97] H. von Lohneysen. J. Phys.: Condens. Matter, 8:9689, 1996. [98] D. Nikl, I. Kouroudis, W. Assmus, B. Luthi, G. Bruls, and U. Welp. Phys. Rev. B, 35:6864, 1987. [99] H. Suzuki, H. Kitazawa, T. Naka, J. Tang, and G. Kido. Solid State Commun., 107:447, 1998. [100] J. McDonough and S. R. Julian. Phys. Rev. B, 53:14411, 1996. [101] K. Kadowaki and S. B. Woods. Solid State Commun., 58:507, 1986. [102] D. Di.irkop, E. Braun, B. Politt, H. Schmidt, B. Roden, and D. Wohlleben. Z. Phys. B, 63:55, 1986. [103] T. Ebihara, K. Koizumi, S. Uji, C. Terakura, T. Terashima, H. Suzuki, H. Kitazawa, and G. Kido. Phys. Rev. B, 61:2513, 2000. [104] S. Lipinski. J. Magn. Magn. Mater., 192:553, 1999. [105] B. Renker, E. Gering, F. Gompf, H. Schmidt, and H. Rietschel. J. Magn. Magn. Mater., 63-64:31, 1987. [106] C. Vettier, P. Morin, and J. Flouquet. Phys. Rev. Lett., 56:1980, 1986. [107] A. Schenck, D. Andreica, P. Pinkpank, F. N. Gygax, H. R. Ott, A. Amato, R. H. Heffner, D. E. MacLaughlin, and G. J. Nieuwenhuys. Physica B, 259261:14, 1999. [108] V. T. Rajan. Phys. Rev. Lett., 51:308, 1983. [109] J. C. Areas Soberino, J. J. Rieger, E.-W. Scheidt, and G. R. Stewart. Phys. Rev. B, 51:11469, 1995. [110] S. Rahman, J. Timlin, J. E. Crow, T. Mihalisin, and P. Schlottmann. J. Appl. Phys., 67:5209, 1990. [111] S. Rahman, T. Mihalisin, J. E. Crow, and P. Schlottmann. Solid State Commun., 75:279, 1990. [112] J. Teter, R. Freitag, A. Maury, J. E. Crow, and T. Mihalisin. J. Appl. Phys., 53:7910, 1982. [113] C. L. Lin, J. E. Crow, P. Schlottmann, and T. Mihalisin. J. Appl. Phys., 61:4376, 1987.

PAGE 203

19 5 [114] H. von Lohneysen T. Pietrus G. Portisch, H. G Schlager A. Schroder, M. Sieck and T. Ttappmann. Phys Rev. L ett., 72:3262, 1994. [115] James F. Shackelford. Introduct ion to Materials Science for Eng ineers. MacMillan Publishing Co., New York, NY, p. 180, 1985 [116] G. E. Brodale, R. A. Fisher C. M. Lisse N. E. Phillips and A. S. Edelstein. J. Magn. Magn. Mater ., 54-57:416, 1986. See also references therein. [117) B. D. Cullity. Elements of X-Ray Diffraction, Second Ed ition. Addison Wesley, Reading MA 1978. [118] R. Bachmann Jr. F. J. DiSalvo T. H. Geballe, R. L. Greene R. E. Howard C. N. King H. C. Kirsch K. N. Lee, R. E. Schwall, H.-U. Thomas and R B Zubeck. Rev. Sci. Instrum. 43:205, 1972. [119) R. E. Schwall R. E. Howard and G. R. Stewart. Rev Sci. Instrum. 46:1054, 1975. [120) G. R. Stewart. Rev. Sci. Instrum., 54:1 1983. [121) J. S. Kim. PhD thesis University of Florida, 1992. [122] M. J Naughton S. Dickinson, R. C. Samaratunga J. S. Brooks and K. P Martin. Rev. Sci Instrum., 54:1529 1983. [123] T. Kagayama and G. Oomi. Physica B, 186-188:624, 1993. [124) T. Kagayama and G. Oomi. J. Magn. Magn. Mater ., 140-144:1227 1995. [125) D. M. Bailey. Acta Cryst., 23:729, 1967. [126] R. L. Snyder. PhD thesis, Iowa State University, 1960. [127) J. Callaway. Quantum Theory of the Solid State. Academic Press Inc. San Diego CA, 1991. 2nd Editon, p. 448. [128] A. S. Edelstein R. L. Holtz D. J. Gillespie R. A. Fisher, and N. E. Phillips. J. Magn. Magn. Mater., 63-64:335 1987. [129) C. S. Jee, B. Andraka, J. S. Kim, H. Li, M. W. Meisel and G R. Stewart. Phys. Rev. B 42:8630, 1990. [130) C. S. Jee, B. Andraka, J. S. Kim and G. R. Stewart Phys. R ev. B 43:2656 1991. [131] A. J. Millis. Phys ica B 259-261 : 1169 1999. [132] J. S. Kim, B. Andraka C S. Jee S. B. Roy, and G. R. Stewart Phys Rev B 41:11073, 1990

PAGE 204

196 [133] C M. Varm a. Phy s. R ev L e tt ., 55:2723 1985. [134] C M Varma. Comm en ts Sol i d Stat e Phys. 11:221, 1985. [135] F. Steglich P. Gegenwart R Helfrich C. Langhammer, P. Hellmann L. Donnevert C Geibel M. Lang G. Sparn W. Assmus G. R Stewart and A. Ochiai Z. Phys B 103:235 1997. [136] F. Steglich C Geibel R. Helfrich F Kromer M. Lang, G. Sparn P. Gegen wart L. Donnevert C. Langhammer A. Link J. S. Kim and G R. Stewart. J. Phys. Chem Solids 59:2190 1998. [137) F Steglich P. Gegenwart, C Geibel, P. Hinze M. Lang C. Langhammer G. Sparn and 0. Trovarelli. Physica B 280 : 349, 2000 [138] A. Schroder G. Aeppli R. Coldea M. Adams 0. Stockert H. von Lohneysen E Bucher, R Ramazashvill and P. Coleman. Nature 407:351, 2000. [139] S A. M. Mentink G. J. Nieuwenhuys A A. Menovsky, J. A. Mydosh H. Tou and Y. Kitaoka. Phys. Rev. B 49:15759 1994. [140] A. N. Medina D. P. Rojas F. G. Gandra W.R. Azanha and L. P. Cardoso. Phys. Rev. B 59:8738 1999. [141] M. Lorenzen M. Hanfland E. Bauer F.-W. Schaper and A. Eichler. Physica B 259-261:20 1999 [142] E. Bauer G. Amoretti L. C Andreani B Delley M. Ellerby, K. McEwen, R. Monnier, E. Pavarini and P. Santini. J. Phys.: Condens. Matter, 10:4465, 1998. [143] G. R. Stewart A L. Giorgi J. 0. Willis, and J. O'Rourke. Phys. Rev. B 34:4629, 1986. (144] B Andraka and G. R. Stewart. Phys. Rev B, 47:3208, 1993. [145] M. B Maple, M. C. de Andrade, J. Herrmann, Y. Dalichaouch, D. A. Gajew ski, C. L. Seaman, R. Chau R Movshovich M. C. Aronson and R. Osborn. J. Low Temp. Phys., 99:223, 1995. [146] C. Broholm, J. K. Kjems, W. J. L Buyers P. Matthews, T. T. M. Palstra, A. A. Menovsky and J A. Mydosh. Phys. Rev. Lett ., 58:1467, 1987. (147] B. Andraka and Y. Takano. Rev. Sci. Inst., 67:4256, 1996. (148] S. Chakravarty Phys Rev Lett. 49:681 1982. [149] R. Pietri, K Ingersent and B. Andraka. Phys. Rev. Lett., 86:1090 2001.

PAGE 205

1 9 7 [150] K. Heus e r J. S Kim E-W. S c h e id t, T Sc h re in er, an d G. R Stewart. Physica B 259-261 : 392 1999. [151] G Oomi K Izuki J. Suzaki a nd N Mori. J Ma g n. Magn. Mater., 7677:647 1988 [152] T Takimoto and T. Moriya Sol i d Stat e Comm u n ., 99 :4 57 1996 [153] F Lapierre P. Haen A. Briggs a nd M. S e r a. J. Magn M a g n. Mater., 63-64:76 1987. [154] S. Paschen, E. Felder and H. R. Ott. Eur. Phys J. B 2:169 199 8. [155] J. L. Gavilano P. Vonlanthen B Ambro s ini J Hunzik e r F. Hulli ger, an d H. R Ott. Europhys. Lett. 32:361 1995. [156] D. Kaczorowski A Leithe-Jasper P Rogl H Flandorfer T C ic hor e k R. Pietri and B. Andraka. Phys. Rev. B 60:422 1999. [157] K. Heuser E.-W. Scheidt T. Schreiner and G R. Stewart Phy s R ev. B 57:R4198 1998. [158] E. S. R. Gopal. Sp e c i fic Heats at Low T e mp e ratur e s. Pl e num Pr ess, ew York 1966. [159] B. Andraka J S Kim G R. Stewart and Z. Fisk. Phys Re v. B 4 4:4 371 1991. See also references therein. [160] K D. Schotte and U. Schotte Phys. Lett. 55A:38 1975. [161] H.-U. Desgranges and K. D Schotte. Phys L e tt. 91A:240 1982 [162] P. Schlottmann. Jour. Magn. Magn. Mat e r ., 63-64:205 1987 [163] V T. Rajan J. H Lowenstein, and N. Andrei. Phys Rev Lett. 49:497 1982 [164] B. Andraka, G R. Stewart and F. Steglich. Phys. Rev B 48:3939 1993 [165] G. Bruls, B. Wolf, D. Finsterbusch P Thalmeier I. Kouroudis W Sun W. Assmus B. Luthi M. Lang K. Gloos F. Steglich and R Modl e r Phy s Rev. Lett. 72:1754, 1994 [166] T. C. Kobayashi A. Koda H. Honda K. Am a y a, Y Kitaoka K. A saya m a, C Geibel and F Steglich. Phys i ca B 206-207:600 1995.

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BIOGRAPHICAL SKETCH Richard Pietri Santiago was born August 7 1971 in Hato Rey Puerto Rico to Gilberto Pietri and Palmira Santiago. Raised in Rio Piedras Puerto Rico he attend e d Colegio Calasanz, where he graduated from high school in May 1989. Motivated by a strong interest in the physical sciences he then decided to cross the Atlantic Ocean in search of new challenges. He attended Massachusetts Institute of Technology where he graduated with a Bachelor of Science degree in Physics in May 1993. While at MIT he worked as an undergraduate assistant at the Center for Space Research CCD Laboratory wh e re his r e s e ar c h interests developed toward condensed matter physics. There is a saying that an MIT education is like attempting to drink water from a firehose. Therefore after spending 4 years in front of a firehose, he attended graduate school at the University of Florida where he pursued a Ph. D. degree in experimental condensed matter physics. His area of study was on uranium, cerium, and ytterbium-based heavy-fermion systems While at UF he worked in Prof. Greg Stewart s lab under the supervision of Dr. Bohdan Andraka He also worked as a Physics I and II laboratory instructor, presented results at conferences and condensed matter seminars (Johns Hopkins U., William & Mary), and co-authored many publications in journals such as Physical Review B and Physical Review Letters. 198

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I certify that I have read this study and that in my opinion it onform to acceptable standards of scholarly presentation and is fully adequate in cop and quality, as a dissertation for the degree of Doctor of Philosoph y. Bohdan Andraka Chairman Associate Scientist, Ph y ic I certify that I have read this study and that in my opinion it conform to acceptable standards of scholarly presentation and is fully adequate in cop and quality as a dissertation for the degree of Doctohof Philo :;'.)' A,f<_,~ Gregory R. Stewart Professor of Physics I certify that I have read this study and that in my opinion it conform to acceptable standards of scholarly presentation and is fully adequate in scope and quality, as a dissertation for the degree of Doctor of Philosophy I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality as a dissertation for the degree of D ~ or of Philo ophy. ~tf l-t~ Pradeep Kumar Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality as a dissertation for the degree of Doctor Philosophy ca~ l Cammy R. Aq ~ rnathy Professor of Materials Science an Engineering This dissertation was submitted to the Graduate Faculty of the Department of Physics in the College of Liberal Arts and Sciences and to the Graduate School and was accepted as partial fulfillment of the requirments for the degree of Doctor of Philosophy. August 2001 Dean Graduate School

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