magnetism, superconductivity and their interplay a …

MAGNETISM, SUPERCONDUCTIVITYAND THEIR INTERPLAY

A STUDY OF THREE NOVEL. INTERMETALLIC COMPOUNDS:

La(Fe,Al)l3 UNiSn * URu2Si2

Thorn Palstra

STELLINGEN

1. De kritieke stroomdichtheid van gesputterd polykristallijn NbN

kan worden vergroot in de buurt van het bovenste kritieke veld

B o door het sputteren uit te voeren met tegenspanning op het

substraat.

2. In quasi-kristallijn U-Pd-Si, waarin vijfvoudige roostersymmetrie

is gevonden, kan de puntsymmetrie beter worden begrepen door

metingen van de kristalveldeigenschappen.

S.J. Poon, A.J. Dféhman en K.R. Lawless, Phys. Rev. Lett. 55

(1985) 2324.

3. In de analyse van het Mössbauerspectrum van het organo-metallisch

cluster Au55(F(C5H5)3)i2Cl6 door G. Schmid et al. is ten onrechte

de quadrupoolsplitsing van de ongebonden oppervlakte goudatomen

verwaarloosd.

G. Schmid, R. Pfeil, R. Boese, F. Bandevmann, S. Meyev, G.H.M.

Calls en J.W.A. van der Velden, Chem. Ber. 114 (1981) 2634.

4. Het verdient aanbeveling de optische zuiger, gebaseerd op het

principe van laser-geïnduceerde drift, te onderzoeken in een

quasi-stationalre toestand. Dit kan worden bereikt in een open

capillair omgeven door het te onderzoeken gasmengsel.

H.G.C. Wevij, J.P. Woevdman, J.J.M. Beenakkev en J. Kusoer>, Phys.

Rev. Lett. 52 (1984) 2237.

5. Ten onrechte wordt de soortelijke warmte van quasi-ëéndimensio-

nale magnetische verbindingen tegenwoordig geïnterpreteerd in

termen van soliton-gas modellen.

F. Bovsa, M.G. Pini, A. Rettori en V. Tognetti, J. Uagn. Magn.

Matef. 31-34 (1983) 1287.

6. Het beschrijven van een supergeleidende ring, onderbroken door

een puntcontact, met een circuit waarin de Josephson-junctie

parallel staat aan de intrinsieke capaciteit van de junctie in

plaats van de capaciteit van de gehele ring, doet geen afbreuk

aan het macroscopische karakter van het optredende tunnelproces.

A.J. Leggett, in "Essays in Theoretical Physiae".

7. De minimum temperatuur die Bradley et al. bereikt hebben bij het

afkoelen van ^He-Tfe mengsels, wordt beperkt door het warmtelek

door de vloeistof in het capillair tussen de meetcel en de

omringende thermische afschermingscel.

D.I. Bradley, A.M. Guénault, V. Keith, C.J. Kennedy, I.E. Miller,

S.G. Museett, G.R. Piakett en W.P. Pratt Jr>., J. Low Temp. Phys.

57 (1984) 359.

8. De waarneming van de ruimtesonde Giotto, dat de kern van de

komeet van Halley donker is, komt eerder voort uit het feit dat

deze kern is opgebouwd uit een losse structuur van zeer kleine

deeltjes dan dat het oppervlak sterk licht absorbeert.

9. Bij besturingsproblemen in organisaties wordt vaak ten onrechte

meer aandacht besteed aan een (geautomatiseerd) informatiesysteem

dan aan de besluitvormingsstructuur.

10. Gezien de toenemende vervolmaking van de moderne zeilvlieger is

een volgende voor de hand liggende stap het vervangen van de

piloot door een druppelvormige massa.

T.T.M. Palstra

Leiden, 21 mei 1986


A STUDY OF THREE NOVELINTERMETALLIC COMPOUNDS:

La(Fe,Al)13 UNiSn URu2Si2


A STUDY OF THREE NOVELINTERMETALLIC COMPOUNDS:

La(Fe,Al)13 UNiSn URu2Si2

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTORIN DE WISKUNDE EN NATUURWETENSCHAPPEN

AAN DE RIJKSUNIVERSITEIT TE LEIDEN,OP GEZAG VAN DE RECTOR MAGNIFICUS

DR. J.J.M. BEENAKKER,HOOGLERAAR IN DE FACULTEIT DER

WISKUNDE EN NATUURWETENSCHAPPEN,VOLGENS BESLUIT VAN HET COLLEGE VAN DEKANEN

TE VERDEDIGEN OP WOENSDAG 21 MEI 1986TE KLOKKE 16.15 UUR

door

THOMAS THEODORUS MARIE PALSTRAgeboren te Kerkrade in 1958

NKB OFFSET BV — BLEISW1JK

Samenstelling Promotiecommissie

Promotor

Co-promotoren

Referenten

Overige leden

: Prof.Dr. J.A. Mydosh

: Dr. K.H.J. Buschow

Dr. G.J. Nieuwenhuys

: Prof.Dr. E.P. Wohlfarth

Dr. J.J.M. Franse

: Prof.Dr. R. de Bruyn Ouboter

Prof.Dr. G. Frossati

Prof.Dr. W.J. Huiskamp

Prof.Dr. P. Mazur

This investigation is part of the research program of the

Stichting voor Fundamenteel Onderzoek der Materie (Foundation for

Fundamental Research on Matter) and was made possible by

financial support from the Nederlandse Organisatie voor Zuiver

Wetenschappelijk Onderzoek (Netherlands Organisation for the

Advancement of Pure Research).

Exegi monumentulum

CONTENTS

Chapter 1 GENERAL INTRODUCTION 9

Chapter 2 EXPERIMENTAL PROCEDURES 15

2.1 Electrical resistivity 15

2.1.1 Cryogenics 15

2.1.2 Automation 16

2.2 Magnetisation 16

2.3 ac susceptibility 17

2.4 Specific heat 17

2.5 3He cryostat 17

2.6 Theraal expansion 19

2.7 Other techniques 19

Chapter 3 STRUCTURAL AND MAGNETIC PROPERTIES OF THE

CUBIC La(Fe,Al)13 AND I,a(Fe,Si)13

INTERMETALLIC COMPOUNDS 21

3.1 Introduction 21

3.2 Crystal structure 23

3.3 Composition and stability 25

3.4 Experimental results 27

3.4.1 Zero-field measurements 27

3.4.2 Field measurements 31

3.5 Discussion 36

3.5.1 Magnetic properties 36

3.5.2 Metamagnetism 39

3.5.3 Electrical resistivity 40

3.5.4 Spontaneous and forced magnetostriction 44

3.6 Neutron scattering and Mössbauer spectroscopy 46

3.6.1 Experimental procedures 46

3.6.2 Experimental results 47

3.6.3 Discussion 49

3.7 The critical behaviour of La(Fe,Si)13 53

3.7.1 Introduction 53




3.8 Summary 59

Chapter 4 MAGNETIC PROPERTIES AND ELECTRICAL RESISTIVITY OF

SEVERAL EQUIATOMIC TERNARY U-COMPOUNDS 63

4.1 Introduction 63

4.2 Experimental procedures and results 64

4.2.1 Crystal structure 64



4.2.4 Magnetoresistivity 73

4.2.5 Hall resistivity 74

4.2.6 Specific heat 77

4.3 Discussion 77


4.3.2 Resistivity 79

4.4 Conclusions 82

Chapter 5 MAGNETIC AND SUPERCONDUCTING PROPERTIES OF

SEVERAL RT2Si2 INTERMETALLIC COMPOUNDS 85

5.1 Introduction 85

5.2 Structure and crystal growth 85

5.3 Superconductivity of the RT2Si2~ternary

compounds (R=Y,La,Lu) 87



5.3.3 Discussion 91

5.4 Magnetic properties of the RT2Si2~ternary

compounds (R=Ce,U) 95


5.4.2 Crystal structure 95


5.4.4 Discussion 103

5.5 The heavy-fermion compound URu2Si2 112

5.5.1 Introduction to heavy-fermion behaviour 112

5.5.2 Magnetism and superconductivity of the

heavy-fermion system URu2Si2 115

5.5.3 Anisotropical electrical resistivity of URu2Si2 121

Summary 132

Samenvatting 133

Nawoord 135

Curriculum vitae 136

General Introduction

The interplay between magnetism and superconductivity is an intriguing

topic, which has been studied for more than 30 years. The first experimental

efforts were to dilute a superconductor with magnetic impurities [1]. This

resulted in an understanding of the (Cooper)pair-breaking mechanism for para-

magnetic impurities. A second stage was reached with the discovery of the

rhodium-boride and Chevrel-phase systems. Here, a coexistence of superconduc-

tivity and a magnetically long-range ordered state was established [2].

However, the superconductivity and the magnetism are carried by different

types of electrons, spatially separated by the special crystal structure, with

the net result to reduce the pair-breaking effect.

A completely new research area was commenced by the discovery of the

heavy-fermion system CeCu2Si2 [3]« Now, another kind of balance between

magnetism and superconductivity is found. At high temperature local-moment

behaviour is observed. Nevertheless, with decreasing temperature the moments

disappear and a strongly interacting electron system remains at about IK.

Surprisingly, this strongly interacting electron system becomes super-

conducting below IK. Indeed, the balance between magnetism and superconduc-

tivity is very delicate, as even a coexistence of superconductivity and a

long-range ordered antiferromagnetic state was found for one of the systems,

URu2Si2> in this class of heavy-fermion compounds[4]. The most puzzling aspect

of the coexistence is that the magnetism and the superconductivity are carried

by the same 5f-electrons, hybridized with the conduction electrons.

The theory of this interplay developed along similar lines. First, the

pair-breaking effect of paramagnetic impurities was formulated in the

Abrikosov-Gor'kov theory [5], which has been extended in many aspects, e.g.

the Kondo effect. Soon it was realised that ferromagnetism and superconduc-

tivity are mutually exclusive [6], although several claims of coexistence have

recently been made [7,8]. However, there is no rigorous theoretical argument

that excludes the coexistence of spin-density waves or antiferromagnetism and

superconductivity. Still, it was not until the discovery of these properties

in URu2Si2, that a confirmation was given experimentally. A simple theoretical

picture supposes that part of the Fermi surface carries the magnetism and

another part the superconductivity [9].

Presently it is generally believed that the ordinary electron-phonon inter-

action is insufficient to create Cooper-pairing in the strongly interacting

electron system of these heavy-fermion compounds* Consequently, the

electron-phonon interaction must be dramatically enhanced, or another

attractive interaction must be present [10]. It was recently suggested that

the large electron-electron interactions, present in the normal state, also

provide the attractive mechanism, required for superconductivity. Furthermore,

there are indications that the order parameter vanishes over part of the

Fermi-surface[11]. As this is impossible for singlet spin pairing, it was

argued that triplet (or better "odd-parity") spin pairing could be present.

Unfortunately, thus far no decisive experiment has been performed or suggested

to unambiguously distinguish the possible pairing mechanisms.

Another type of magnetism, discussed in this thesis, is the magnetism of

iron-based compounds and the related Invar problem [12]. The name Invar

originates from a vanishing of the thermal expansion coefficient around room

temperature. Such an effect was originally observed for Fe-Ni alloys, but now

Invar is used for a more general class of compounds and alloys. The Invar

property has important technical applications, but it also gives basic

information about the origin of magnetic moments and fheir interactions in

Fe-based compounds and alloys. More generally, the study of Invar phenomena

seeks to deduce a fundamental understanding of the ferromagnetism of 3d-metals

and alloys, with respect to their static and dynamic properties.

In order to explain the magnetism of the face-centered cubic (fee) Fe-Ni

alloys, it was necessary to assume an antiferromagnetic Fe-Fe exchange

coupling. Unfortunately, the fully antiferromagnetic state could not be

achieved, because the fee crystal structure of Ni is not preserved, when

alloying more than 65% Fe. This results in a highly inhomogeneous magnetic

structure for the fee alloys with less than 65 % Fe. The cause of this

structure originates from ferromagnetic Ni-Ni and Fe-Ni, and antiferromagnetic

Fe-Fe exchange interactions [13]. The dynamical properties of these systems

are still the subject of much controversy.

It is highly desirable to study the iron magnetism in the face-centered

cubic crystal structure in order to obtain more insight into the origin of

these interactions. First, this has been done by band structure calculations.

Additionally, high-pressure studies were undertaken to stabilize the fee

10

structure. Also, fee iron particles were grown in an fee nonmagnetic matrix

like gold or copper, to obtain an fee iron system.

We have approached this problem not by preserving the fee crystal

structure, but by investigating an intermetallic compound with another

structure, where the Fe-Fe coordination number of the fee structure, viz. 12,

is approached. This was accomplished through a study of the LaFe^-like

compounds, where indeed an antiferromagnetic state is found. Here, there are

two different Fe-sites, one of which has an fee-like coordination of 12 atoms,

and the other of 10 atoms. Interestingly, the application of relatively small

magnetic fields results in a metamagnetic phase transition to the ferro-

magnetic state. This metamagnetic phase transition can also be achieved by

applying pressure. Thus, we are offered a unique opportunity to study various

properties in both magnetic states, and to observe how physical quantities

are related to each magnetic state of the system.

In chapter 3 the intermetallic compounds La(Fe,Al)^-j and La(Fe,Si)^3 are

discussed. First, the crystal structure and the metallurgical limitations are

treated. Then, the magnetic properties of La(Fe,Al)^3 are described including

the magnetic phase diagram, the metamagnetic properties, the electrical resis-

tivity and the magnetostriction. The symmetry of the antiferromagnetic state

is resolved by neutron diffraction experiments, from which a model for the

magnetic structure is proposed. Finally, the LaCFe.Si)^ compounds are

discussed. This system is similar to La(Fe,Al)13, but additionally exhibits

interesting critical behaviour.

Chapter 4 deals with several ternary equiatomic (1-1-1) uranium compounds.

These compounds exhibit a broad variety in their magnetic properties, ranging

from local-moment magnetism to Kondo-lattice behaviour. The concept

"Kondo-lattice" is applied to a strongly interacting electron or heavy-fermion

system. The magnetic properties were studied with magnetisation measurements.

Surprisingly, electrical transport measurements indicate for the Kondo-lattice

systems a semiconducting-like behaviour, with an energy-gap of about O.leV.

This suggests that the large electron-electron interactions, which are

observed for the heavy-fermion systems, are still present, in spite of the

reduced number of conduction electrons.

In chapter 5 the properties of various (1-2-2) compounds are discussed.

This investigation started with a study of the unoccupied-4f system LaRVi2Si2«

which was previously reported to have a coexistence of superconductivity and

itinerant ferromagnetlsm[7]. From a detailed investigation of the metallurgy,

which is described in the sections 5.2 and 5.3, we conclude that the reported

11

superconductivity is an artifact of second phases, and that the magnetic order

is absent. Nevertheless, for single-phase samples type-I superconductivity was

observed two decades lower in temperature for LaRh2Si2» a s well as. for the

compounds RPd2Si2, with R=Y,La and Lu. The observation of type-I superconduc-

tivity in a ternary compound is very rare and discussed in detail in section

5.3.

Subsequently, the question was addressed whether the properties of the

heavy-fermion superconductor CeCu2Si2 are unique. This led to a systematic

investigation of the magnetic properties of the CeT2Si2 compounds, with T a

3d-, 4d-, or 5d-metal. After the discovery of superconductivity in the

uranium-based heavy-fermion compounds UBe^j and UPt3, the UT2Si2 compounds

were included in this investigation. From the observed trends in the magnetic

properties of the CeT2Si2 and UT2Si2, we were able to locate where the

heavy-fermion behaviour in these compounds should occur and this is described

in section 5.4. Such systematics resulted in the discovery of a new

heavy-fermion compound URu2Si2» This compound exhibits both an antiferro-

magnetic phase transition at 17.5K and a superconducting one at about IK. Both

of these states are carried by the same hybridized 5f-electrons of uranium.

Recent neutron scattering experiments have shown that the magnetism and super-

conductivity coexist, thus making this compound completely unique.

A description of the experimental properties of heavy-fermion systems, and

their relation to the theory, is given in section 5.5.1. Then, we present in

section 5.5.2 our experimental evidence for antiferromagnetism and supercon-

ductivity of URu2Si2» In section 5.5.3 the electrical transport properties are

studied and a qualitative picture of the magnetic heavy-fermion superconductor

URu2Si2 is offered.

In conclusion, the magnetism of iron-based compounds, which is carried by a

broad 3d-band, agrees nicely with the existing theories, as discussed in

chapter 3. On the other hand, the magnetism of the rare earths, created by a

very narrow 4f-band, is also well understood. However, the magnetism of

uranium, caused by the 5f-band, whose bandwidth is intermediate between the

3d- and 4f-bandwidths, is not well comprehended. This offers exciting possibi-

lities for encountering completely new phenomena, like the coexistence of a

strongly interacting electron system and an extremely high resistivity, as

discussed in chapter 4, and the coexistence of magnetism and superconduc-

tivity, discussed in chapter 5.

12

References

1. B.T. Matthias, H. Suhl and E. Corenzwit, Phys.Rev.Lett. 1 (1958) 449.

2. Superconductivity in Ternary Compounds (I,II), edited by 0. Fisher and

M.B. Maple (Springer, Berlin, 1982).

3. F. Steglich, J. Aarts, C D . Bredl, W- Lieke, D. Meschede, W. Franz and H.

Scha'fer, Phys.Rev.Lett. 43 (1979) 1892.

4. T.T.M. Palstra, A.A. Menovsky, J. van den Berg, A.J. Dirkmaat, P.H. Kes,

G.J. Nieuwenhuys and J.A. Mydosh, Phys.Rev.Lett. 55 (1985) 2727.

5. A-A. Abrikosov and L.P Gor'kov, Soviet Phys. JETP 12 (1961) 1243.

6. V.L.Ginzburg, Soviet Phys. JETP 4 (1957) 153.

7. I. Felner and I. Novik, Sol. State Comm. 47 (1983) 831.

8. Itinerant ferromagnetism and superconductivity were suspected to coexist

in Y4C03. See, for example, A.K. Grover, B.R. Coles, B.V.B. Sarkissian and

H.E.N. Stone, J. Less Comm. Met. 86 (1982) 29 and references therein, and

A. van der Liet, P.H. Frings, A. Menovsky, J.J.M. Franse, J.A. Mydosh and

G.J. Nieuwenhuys, J. Phys. F 12 (1982) LI53.

9. K. Machida, J. Phys. Soc. Jpn. 53 (1984) 712.

10. P.A. Lee, T.M. Rice, J.W. Serene, L.J. Sham and J.W. Wilkins, Comm. Sol.

State Phys. (to be published).

11. D.J. Bishop, CM- Varma, B. Batlogg, E. Boucher, Z. Fisk and J.L. Smith,

Phys.Rev.Lett. 53 (1984) 1009.

12. See, for an overview, The Invar Problem, edited by A.J. Freeman and M.

Shimizu (North-Holland, Amsterdam,1979).

13. A.Z. Menshikov, J. Magn. Magn. Mater. 10 (1979) 205.

13

Experimental Procedures

2.1 Electrical resistivity

The electrical resistivity was measured via a standard four point probe

technique. A dc current of about 5mA was used and could be adjusted in order

to avoid self-heating of the samples at low temperature. The current was

commuted by a relay to correct for the thermal voltages- The thermal voltages

were minimized by using non-interrupted copper leads from the samples to a

plug at room temperature. The leads were attached to the samples with silver

paint DAG 1415. The noise was reduced by twisting together the two current and

two voltage leads over their entire length and placing both pairs in different

stainless steel capillaries. The voltages were measured with a Keithley 181

nanovoltmeter. It was possible to measure up to nine samples simultaneously

with a relay system. The number of leads was reduced to 2n+2, with n the

number of samples, by using voltage leads of neighbouring samples as currents

leads for the sample to be measured. This reduces to total heat input in the

system. Most samples had a resistance of order of 0.01Q and could be

measured with a relative accuracy of 10"^. The absolute value of the

resistivity is accurate within 2xl0~2 due to the brittleness of the samples

and the uncertainties in the determination of the sample dimensions. Errors

due to macro-cracks were eliminated by measuring at room temperature the

voltage drop at various distances between the voltage leads, using one movable

voltage lead mounted on a micrometer. Effects of possible microcracks remain,

however, uncorrected. A magnetic field up to 7T could be applied with a

superconducting solenoid.

2.1.1. Cryogenics

The samples were mounted in an OFHC-copper box and were electrically insu-

lated by thin cigarette paper[1,2]. All leads were thermally anchored on this

box. A permanent heat leak to the helium bath was made by a platinum wire. The

temperature was measured better than 0.22 by calibrated carbon-glass and Pt

resistors using a It-VS-3 resistance bridge. The temperature was varied

15

stepwise from 1.4K to 300K with a specially designed PID temperature

controller. In order to achieve the best temperature control parameters, the

following method was chosen. The shortest relaxation time T is obtained with

the smallest heat capacity K of the system and the largest heat leak Q to the

thermal bath: T=K/Q. However Q must be minimized in order to reduce helium

consumption and thus a compromise for Q must be found. The heat capacity K is

minimized by using the least possible amount of material and by using a

material (Cu) which has a small specific heat at low temperature- The time lag

and homogeneity of temperature over the Cu-box were optimized by winding the

heater directly around the copper box. The thermometers were placed in holes,

drilled in the copper box to ensure good thermal contact.

The resistivity of several selected samples was measured up to 1000K in an

electric furnace. The samples were mounted in a stainless steel tube, adjoined

to a platinum thermometer, and continuously evacuated by an oil diffusion

pump. Here, the temperature was increased continuously at a rate less than 3K

per minute.

2.1.2 Automation

The experimental set-up was automized, using an Eagle personal computer

(IBM-PC compatible). This computer controls the complete experiment and stores

the data on floppy disk, after which the data can be futher elaborated on a

larger PDP-45 computer. All input/output was processed via standard IEEE

procedures. The existing binary data were converted to IEEE by a Biodata

microlink-III. The computer controls the relay system, which selects the four

wires of one sample and commutes the current, and controls a 12 bits DAC. This

DAC provides a reference voltage, which controls either the Hewlett-Packard

6260B current supply of the superconducting 7T magnet or the PID temperature

controller. The Input data consist of the measured voltages of the Keithley

181 and of the resistance values of the thermometers of the It resistance

bridge. Thus, one temperature cycle from 4K to 300K at a fixed magnetic field

or one field cycle up to 7T at fixed temperature can be fully automized.

Interrupt procedures ensured manual change of parameters during the

measurements.

2.2 Magnetisation

The magnetisation was measured using a Foner vibrating-sample magnetometer

operating at a frequency of 21Hz. The vibrating mechanism was controlled by a

specially designed Mössbauer drive, giving a sinusoidal output signal. The

16

magnetisation was measured with a PAR 126 detecting the pick-up voltage of two

coils of 10000 turns, separated about 10mm. A PAR 220 detects the amplitude of

the vibration in order to correct for possible changes in amplitude. The

height of the sample is adjustable via a simple screw mechanism which elevates

the complete drive unit, in order to place the sample exactly between the

pick-up coils. This equipment has a top loading mechanism, so that a sample

can be exchanged at helium temperature with a dip-stick. The thermometer is a

calibrated carbon-glass resistor placed directly next to the sample and also

built into the dip-stick. Tht temperature is measured with a SHE-PCB con-

duction bridge. The temperature is controlled with a PID temperature

controller and a heater wound around the sample room. A helium atmosphere of

about 1 Torr provides the thermal contact between the heater, sample and

thermometer. This sample room is placed in an exchange room, which can be

evacuated in order to thermally insulate the system. Thus, a temperature of

300K can easily be reached. The helium dewar system consists of two parts. In

the inner dewar the pressure can be reduced to achieve a temperature down to

1.6K. The outer helium dpwsr contains a 5T superconducting solenoid mounted

along the vertical direction which is also the direction of the vibration.

2.3 ac susceptibility

The ac susceptibility was measured with a standard mutual inductance tech-

nique using a driving field less than O.lmT. In the low temperature regime

(T<50K) a set-up was used, completely constructed of glass, which is exten-

sively discussed in Ref.3. The measurements up to room temperature were

performed in a similar apparatus constructed of German silver, which is

discussed in Ref.l.

2.4 Specific heat

The specific heat was measured with an adiabatic heat pulse technique. The

sample was mounted with apiezon N grease on a thin sapphire substrate. A NiCr

heater was evaporated on this substrate and a non-encapsulated Ge resistor was

used as thermometer. A copper clamp mechanism[4] enabled a starting

temperature of the measurement down to about 2K.

2.5 3He cryostat

A ^He cryostat, designed by J.P.M. van der Veeken [5], was used to perform

experiments below IK and down to 0.33K. Three experimental techniques were

built into this cryostat: ac susceptibility, magnetisation and resistivity[6].

17

The first cooling stage is a IK pot, cooling a thermally insulated flange down

to 1.1K. 3He gas is led via heat-exchangers at 4.2K to this flange, where it

condenses into a small reservoir. Then, the liquid % e flows via a thin

capillary into a 3He pot, which is continuously pumped by an oil diffusion

pump. The diffusion pump is evacuated by a rotary pump and then the He gas is

again fed into the condensor line. Thus, a temperature of about 0.4K could be

achieved continuously. Using a single shot mode, i.e. stopping the

condensation of He, a temperature of 0.33K was achieved which could be

sustained for several hours.

2.5.1. ac susceptibility

ac susceptibility was measured in the 3He cryostat via a standard mutual

inductance technique operating at a frequency of 10.9, 87 and 121Hz and a

driving field of 50|iT. The coil system consisted of four superconducting

primary coils, each having two secondary pick-up coils of copper wire. The

primary coils were cooled below their superconducting transition temperature

with coil foil, i.e. a sheet of adjacent thin insulated copper wires glued

together with GE-varnish. This procedure is required because the experiments

are performed in vacuum and furthermore it is necessary to avoid eddy current

effects due to larger metal parts. The samples were thermally attached to the

thermometer and heater using a bunch of copper wires (<)>=70|j.m) put together in

an epoxy cylinder (<t>=5mm). Then, the wires were fixed in the cylinder with

an epoxy glue and finally cut perpendicular to the cylinder axis. The

resulting surface provides a good thermally attached plate to mount the

samples, using small amounts of apiezon N grease. Finally, the cylinder

together with the bunch of copper wires and sample can be mounted inside one

of the pick-up coils. The other end of the copper wires is attached to a

copper bar (ct>=5mm) on which a heater was wound and in which a thermometer was

mounted. This bar was connected via a heat leak to the 3He pot. The

temperature was measured with a calibrated Ge resistor and controlled within

imK with a PID temperature controller. A magnetic field up to 3T could be

applied by means of a superconducting magnet.

2.5.2. Magnetisation

Different techniques were used in the 3He cryostat to measure the

magnetisation. The easiest way is to measure the dc susceptibility xd by

recording the induced voltage V i n d of the pick-up coils while ramping the

magnetic field. The magnetisation can be obtained by numerical or analog

18

integration. However, this method has several disadvantages: (1) The

sensitivity is low. (2) The experiment is dynamic and the field must be ramped

continuously. (3) Integration is difficult because of a zero offset especially

in the case of extreme type II superconductors.

In order to avoid these difficulties, a far superior technique was

developped, similar to that described by Andres and Wernick [7]. Here a

superconducting coil of about 30 turns is wound around the sample. Then the

leads of this coil are connected with non-interrupted superconducting wire to

a flux-transformer far away from the magnetic field, but still immersed in the

liquid helium. Finally, the induced current in the secondary circuit of the

flux transformer is detected by means of a flux-gate meter (Hewlett-Packard

428B). It should be noted that this method measures the magnetic induction,

but the external field contribution can easily be reconstructed by measuring

the sample in the normal state-

2.5.3. Electrical resistivity

For electrical resistivity measurements in the % e cryostat, the samples

were mounted on a flange and connected via a weak heat link to the He pot.

The samples could not be directly mounted on the He pot as it is impossible

to heat the ^He pot above IK with reasonable accuracy, because of a lack of

cooling power in this temperature regime. The same electronic equipment was

used as described earlier in section 2.1.

2.6 Thermal expansion

Thermal expansion measurements were carried out at the Free University of

Amsterdam between 6 and 300K by means of a three-terminal capacitance

technique, similar to that described by BrSndli and Griessen [8]. The length

changes were measured relative to Berylco 25 out of which the dilatometer was

constructed. Corrections for the length changes of the dilatometer were made

by measuring 5N Cu and comparing the results with the thermal expansion data

of Cu given by Hahn [9]. Magnetcstrictlon at 4.2 and 77K was measured by

immersing the dilatometer in liquid helium or nitrogin. This cryostat was then

placed inside another one containing a 12T superconducting solenoid.

2.7 Other techniques

The samples discussed in chapter 3 and 4 of this thesis were prepared and

their crystal structure determined by Dr. K.H.J. Buschow at Philips Research

Laboratories (Eindhoven). The samples discussed in chapter 5 were prepared by

19

the Lelden Mt-4 metal physics group under the supervision of Dr. A. Menovsky.

The high-field (40T) magnetisation experiments on La(Fe,Al)j3 and CePd2Si9

were performed by Dr. F.R. de Boer in the high-field magnet at Amsterdam [10].

Mössbauer experiments on La(Fe,Si)j3 and La(Fe,Al)j3 were performed and

analysed by Dr. A.M. van der Kraan at I.R.I. (Delft). The neutron diffraction

experiments on La(Fe,Al)13 were performed and analysed by Dr. R.B. Helmholdt

at the high-flux reactor (HFR) at E.C.N. (Petten).

References

1. T.T.M. Palstra, M.S. Thesis, University of Leiden (1981).

2. H-C.G. Werij, M.S. Thesis, University of Leiden (1983).

3. D. Hüser, Ph.D. Thesis, University of Leiden (1985).

4. B.M. Boerstoel, W.J.J. van Dissel and M.B.M. Jacobs, Physica 38 (1968)

287.

5. J.P.M. van der Veeken, Ph.D. Thesis, University of Leiden (in

preparation).

6. B. Ouwehand, M.S. Thesis, University of Leiden (1984).

7. K. Andres and J.H. Wernick, Rev. Sci. Instrum- 44 (1973) 1186.

8. G. Bra'ndli and R. Griessen, Cryogenics 13 (1973) 299.

9. T. Hahn, J. Appl. Phys. 41 (1970) 5096.

10. R. Gersdorf, F.R. de Boer, J.C. Wolfrat, F.A. Muller and L.W- Roeland in

High Field Magnetism, edited by M. Date (North-Holland, Amsterdam, 1983).

20

Structural and Magnetic Properties of the CubicLa(Fe,Al)1„ and La(Fe,SiL„ Intermetallic Compounds

Abscract

The properties of the pseudobinary compounds La(Fe,Al)jg and La(Fe,Si)j3 have

been studied with X-ray diffraction, ac susceptibility, magnetisation, elec-

trical resistivity, thermal expansion, Mössbauer spectroscopy and neutron

diffraction. These compounds crystallize in the NaZn13~type crystal structure,

which permits a Fe-Fe coordination number larger than in a-(bcc)Fe. This

leads to a magnetic phase diagram of La(Fe,Al)13, consisting of a

mictomagnetic, ferromagnetic and antiferromagnetic regime. This phase diagram

can be considered as an extension of the magnetic phase diagram of binary

(Fe,Al), with an antiferromagnetic state. However, the ferromagnetic state can

be recovered from the antiferromagnetic state by applying moderate magnetic

fields. Although the origin of the antiferromagnetic state is not fully clear,

this Chapter offers a consistent picture of the magnetic properties of

La(Fe,Al)^2 and La(Fe,Si)i3 as studied with the various experimental

techniques.

3.1 Introduction

The magnetism of iron-based intermetallic compounds is a rich source of

fundamental problems of modern physics. Simultaneously, the commercially

important properties can be exploited, like the thermal expansion in Invar

compounds and the anisotropy in the recently discovered l^Fe^B permanent

magnets. In this Chapter the magnetic properties of the La(Fe,Al)13 and

La(Fe,Si)i3 intermetallic compounds are studied via a broad series of experi-

ments, ranging from ac susceptibility to neutron scattering. The former

compound has an interesting phase diagram with three different types of

magnetic order, namely mictomagnetism, ferromagnetism and antiferromagnetism.

The antiferromagnetic regime exhibits sharp spin-flip transitions to the

ferromagnetic state in moderate magnetic fields, which enables us to compare

various magnetic properties of one compound in both magnetic states. This

21

Fig. SA. Part of the LaFa-^g unit aell. Shown are one snub cube of 24 Fe

atoms and one iaosdhedvon of 12 Fe atoms, shaving 3 Fe atoms. The

Fe1 atoms ave indicated by full and the Fe11 atoms by open

aivales. The La atoms (not shown) are located in the centers of

the snub oubes.

Fig. 3.2. The 3=0 plane of the hypothetical compound LaFe13, with the same

symbols as in Fig. 3.1.

22

unique property gives insight into how fundamental properties, like thermal

expansion and resistivity, are related to the magnetic state of the system. On

the other hand, the range of substitution of the Fe-atoms by Al or Si gives a

handle to vary, systematically the magnetic properties and to observe how

these properties are related. Indeed, the most striking conclusion of this

study is that the La(Fe,Al)j-j intermetallic compounds can be considered as a

system in which the magnetic properties vary from a-Fe-like ferromagnetism to

y-Fe-like antiferromagnetism.

3.2 Crystal structure

La(Fe,Al)-^ and LaCFe.Si)-^ have the cubic NaZn-^ (D2g) structure with

Fm3c (0, ) space-group symmetry. In the hypothetical compound LaFe^j the Fe

atoms occupy two different sites, Fe1 and Fe 1 1, in a ratio 1:12. In Wyckoff

notation[l] these sites are designated by the symbols 8(b) and 96(i), each

unit cell comprising 8 formula units LaFe-^. The La and Fe atoms from a CsCl

(B2) structure. Additionally, the La atoms are surrounded by a polyhedron

("snub cube") of 24 Fe* atoms. The Fe atoms are surrounded by an icosahedron

of 12 Fe* atoms and the Fe atoms are surrounded by 9 nearest Fe* atoms and

1 Fe1 atom.

In Fig.3.1 we show part of a unit cell, viz. one snub cube and one

icosahedron. The Fe** sublattice can be constructed by both snub cubes or by

icosahedra since both polyhedra are constructed by the same atoms. The snub

cubes, resp. icosahedra, are arranged In alternate directions so that the

lattice parameter is twice the distance between the centers of the snub cubes,

resp. icosahedra, and one unit cell contains 8 snub cubes, resp. 8 icosahedra.

Fig. 3.2 shows the z=o plane of the hypothetical compound LaFe^-j. From this

plane the complete iron sublattice can be obtained by cubic symmetry. The La

atoms occupy the (i,i,i) sites plus those obtained via symmetry operations.

The solid lines on the right-hand side of the figure connect the 6x4=24

nearest neighbours of La (snub cube), and on the left-hand side they connect

the 3x4=12 nearest neighbours of Fe1 (icosahedron). This picture further

demonstrates how the Fe sublattice can be constructed both by snub cubes and

by icosahedra. However, the snub cube and the icosahedron cannot

simultaneously be regular. This arises because these two different polyhedra

set incompatible conditions on the free parameters y and z of the NaZnj^-type

crystal structure. A regular isosahedron requires y=1.618z, whereas a regular

snub cube sets the condition y*0.1761 and 2=0.1141. This results in a small

deviation of regularity, without distorting the cubic symmetry. It will turn

23

5.O

4.0-

0.2 0.4 0.6 0.8 1.0O

Fig. 3.3. Number1 of Fe atoms with a certain Fe coordination numbev, ae

indicated, per unit cell LafFe^Alj^-i^ ae a function of x.

-2.54

-2.52

-2.50Q.

-2.48

-2.46

-2.440.6 0.8

X

Fig. 3.4. Iron aoneentration x dependence of the lattice pavametev a (left-

hand scale) and the distance d between the Fe1 and Fe11 atoms. The

inset shows a projection of four1 iaosahedva along the c-axis.

24

out that the Fe-Fe coordination number is an important parameter for the

magnetic properties. Therefore, Fig.3.3 shows the number of Fe atoms with a

fixed Fe coordination number per formula unit La(FexAli_x)i3 as a function of

iron concentration x.

The lattice parameter, a, decreases linearly with iron concentration x from

11.925 A for x=0.46 to 11.550 for x=0.92, as shown in Fig.3.4. The FeI-Fe11

distance (d=(y^+z )'e) is dependent on the parameters y and z. As these

parameters do not affect the periodicity of the lattice, they can only be

calculated from an intensity analysis of the X-ray powder diffractogram.

However, the neutron-scattering results (see section 3.6) give a much better

accuracy. Here, we derive the values y=0.178 and z=0.115 resulting in Fe*-Fe*

distances, ranging from d=2.527 A for x=0.46 to d=2.448 A for x=0.92, also

indicated in Fig.3.4. The inset of Fig.3.4 shows the alternate stacking of the

icosahedra, projected here along the z-axis. These four icosahedra form half a

unit cell.

The occupation of the Fe1 and Fe 1 1 sites by Fe and Al does not proceed in a

random way. Neutron scattering experiments on LaCFe^l^.j^)^ samples with

x=0.69 and 0.91 indicated that the Fe1 site is fully occupied by Fe. Thus a

considerable amount of Fe atoms will have an fcc-like local environment with

12 nearest neighbours. The Fe sites are distributed randomly by the

remainder of the Fe and Al atoms. This means that the mean Fe-Fe coordination

number for both Fe1 and Fe 1 1 sites can vary from 4.8 for x=0.46 to 9.4 for

x=0.92.

3.3 Composition and stability

The La(Fe,Al)-^3 and La(Fe,Si)^3 samples were prepared by arc melting in an

atmosphere of ultrapure argon gas. The purities of the three starting elements

were better than 99.9%. After repeated arc melting the samples were annealed

for about 10 days at 900°C. X-ray diffraction analysis showed that single

phase samples of the NaZn^j-type of structure were obtained in the concen-

tration regime between x=0.46 and x=0.92 for LaCFejjAlj.^)^ and between x=0.8

and x=0.9 for I^(FexSi1_x)13. H°wever, neutron diffraction and MBssbauer

spectroscopy showed that the samples are contaminated with a few percent of a-

Fe. The compounds are stable in air, very hard and brittle.

An intermetallic compound of the NaZn^^-type structure is found in only one

of the 45 binary systems consisting of a rare earth metal and Fe, Co and Ni,

viz- LaCo^j. There are two main reasons why an Intermetallic compound cannot

be stabilized. First, the heat of alloying may be positive and second, a

25 i

neighbouring phase may be preferred. In case of La and Fe the heat of alloying

is positive because there exist no stable La-Fe intermetallics. Nevertheless,

Kripyakevich et al.[2] showed that the NaZnj^-type structure can be stabilized

(i.e. the heat of alloying be made negative) by substituting the transition

metal in part by Si. However, at too large Si concentration, a structure of

different composition becomes favoured. This limits La(Fexsii_x)i3 to iron

concentrations x between 0.8 and 0.9 [3]. When substituting Al for Fe, a

broader concentration regime is found with 0.46<x<0.92 [4,5]. If the Al

concentration becomes too large, the tetragonal compound LaFe^Alg becomes

favoured. On the low Al concentration side the compound is not stable with

respect to a-Fe, i.e. LaFej3 does not exist. On the other hand, the heat of

alloying for La and Co is already negative since the intermetallic compound

LaCo13 (Curie Tc=1290K) and several other LaxCo intermetallics do exist [3].

For La(CoxSi1_x)13 the NaZn13-structure is stable for 0.8<x<1.0. For La-Ni

intermetalllcs almost the same situation occurs as for La-Fe[3]. LaNi^3 is not

stable and no intermetallics are found between pure Ni and the Haucke phase

« Here also, substitution of Ni by Al or Si is required to stabilize the

^ -j-s tructure.

For the binary systems Y-Fe and Lu-Fe the heat of alloying is negative,

since several vxFe y and LuxFe„ compounds do exist. Still, YFei3 and LuFe^3

cannot be stabilized because Y2Fe17 a n d Lu2Fe1^ are strongly preferred[6].

Note that the compound La2Fe17 does not exist.

Besides a calculation of the heat of formation of a compound, which can be

done using the Miedema model[7], there is an other approach by means of which

it is possible to predict the relative stability of a crystal structure. This

method, Initiated by Pearson[8], exploits a coordination factor, i.e. the

number of neighbours, and a geometrical factor, i.e. the ratio of atomic radii

of the different atoms and the difference between the atomic diameter and the

interatomic distance. The resulting near-neighbour diagram indicates that the

NaZnij-type structure is expected to occur near a radius ratio of the two

components of 1.6-1.7, where the line for the 24 Na-Zn contacts crosses those

for 12 and 10 Zn-Zn contacts. As the radius ratio for La-Fe is about 1.5, this

explains why the Fe-atoms have to be replaced in part by a smaller atom like

Al or Si, in order to stabilize the NaZn13-type structure.

26

3.4 Experimental Results

3*4.1 Zero-field Measurements•

The magnetic phase diagram for La(FexAl1_x)13 can be divided into three x

regimes as distinguished by the behaviour of the ac susceptibility, resis-

tivity, and magnetisation. In Fig.3.5 we show a typical example for the sus-

ceptibility of each regime. The susceptibility is plotted in units of the

inverse demagnetizing factor D~l(D=4it/3 for a sphere), thus yielding 1.00 for

a soft ferromagnet. In the first regime (I), 0.46<x<0.62, the behaviour of

the susceptibility is characterized by a sharp cusp at about 50K, indicative

of mictomagnetism (i.e., a random freezing of ferromagnetic clusters). Figure

3.5(a) shows the susceptibility of a x=0.58 sample along with the inverse

susceptibility. The large positive Curie-Weiss temperature intercept,

6=+110K, indicates the presence of predominantly ferromagnetic exchange inter-

actions. Deviations from Curie-Weiss behaviour start from 23OK which is about

5 times the freezing temperature, Tf=44.5K. The susceptibility increases

rapidly with increasing x, reaching 0.25% of D-1 at Tf for x=0.46, 1.1% for

x=0.54, and 14% for x=0.58, respectively.

0.1 5 2OO

IOO

(c)

0 3OO

fig. 3.5.

100 200T(K)

Temperature dependence of the low-field as-susceptibility fov the

three regimes of ^^e^Al^^.)^. (a) In regime I a typical

miotomagnetio behaviour is shown; (b) in regime II a ferromagnetic

transition; (a) in regime III an antiferromagnetio one. The inset

in (b) shows the low-temperature deviations from the soft

ferromagnetic state. Note the different \-eaales.

27

The susceptibility in the second regime (II), 0.62<x<0.86, exhibits soft

ferromagnetic behaviour. The Curie temperature first increases with x up to a

maximum Tc=250K for x=0.75 and then decreases. At lower temperatures the

susceptibility deviates from the inverse demagnetizing factor D~* limit [see

inset of Fig.3.5(b)]. These deviations are the smallest for the samples with

the highest Tc. This means that the soft ferromagnetic state is being

destroyed and a reentrant mictomagnetic state is probably appearing. In a

small interval, 0.84<x<0.86, a slight hysteresis has been observed at high

temperatures- Here the susceptibility above Tc behaves differently when

heating or cooling. Yet both curves yield the same Tc, which Is defined in

Fig.3.5(b) as the intercept of the two straight lines extrapolated from just

above and below Tc-

In the third regime (III), 0.86<x<0.92, the susceptibility has an anti-

ferromagnetic character. The broad maximum in the susceptibility for all

samples is about 10% of D"1. Only at the concentration limit x=0.92 does the

susceptibility obtain a value of about 80% of D~l. This is probably due to a

second phase that has been observed at the grain boundaries and in the X-ray

spectrum and probably consists of pure a-(bcc)Fe. The Néel temperatures,

defined as the maximum in d(Tx)/dT, increase with increasing x. Here also

hysteresis at high temperatures has been observed in the limited concentration

region 0.91<x<0.92.

The temperature dependence of the total resistivity is displayed in Fig.3.6

for typical examples of all three regimes. The general trend is that the room-

temperature resistivity decreases from 2OOji£2cm for x=0.58 down to 157u£3cm for

x=0.91- In regime I we observe a negative dp/dT at low temperatures. The slope

increases with Increasing x, but remains negative up to the low x part of

regime II. For x=0.73 the relative change in resistance between helium and

room temperature is ?°s' than 0.3%. For x>0.77 the slope dp/dT is positive. In

regime III dp/dT becomes negative again.

Large anomalies in the resistance are observed around the magnetic ordering

temperatures. In order to elucidate these anomalies we have plotted dp/dT

versus T in Fig.3.7. In the mictomagnetic regime (I) no anomaly is observed

around T£. In the ferromagnetic regime (II) a negative cusp develops around T

and increases in magnitude with increasing x until a sharp minimum is reached

for x=0.84. The ferromagnetic x»0.86 sample deviates from all other concen-

trations by having a ^-shaped anomaly. Finally in the antiferromagnetic

regime (III) a sharp negative cusp is found again.

28

21 Or

200-

La(FexAl,.x),3

f

190

160-

X = 0.58

X=0.73

100 200T(K)

300

0-

100 200T(K)

300

Fig. 3.S. Zero-field eleatrioal resistivity p vs temperature for

La(FeJi.l^_x)ii- The arrows indicate the magnetic ordering

temperatures.

Fig. 3.7. Temperature derivative of electrical resistivity dp/dT vs

temperature for

29

Figure 3.8 shows the spontaneous volume magnetostriction w =AV/V=3AA/-H

versus temperature (T) and reduced temperature (T/Tc). Three samples were

measured in the ferromagnetic regime (II) and one in the antiferromagnetic

regime (III). The spontaneous volume magnetostriction <o is obtained by

subtracting a Griineisen function, defined by the linear high-temperature

(300K) slope of ML/Ü, or at=13xl0"6K~1, and a Debye temperature 9D=300K, from

the observed thermal expansion[10]. These values of at and 9D are appropriate

for all samples. The always-negative slope of the magnetic a) , shown in

Fig.3.8, clearly indicates the Invar character of the La(FexAl1_x)13

intermetallic compounds. For x=0.65 a zero total thermal-expansion coefficient

a =SL~ldSL/<ÏV has been found at 140K, and for the other three samples this takes

place at about 24OK. usually, the negative magnetic thermal-expansion

coefficient is related to the increase of the magnetic correlation function as

the temperature is lowered. This also seems to occur in the antiferromagnetic

region. Figure 3.8 further shows that the magnetic moments extend to far above

La(FcxAl,_x)13

100 200 300TOO

Fig. 3.8. Spontaneous volume nugnetoetviotion u we temperature T and

veduaed temperatuve T/Ta.

30

3.4.2 Field measurements.

In Fig.3.9 we show the field dependences of the magnetisation at 4.2 K. In

the first regime, 0.46<x<0.62, it was not possible to saturate the magneti-

sation in fields up to 5T and an "S-shaped" M-H curve was found, typical of

the mictomagnetic state. Regime II, 0.62<x<0.86, exhibits a soft ferromagnetic

state with a remanent magnetisation less than 1% of the saturation

magnetisation. In the third regime, 0.86<x<0.92, the magnetisation increases

only slowly with increasing field until at moderate fields a sharp spin-flip

transition is found to the fully saturated (2.2u /Fe) moment[12]. This

transition takes place within 1 mT, which is our measuring accuracy.

Figure 3.9(c) exhibits the measured magnetisation curves for x=0.88 as a

typical example for the third regime. All samples were cooled in zero field to

helium temperature and then the magnetic field was increased. The spin-flip

field at x=0.88 and 4.2K, measured with increasing field, is 3.88T, but only

0.61T with decreasing field. Analogous behaviour was found for the other

samples with x>0.88.

0.5-

a)a.

I.Ol-= 0.73

l_a(FevAl.x)13

fig. 3.9. Magnetieation as a function of magnetic field for the three

regimes of LafFe^Alj^jg at helium temperature. In regime I we

show iihe behaviour of a mietomagnet; in regime II, of a

ferromagnet; and in regime III we show the metamagnetia behaviour

of the mtiferromagnetic regime for an os=O.88 sample.

31

4 y

es) 3

in

5 2

1 -

o.

1 1

's

1 1 1 ' '

La (Fex ALX= 0.877

-°•

1 > i

i i

l-x),3

i i

50T(K)

100

Fig. 3.10. Tempevatuve dependence of the spin-flip fields for inaveaeing(open airalee) and deaveaeing fields (full eiveles) forI>a('Pe:lAl1_x)ls with x=0.877.

8.85 0.90

Pig. 3.11. Concentration dependence of the spin-flip fields observed inLa(Fe;lAl^_x)2s a* 4.2K for insveasing (open airales) anddecreasing fields (full airvlee).

32

When the temperature increases, the hysteresis loops become narrower and

the center field shifts to lower values. The resulting phase diagram is shown

in Fig.3.10, again for x=0.88 as a typical example. In Fig.3.11 we show the

concentration dependence of the transition fields at 4.2K. The spin-flip field

is almost linear in x, and with increasing x the hysteresis loops become

wider[12].

Figure 3.12 shows the saturation moments per Fe atom for x>0.62. The

magnetic moment increases linearly with x in regimes II and III having a slope

of 0.24n_/Fe resulting in 2.4p. /Fe for the hypothetical compound LaFej^. In

regime I, 0.46<x<0.62, it is not possible to saturate the magnetisation in

fields up to 5T. In regime II the magnetisation is saturated in fields

directly above the demagnetizing field and no increase of the magnetisation is

observed in fields up to 20T. For regime III we have determined the saturation

magnetic moments in fields larger the spin-flip field.

2.5

Fig. 3.12. Saturation magnetic moments of La(FexAl-l_x)-ls as a function of x.

33

In Fig.3.13 we show the resistivity of a x=0.88 sample in a field of 4.76T,

along with the zero-field resistivity as a typical example of the antiferro-

magnetic regime (III). Upon applying a field at helium temperature, the resis-

tivity p(H) first decreases at a rate l^Qcm/T and at the spin-flip transition

a jump Ap of 20\xQaa occurs for the x=0.88 sample. Thus, there is a total

decrease of the resistivity in a field of 4.76T of about 17%. Furthermore, the

negative dp/dT in zero field becomes positive beyond the spin-flip field.

Above Tjq there is no observable field dependence of the resistivity. The

magnetoresistance of the spin-flipped antiferromagnetic samples (III) is quite

similar to the zero-field resistance of the ferromagnetic samples (II).

Samples in the ferromagnetic regime (II) do not show pronounced changes upon

applying a magnetic field.

In order to further elucidate the anomalies around TJJ, we have plotted

dp/dT versus T for both zero field and a 4.76T field in Fig.3.14. In both

]7O

E 16O-

150

140J—

La(FexAl,.x)I3X=0.88

0.10

,0.05

a.•a

- 0.05 -

100 2OOT(K)

300-0.10.

Lfl(FexAl,.x)X=0.88

1!OO 200

T(K)300

Fig. 3.13. Eleotriaal resistivity p vs temperature for an antifervomagnetia

£<z^tea!4Z2_aJi3 sample (x=0.88) in zero field and in a field

H H=4.?6T, greater than the spin-flip field n Hgf. The inset shows

the ratio p(4K)/p(300K) vs iron aonaentvation x. M indieates the

ferromagnetic or indue ed ferromagnetic state and AF the

antiferromagnetia ground state.

Fig. 3.14. Temperature derivative dp/dT vs temperature for an anti-

ferromagnetia La(Fe3Al2_x)jg sample (x=0.88) in zero field and in

a field \i H=4.76 T (B>H J.

34

cases a sharp negative peak is found at TN. In regime III we have used exactly

this criterion to define TN. The theoretical TN definition, namely the maximum

in d(xT)/dT, is not as well defined because the zero-field susceptibility in

this regime shows a rather smooth transition. Figure 3.14 also illustrates

that the magnetic ordering temperature T N increases 14K by applying a field of

4.76T. In both curves there is a second anomaly above TN whose origin is not

clear. This anomaly also shifts in temperature upon applying a field.

In Fig.3.15 we display the magnetostrictive effects of a x=0.89 sample at

4.2K. The behaviour of the other samples in the antiferromagnetic regime (III)

is analogous. Up to the spin-flip transition the relative volume change oo is-4

rather small (u> =6x10 ). At the spin-flip transition there is a huge magnetic-2

expansion (u,=+lxlO ). Upon decreasing the field the same hysteresis loop is

followed as has been observed with the magnetisation [see Fig.3.9(c)]. The

irreversibility at low fields is due to the appearance of visible cracks in

the sample. To reduce this irreversibility the sample can be previously cycled

at helium temperature in a magnetic field before u^ versus H is measured. At

77K the magnitude of the expansion at the spin-flip transition decreased to

uf=+7.2xl0

77K.

-3 and the hysteresis width decreased from 3.ST at 4.2 K to 0.5T at

1.0

'o

3~0.5

1 r

La(FexAl,_x)

_ X = 0.89T=4.2K

13

Fig. 3.16. Forced volume magnetostriction u)*=hV/V as a function of mignetio

field for an antiferromagnetiahelium temperature.

)*=h

sample (x=0.89) at

35

3.5 Discussion

3.5.1 Magnetic properties.

The magnetic phase diagram of La(FexAli_x)]L3 c a n ^e constructed from the

results of the susceptibility, resistivity, and magnetisation experiments. The

first regime (I), 0.42<x<0.62, consists of a mictomagnetlc state with a

distinct cusp in the ac susceptibility and an S-shaped magnetisation curve.

Upon increasing the iron concentration x, we find a soft ferromagnetic state

in regime II, 0.62<x<0.86. Finally, at the highest iron concentration,

0.86<x<:0.92, an antiferromagnetic state exists, with a sharp metamagnetic

transition in a magnetic field of a few teslas. The experimental phase diagram

of La(Fe3jAlx-x)l3 i s constructed from the magnetic ordering temperatures and

is displayed in Fig.3.16.

For x<0.75 there are striking similarities between La(FexAli_x)i3 and

FexAlx-x" Although the crystal structure is different, they both are cubic.

Furthermore, we find a mictomagnetic phase in I-'a(FexAlx_x)i3 for x<0.6,

whereas FexAlj_x also has a mictomagnetic phase for x<0.73[13]. This means

that both compounds become mictomagnetic when the average number of nearest-

300

200

100

La(FexAL,_x))3

0.4

micto- Imagnetism

0.6

Fig. 3.16. Magnetic phase diagram of La^Fe^l}^)^. The freezing temperatureie indicated by A, the Curie temperature by 0, and the fleettemperatures by D

36

neighbour Fe atoms is less than 6.0, even though the local environments of the

Fe atoms and the lattice parameters are different. Recently, a semiquanti-

tative model has been proposed for the phase diagram of FexAli_x[14]. We

believe that the main ideas of this model are also applicable to

La(FexAl^_x)l3. Here it was proposed that mictomagnetic behaviour arises by

virtue of competition between a nearest-neighbour Fe-Fe ferromagnetic exchange

and a further neighbour Fe-Al-Fe antiferromagnetic superexchange. With such

coupling the magnetic moments will be frozen-in below the freezing temperature

Tj in random orientations without long-range ferromagnetic or antiferro-

magnetic order, i.e., a mictomagnetic cusp appears in the low-field

susceptibility. Short-range ferromagnetic order (clustering) causes the

deviations from Curie-Weiss behaviour up to 5Tj and the large positive

Curie-Weiss temperature 9=+110K. It has been shown in Fe^lj.^ that the

magnetic moment of Fe is strongly dependent upon the number of nearest-

neighbour (NN) Fe atoms- In F e ^ l ^ ^ the moment is about 2.2^ for Fe atoms

having more than five NN Fe atoms[15]. When the number of NN Fe atoms is less

than five, the magnetic moment decreases and becomes zero if this number is

less than four. Thus, by decreasing the iron concentration, more and more iron

atoms will loose their magnetic moment, thereby decreasing the number of both

ferromagnetic and antiferromagnetic interactions, and eventually leading to

Pauli paramagnetism. For La(Fe1_xAlx)13 this model explains the decrease in

the magnitude of the susceptibility at Tf with decreasing x.

Upon increasing the iron concentration above x=0.6, long-range ferro-

magnetic order is found. Here the Curie temperature increases with increasing

x because the number of NN ferromagnetic exchange pairs increases at the cost

of the antiferromagnetic superexchange, and because the lattice parameter

decreases. The latter argument is supported by Mössbauer spectroscopy and

saturation- magnetisation measurements[16], and recent neutron scattering

experiments on a variety of Fe-based alloys[17]. These measurements showed

that in our range of Fe-Fe distances the exchange constant is positive and

increases with decreasing Fe-Fe distance. This result is consistent with the

higher T c values of La(FexSi1_x)13 compared to La(FexAl1_x)13 as the lattice

parameter of the former compound is smaller. However, upon increasing the iron

concentration above x=0.75, the Curie temperature begins to decrease and for

x>0.86 antiferromagnetic order appears. This unexpected collapse of long-range

ferromagnetic order with increasing iron concentration has long been studied

in connection with y-Fe (fee) and F exNi^_ x alloys in the Invar region (fee,

x-0.65).

37

Calculations within the Hartree-Fock approximation (HFA) for the impurity

states in ferromagnetic transition metals show that an Fe impurity in a ferro-

magnetic host has two stable solutions, crucially depending on the local

environment[18]. One solution, Fe(I), corresponds to a magnetic moment mj,

parallel to the bulk magnetisation.The other solution, Fe(II), represents a

magnetic moment mjj antiparallel to the bulk (host) magnetisation. The ratio

of Fe(I) to Fe(II), which depends on the local environment, can be determined

by minimizing the total energy[19]. This model has been extended to

concentrated alloys and it has been argued that when the iron concentration

increases beyond a certain limit, the Fe(II) solution becomes the stable one

[18]. Furthermore, it was suggested that even when a small fraction of the

atomic moments is antiparallel to the magnetisation, the ferromagnetic state

can be unstable[20]. However, it is not clear what the resulting magnetic

ground state will be in such an alloy after the collapse of long-range

ferromagnetic order. Many years ago Weiss[21] introduced a two-level model for

y-Fe, based on low-temperature measurements. Here there is a low-volume, low-

magnetic moment (0.5u /Fe) antiferromagnetic ground state, and a thermallya

excited upper level with a high-volume and high-magnetic moment

(2.8u /Fe) ferromagnetic state. This model is in many respects similar to the

results obtained by the HFA calculations. Unfortunately, fcc-Fe only exists,

under normal pressures, at high temperatures where no long-range order of the

magnetic moments occurs. Nevertheless, this model was used by other authors in

order to explain the magnetic behaviour of Fe-Ni Invar alloys[22,23]. Neutron

scattering experiments on such alloys have revealed a negative Fe-Fe exchange

constant, but an antiferromagnetic state has not been found owing to an y+a

martensitic-crystallographic transformation. This antiferromagnetic state has

indeed been found in Fe-Ni-Mn alloys where the y-m martensitic transition can

be suppressed[24 ].

We believe that the collapse of long-range ferromagnetic order in

La(FexAl^_x)^3 at the highest iron concentration, 0.86<x<0.92, has the same

origin as in Fe-Ni, Fe-Ni-Mn, and y-Fe. In this concentration range a con-

siderable portion of Fe1 sites has a Fe-Fe coordination number approaching 12,

and a considerable number of Fe** sites has a Fe-Fe coordination number up to

10. At these high coordination numbers, the Fe(II) state becomes stabilized

and when a sufficiently high fraction Fe atoms occupies this state, the

ferromagnetic order collapses. However, for La(FexAl1_x)^3 the ferromagnetic

state can be recovered by applying a magnetic field.

It was suggested that the instability of the Fe(I) state originates in

38

iron-rich environments, and takes place already before the collapse of the

long-range ferromagnetic order[20]. Furthermore, this instability of the

ferromagnetic state should be accompanied by fluctuations of the now weakly

coupled magnetic moments. Then, near the critical concentration, these

fluctuations must be taken into account, since they cause the Fe moments to

form a low-temperature asperomagnetic state (i.e. a disordered, noncollinear

ferromagnetic state)[18]. This would correspond with the decrease of the low-

field susceptibility from D observed at low temperature for 0.81<x<0.86 [see

inset of Fig.3.5(b)].

The linear decrease of the saturation magnetic moment with decreasing iron

concentration from 2.14uB/Fe for x=0.92 to 1.35(i /Fe for x=0.65 (see Fig.3.12)

can be compared with the Slater-Pauling curve[25]. This curve was constructed

for binary 3d-alloys and correlates the magnetic moment with the total number

of (3d+4s)-electrons. Here, it is assumed in a-Fe with 8 (3d+4s)-electrons

that the majority band is almost completely filled, whereas the Fermi level is

at about the middle of the minority band. This leads to a magnetic moment of

2.2|ig/Fe. The magnitude of the moments in La(Fe,Al)i3 indicates that such a

band structure might also hold in this compound. When substituting Fe by

another 3d-metal the moment will decrease because of a change in the

occupation of the majority and minority spin-band. However, when substituting

Fe by Al(or Si) the Fe moment will decrease owing to a decrease of the

exchange splitting between the majority and minority spin-band.

3.5.2 Mètaaagnetisn.

Metamagnetism and spin-flip transitions, while rather common in insulating

systems[26], especially layered compounds, are more unusual in metallic

systems. Still, in the few examples which are known to exist several kinds of

metamagnetism have been found. Without being exhaustive, we recall several

mechanisms and examples. First, there are layered structures like

Au2Mn[27,28], Au3Mn[29], HoNi[30], ErGa2[31I, etc with ferromagnetic

interactions within the layer and antiferromagnetic interactions between the

layers. Second, we have temperature-induced phase transitions with

metamagnetic features around the transition temperature like in Y2Ni7[32],

FeRh[33] and MnAs[34J. Third, we have collective or itinerant electron

metamagnetism in exchange-enhanced paramagnets like TiBe2, YCoo and

Co(SxSei_x)2f35].

As a pseudobinary intermetallic compound, La(FexAli_x)j3 certainly belongs

to another class with its metamagnetic transition from the antiferromagnetic

39

ground state to the induced ferromagnetic state. In this case a layered

structure can be excluded because of the perfect cubic arrangement of the Fe

atoms with a coordination number up to 12. Therefore a comparison with

Pt3Fe[36] is not warranted since here layered sheets of Fe atoms have also

been observed.

Some striking metamagnetic properties of Ija(FexAl1_x)13, which distinguish

it from other metamagnets, are as follows.

(1) The transition fields (<15 T) are small compared to the magnetic

ordering temperatures («200 K) converted to the same units.

(2) For a fixed composition the mean spin-flip field H g f decreases slowly

with increasing temperature.

(3) The hysteresis loops are sharp and can be as wide as 5 T.

(4) The mean spin-flip field increases with increasing 3d moment.

(5) With increasing 3d concentration x, the metamagnetic region lies in the

highest x range leading to the ordering sequence spin glass or

mictomagnetic •» ferromagnetic •>• antiferromagnetic. In Co(SxSe1_x)?[37] the

metamagnetic region lies in between a paramagnetic and a ferromagnetic region

and in PtjFe the metamagnetic region lies in between a ferromagnetic and an

antiferromagnetic region.

In local moment theory the rapid increase of the spin-flip fields with

increasing iron concentration x should be related to an increase of the

anisotropy field H a n, H fa(2H H ) , since the exchange field H e x increases

only little. As there is no apparent reason for this rapid change in the

anisotropy, a model of itinerant electron magnetism seems to be more

appropriate. An early theory for itinerant antiferromagnetism was proposed by

Lidiard[38]. However, to make a proper analysis, a detailed knowledge of the

band structure is required[39]. A very recent phenomenological theory was

proposed by Shimizu[40J, who exploits a magnetic free energy expansion in the

uniform magnetisation and staggered magnetisation to obtain magnetic phase

diagrams including ferromagnetism and antiferromagnetism. The resulting

magnetic phase diagrams resemble the diagram found for LaCFe.Al)^^ and an

analysis, yielding the proper coefficients could give a better understanding

of the magnetic phase diagram.

3.5.3 Electrical resistivity.

The main features of the electrical resistivity of ïja(FexAl^_x)^3 are (i)

the resistivity is large (>150uQcm), (ii) in region III (antiferroiaagnetic

ordering) a negative dp/dT is found over the whole temperature range, and

40

(iii) critical effects are observed around the transition temperature.

The large resistance suggests that Mooij's rule[41] may be applied which

describes the effects of various types of disorder on the electrical resis-

tivity of transition-metal alloys. This rule states that in a wide T range

around room temperature, the temperature dependence of p is approximately

linear with a temperature coefficient a =p dp/dT which is small and changes

its sign systematically from positive in alloys with p<100(iBcm to negative

for p>2OOu£5cm.

In the first two regimes (I and II), x<0.86, this rule seems to hold. With

increasing p the temperature coefficient a decreases and dp/dT changes from

positive for p<190(xQcm to negative for p>190(iQcm. However, in the third regime

(III) the room-temperature resistivity (160(iScm) is less than in the first two

regimes, and yet a negative dp/dT is found here. We have to keep in mind that

although Mooij's rule does not explicitly treat magnetic scattering, it should

still be valid in the paramagnetic high-temperature range. We have

investigated two samples in this range up to 700K and found at 700K that

ar=8i-xlQ~6K~l, p=182|iflcm for x=0.84 and C ^ I S A X K T ^ K " 1 , p=163nQcm for x=0.91,

Irt agreement with Mooij's rule. In addition we found no indication of satu-

ration in p(T) at high temperatures[42].

LaCFe.Al)^ enables us to measure the electrical resistivity in the anti-

ferromagnetic ground state as well as in the field-induced ferromagnetic

state. In Fig.3.13 the experimental results are shown. They may be explained

by using the two-current model. For a full description of the validity and

range of this model we refer to Dorleijn[43] and Campbell and Fert[44]. This

model considers transition metals which are magnetic, e.g. Fe, Co, and Ni. In

a ferromagnetic metal it is appropriate to distinguish the electrons according

to the direction of their magnetic moment, viz. either parallel or anti-

parallel to the magnetisation within a domain. We indicate the charge carriers

with magnetic moment parallel to the magnetisation with "up" or +, and those

antiparallel with "down" or +. As was suggested by Mott[45], scattering

events with conservation of spin direction are much more probable at low

temperature (i.e., T«T C) than scattering events In which the spin direction

Is changed. Mott's suggestions lead to a description of the conduction by two

independent currents in parallel. Since the Fermi surfaces for t and

+ electrons can be very different, there is no reason to assume equal

relaxation times or conductivities for the two spin currents. Indeed, a

different resistivity has been found for the two spin currents in Al dissolved

in Fe, p _=48 [iQcm/at.% Al and pj)l=5.6 fjQcm/at.% Al. If one adopts the above

41

values for LaFe^j, instead of pure Fe, one can. calculate the excess

resistivity of the antiferromagnet relative to ferromagnet. When replacing 10%

of Fe in LaFe13 by Al, La(FeOê9AlO-1)l3, the above-mentioned model gives a

magnetic contribution to the resistivity in the ferromagnetic state of

P = At- = 50

However, if the ground state changes from ferromagnetic to antiferromagnetic,

both currents will be scattered equally and the magnetic contribution to the

resistivity is

P

since both currents have the same average resistivity l/2(p +p ). This leads

to an increased resistivity of 84uQcm in the antiferromagnetic state relative

to the ferromagnetic state. We emphasize that our assumptions are over-

simplified and that the numerical estimate is only a rough one, since we used

the values of Al dissolved in Fe instead of Al dissolved in LaFe^^.

Nevertheless, this model can lead to a basic understanding of the observed

phenomena.

Fxperimentally we find a decrease in resistivity of 25uScm when applying a

field and thereby changing the antiferromagnetic ground state into an induced

ferromagnetic state. Upon increasing the temperature, more thermal excitations

will be activated, tending to equalize both currents and above Tc only a

paramagnetic scattering is left. Our measurements indicate that the magnitude

of the paramagnetic spin-disorder scattering lies in between the values for

the ferromagnetic and antiferromagnetic scattering. This leads to a positive

dp/dT for the induced ferromagnetic state and a negative dp/dT for the

antiferromagnetic ground state. The negative temperature coefficient indicates

that the antiferromagnetic state has a very unusual, highly resistive

property.

Similar behaviour has been observed in Feo.sCi-x^l-x^O.S that can likewise

change from ferromagnetic to antiferromagnetism by varying x[46]. Here also,

dp/dT is smaller in the antiferromagnetic state than in the ferromagnetic

state. However, dp/dT is positive in both states, indicating that the para-

magnetic scattering is stronger than the scattering in both long-range ordered

states.

42

Upon increasing the Al concentration the two-current model leads to an

increase in resistivity as observed. At the highest Al concentrations, i.e.,

in the mictomagnetic state, a similar discussion as given above leads again to

a negative dp/dT as has been observed.

The critical behaviour of the resistivity denoted as the third feature

above displays a sharp negative peak in dp/dT for the entire ferromagnetic and

antiferromagnetic region, except for the borderline case x=0.86, which has a

X.-shaped anomaly. The total resistivity consists of three parts: a residual

part, a part due to phonon scattering, and a part due to spin scattering. This

means that the anomalies near Tc must be ascribed to spin scattering and

phonon scattering as affected by magnetic strictive effects, de Gennes and

Friedel[47], Kim[48], and Fisher and Langer[49] have calculated the critical

behaviour of the resistivity of a ferromagnet in terms of spin fluctuations.

Although the results differ in some respects from each other, they all found a

positive peak in dp/dT near Tc- Apparently this is not the case in

La(FexAl^_x)1.j, except for the x=0.86 sample. In the x=0.86 care a remarkable

resemblance is found with other ferromagnets such as Ni, GdNi2, etc.[50]. This

means that for all other concentrations this positive peak, due to spin

fluctuations, must be overwhelmed by another contribution.

Because of the absence of such a \-shaped peak in the ferromagnetic Fe3Pt,

Viard and Gaviolle suggested that the critical scattering of conduction

electrons by phonons must be taken into account[51]. They calculated the

phonon contribution for Fe3Pt and found a negative peak for dp/dT near Tc

arising from the anomalous behaviour of the bulk modulus. Since Fe3Pt and

LaCFe^jAlj.^)^ both have Invar characteristics, we expect that the behaviour

of the bulk modulus is roughly similar. Thus, we propose that an anomalous

decrease of the bulk modulus (lattice softening) below Tc leads to the

observed negative peaks in dp/dT around Tc in La(FexAl1_x)i3- We note that

the Curie temperature does not correspond with the temperature at which the

peak is observed but is always slightly higher-

Beginning with Suezaki and Mori[52], many authors[53] have calculated the

critical behaviour of the electrical resistivity of antiferromagnetic metals

near TN. All calculations suggested a large negative peak in dp/dT at TN due

to scattering of the conduction electrons by thermal fluctuations of spins.

Such is in agreement with the observed behaviour of La(Fe3CAl^_x)13 with

x>0.86. This negative peak might even be enhanced by the aforementioned

critical behaviour of the phonon scattering.

43

3.5.4 Spontaneous and forced Magnetostriction.

The Invar effect has attracted a wealth of Interest from both experimen-

talists and theorists [ 54 ]. The archetypical example Is FexNii_x (x=0.65),

which has a zero thermal-expansion coefficient around room temperature. For

La(FexAl1_x)12 we find a zero thermal-expansion coefficient at at 240K for

samples near the instability of long-range ferromagnetic order (x=0.81, 0.86,

and 0.89). The Invar effect has been explained by a cancellation of the

lattice thermal expansion a by a negative magnetic term a [22].l m

One of the first Invar theories was proposed by Weiss[21]. He suggested a

local-moment model with two nearly degenerate states for the Fe atoms, viz. a

ferromagnetic ground state and an antiferromagnetic excited state. The latter

is characterized by a lower magnetic moment and a smaller atomic volume. By

raising the temperature an increasing number of iron atoms will occupy the

low-volume excited state, leading to a negative a . However, when applied to

)|3, this model cannot account for the behaviour of the x=0.89sample, which already has an antiferromagnetic ground state and yet a is

negative.

A more general local-moment volume-magnetostriction theory was developed by

Callen and Callen[55]. They showed that the spontaneous volume magneto-

striction to =AV/V is given by the two-spin correlation function <mi.m^> as

s *• j

S , 1UC L J

where « is the compressibility, C l o c a magnetovolume coupling constant, and

i,j are the lattice sites. This magnetovolume effect arises from the volume

dependence of the exchange integral.

More recently the magnetovolume effect was studied by extending the Stoner

band model with volume-dependent terms[56]. This leads to a phenomenological

relation, verified for a number of materials[57]:

u) = KC. ,7 m?(T)s band£ iv '

where C^^j is the magnetovolume coupling constant due to the band mechanism

and m^(T) is the temperature-dependent local moment on site 1 as discussed by

Shiga[58], and not the bulk magnetisation M(T). Here, the magnetovolume effect

can be understood in terms of the increase of the kinetic energy of the

electron system due to the splitting of the 3d band[59]. The volume effect

arises because the electron system can reduce its kinetic energy by undergoing

44

a lattice expansion.

In order to explain the magnetostriction results of La(FexAl^_x)13> we must

consider both a local moment and a band part by adding both contributions[58].

Below the Curie temperature in the ferromagnetic state, <mj.ni-> and ra2 can

be approximated by M^ and this leads to the relation

u (T) = K ( C +C ,)M2(T) .s loc band

If we compare the saturation magnetisation of La(FexAl1_x)13 (beyond the spin-

flip transition for x=0.89) with the magnetic contribution of the thermal

expansion at liquid helium temperature, we find large, positive magnetovolume

coupling constants icC = KCC, +C, ,)=1.79, 1.71, and 1.73xlO""8cm6/emu2 for

x=0.81, 0.86, and 0-89, respectively. This result, along with the observed

resistivity behaviour, suggests the equivalence of the ferromagnetic and

induced ferromagnetic state. For x=0.65, near the mictomagnetic regime, we

find an even larger constant KC=2.09xlO~°cm"/emu . These values are about

twice as large as for bcc Fe, FeNi Invar, and Fe3Pt[57,58].

From these measurements we cannot say whether the band or the local-moiaent

contribution is larger. Shiga[58] calculated that for bcc Fe and FeNi-Invar

alloys the band contribution is much larger than the local-moment part at low

temperatures: cband'*'>Cloc• Furthermore, self-consisting spin-polarized energy-

band calculations[59] have shown that hypothetical nonmagnetic bcc Fe is about

3% smaller in volume than ferromagnetic Fe. This conclusion was confirmed by

analysis of Fe-based binary compounds[58]. This value is very close to the

value u =2.34% we observed for LaCFejjAlj.jj)^-

We may estimate the local-moment and band contribution to the thermal

expansion for La(Fe^Vlj_x)j3 by analysing the spontaneous and forced volume

magnetostriction of the x=0.89 sample at helium temperature (see Figs.3.8 and

3.15). We calculate the spin-spin correlation function from the cluster model

obtained from the neutron diffraction measurements (see section 3.6). Here we

found that the spin-spin correlation function is 59% in the antiferromagnetic

ground state with respect to the induced ferromagnetic state, whereas m2 is

still 94%. Experimentally we observed that ta in the antiferromagnetic states

is 57% of the value in the ferromagnetic state. Although the accuracy of these

values must not be overestimated, we conclude that the volume-magnetostriction

in La(Fe,Al)x3 can be described with a local moment contribution. This result

stands in contrast with the knowledge that iron magnetism is a band property

45

due to the largely Itinerant behaviour of the 3d-electrons.

The increase of the volume-magnetostriction u> from 280K downwards must, in

our interpretation, be mainly ascribed to the increase of the local moments

with decreasing temperature. It can be inferred from Fig.3.8 that the magnetic

contribution to the thermal expansion starts to increase at a distinct

temperature (280K), and not at a distinct reduced temperature. Thus, the local

moments start to increase or even to form from 280K downwards, independent of

the concentration x. However, the magnetic ordering temperatures show a

pronounced minimum in this concentration regime (0.81<x<0.89). We believe that

the minimum in magnetic ordering temperatures can be attributed to the

frustration produced by the positive and negative exchange interactions[60].

This is in contrast to FeNi Invar, where it was argued that tho- minimum in

Curie temperatures, which occurs at the borderline concentration for

instability of long-range ferromagnetism, is due to the suppression of spin

fluctuations[61]. In spin-fluctuation theory T c is proportional to

T)(T )=u (T )/u (0) and in FeNi Invar ri(T ) has a minimum in the instabilityc s c s c

regime[61]. However, one can easily see from Fig.3.8 that T)(T ) has maximum in

the instability regime for La(FexAl1_x)13 near x=0.86.

3.6 Neutron scattering and MSssbauer spectroscopy

Besides the aforementioned measurements of macroscopic quantities, the

study of the La(Fe,Al)^3 system has been extended with investigations of

microscopic quantities, viz. neutron scattering[62,63] and Mössbauer

spectroscopy[63,64]. The neutron diffraction measurements were carried out in

order to resolve the symmetry or frustration of the antiferromagnetic order.

This frustration is inferred by the (magneto)resistivity measurements and by

the fact that no simple antiferromagnetlc lattice can be mapped on the NaZn^j-

type crystal structure due to the combined three-fold and four-fold symmetries

which always leads to frustration. Additionally, Mössbauer spectroscopy

measurements give information of the magnetic state of the Fe atom, and of the

local-magnetic environment of the Fe moments.

3.6.1. Experimental procedures•

Neutron-diffraction experiments at 4.2K and 300K were performed on a ferro-

magnetic (x»0.69) and an antiferromagnstic (x=0.91) sample using the powder

diffractometer at the High Flux Reactor (HFR) in Petten. Neutrons of

wavelength 2.5913(4)A were obtained after reflection from the (1,1,1) planes

of a copper crystal. The \/n contamination had been reduced to less than 0.1%

46

using a pyrolytlc graphite filter. Soller slits with a horizontal divergence

of 30' were placed between the reactor and the monochromator and in front of

the four % e counters. All data have been corrected for absorption, uR is 0.48

and 0.51 for x=0.69 and 0.91, respectively.

Neutron diffractograms of two L a ( F ex A l 1 _ x ) 1 3 compounds, x=0.69 and 0.91,

were measured at room temperature, well above the magnetic ordering

temperatures of TC=237K and TN=218K, respectively, and at 4.2K. The

diffraction patterns were analysed using Rietveld's refinement technique [65].

All diffractograms are contaminated by the (1,1,0) and (2,0,0) peaks of cc-Fe,

while the dif f ractograms at 4.2K are contaminated also by 2 peaks due to the

cryostat. The regions in which these two kinds of peaks occurred were excluded

from the refinement analysis.

The Fe Mössbauer spectra were obtained by means of a standard constant

acceleration-type spectrometer in conjunction with a Co-Rh source. The

hyperfine fields were calibrated by means of the field in a-Fe 0. at 295K

(51.5T). The isomer shift was measured relative to SNP at room temperature.

3.6.2. Experimental results.

The refinement analysis of the nuclear structure of the diffractograms at

300K showed that the Fe sites in both compounds were predominantly (>97%)

occupied by Fe. Thus, the Al atoms are statistically distributed only over the

96(i) sites. The results for both the ferromagnetic (x=0.69) and

antiferromagnetic (x=0.91) compound at 300K and 4.2K are given in Table 3.1.

The calculated magnetic moment for the x=0.69 compound (m=1.41(8)u_/Fe) is int>

agreement with the saturation moment m=1.47(2)u /Fe, shown in Fig.3.12.b

In the diffraction pattern of the x=0.91 compound extra peaks were found at

4.2K with respect to that at 300K (see Fig.3.17). These extra peaks have mixed

indices, whereas the nuclear peaks have indices all odd or all even. Hence,

the compound has a long-range-ordered antiferromagnetic state and is not

dominated by frustration effects as was inferred by an extremely high

electrical resistivity of the antiferromagnetic state. Furthermore, this means

that the magnetic unit cell coincides with the nuclear unit cell, which forms

the basis of our cluster model (see below).

Fe Mössbauer spectra were obtained at 4.2K on various La(FexAli_x)^3

compounds. A decomposition of these spectra into subspectra associated with

the Fe1 and Fe 1 1 sites does not seem possible, owing to the fact that for both

sites various types of nearest-neighbour coordinations exist, differing in the

47

c8"o

inc5

50

La(FexAl,_x)]3X=0.91

::::::! observed profilecalculated profile

75 1002-theta (degrees)

125 150 175

Fig. 3.17. Neutron powdev diffraetogmm of (^^l^^jS u^*^ %=0•$!• &t 4.2

and 300K. Both nuclear and magnetic lines ave indicated. The dvawn

line through the data points is the calculated profile of the

final refinement analysis.

Fig. 3.18. Concentration dependence of the average hyperfine field p, Bo

and the isomev shift 6 in La(Fe3Ali_x)ïs at 4.2K.

48

number and arrangement of nearest neighbour Al atoms- Therefore, we have

restricted or selves to determining only the average hyperfine field and

isomer shift, which has been plotted as a function of concentration in

Fig.3.18. In this plot one recognizes the trend of the average hyperfine field

10 increase with x, with the ferromagnetic-antiferromagnetic phase boundary

being revealed by a substantial drop of Heff close to x=0.87. In the

ferromagnetic regime the hyperfine field is proportional to the saturation

moment, with a proportionality constant of about 14T/K, in agreement with

other Fe-based intermetallics[66]•

3.6.3* Discussion

As each unit cell of 8 formula units contains 104 spins, disregarding the

presence of the Al atoms, it is impossible to resolve the magnetic structure

without modelling the system. Therefore, the following simplifications have

been made.(l) Each icosahedron of 12 Fe atoms together with the central Fe

atom is considered as one entity or cluster.(2) The La and Al atoms are dis-

regarded as they have no magnetic moment.(3) We assumed that the 12 Fe 1 1 atoms

of each cluster have their spins parallel, while (4) the central Fe1 atom of

the cluster may have its spin either parallel or antiparallel to the

surrounding spins. The spin of one cluster is represented by the resultant

spin of the Fe spins constituting the cluster. For the x=0.91 sample this

means that the cluster has a spin of [(13)x(0.91)-l]m(Fen) + m(FeI). Thus,

the problem of finding the magnetic structure of 104 spins in the unit cell

has been reduced, i.e. simplified to the magnetic structure of 8 cluster

spins. This cluster assumption is the only reasonable construction which

avoids overlap of the clusters, since the next possible construction invokes

32 clusters. However, although these clusters do not overlap, one has to keep

in mind that the Fe-Fe distances within a cluster are as large as between the

clusters (see inset in Fig.3.4). Four different antiferromagnetic structures

were constructed and they are illustrated In Fig.3.19. Models A, C and D can

be rejected because they require the distinct presence of the (1,0,0) and

(1,1,1) reflections, which are definitely not present in the diffractogram at

4.2K (see Fig.3.17). Additionally, the refinement analysis of these models

results in a magnetic reliability factor R^gi, of 90-100%, which is

considerably worse than ^magn~^^ ^ o r m°del B at the same stage of the

refinement. Furthermore, the extinction conditions for the magnetic

reflections of model B are fully consistent with our findings: h,k,l all

mixed;h+k=»even, h+l=*odd, k+l=odd; and all h,h,l with h»odd or zero forbidden.

49

. • - - - , ( - - • - . «

4> =•• !

V*model b

. 3.25. JTje /our1 models for the antifevvomagnetie structure of

La(FexAl2_x)i^' Eaah spin represents the total spin of the cluster

of thirteen atoms. The dashed lines are guides to the eye, and the

solid lines indioate the magnetic unit aell.

Table 3.1.

Results from the refinements analysis for of model B

a

y

z

d

B

M/Fe

"Fe1

MFeII

RNucl

RMagnv 2

A

AA2

B%

%

x=0.69

300 K

11.7378(3)

0

0

2

0

-

-

-

2

-

.17720(7)

.11399(7)

.470

.64(5)

.2

13.0

4.2 K

11.7235(3)

0

0

2

0

1

-

-

1

3

6

.17738(6)

.11369(7)

.440

.22(6)

.41(8)

.8

.0

.8

x=0.91

300 K

11.5788(3)

0

0

2

0

-

-

-

1

-

8

.17869(6)

.11591(6)

.466

•61(5)

.3

.6

4.2 K

11.5932(3)

0.17938(6)

0.11624(7)

2.478

-0.04(5)

2.05(3)

1.10(7)

2.14(3)

1.3

21.4

5.1

a is the lattice parameter, y and z are parameters of the NaZnjS-type arystau

structure, d is the distance betaeen Fe1 and Fe*1', B the overall temperature

factor, mpel and the magnetic moment of Fe1 and Fe11 atoms,

respectively, Rffuai and R^an the reliability factor of the nuclear and

magnetic structure, respectively, defined as R=\\l(obs)-I(calc)\/I(calc) and

X v2 is defined as XV

2=I W^[yJiobB)-y^aalc)l'l/\, with yi(obs) and y^(calc) the

observed and calculated values of the i, measuring point, w^ its statistical

weight and v the degrees of freedom.

50

Therefore, we conclude that model B represents best the magnetic structure.

The best-fit for model B is obtained with the central Fe1 spin parallel to the

cluster spin and with a different Fe^ moment with respect to the surrounding

Fe*^ moments. Allowing the spins to make an angle with the z-axis did not

improve the fit. The final results of the refinement analysis are given in

Table 3.1. A magnetic moment of 2.14(3)u_/Fe for the Fe*1 moment

and 1.10(7)u. /Fe for the Fe moment have been obtained. From saturation

magnetisation experiments in a field beyond the spin-flip field (9.5T), we

found a value of 2.13(l)n„/Fe • Hence, the neutron measurements indicate thata

the Fe moments have no pronounced change of moment, going from the

antiferromagnetic state to the field induced state. However, they suggest that

the Fe atoms do have a severe change of moment.

The Mössbauer spectra are less revealing in this respect, since they do not

clearly show an additional spectral contribution in the antiferromagnetic

state with a hyperfine field of about half the value, resulting from the

reduced Fe moments. Such is not surprising since one has to take account of

the fact that the additional spectrum would have only a relative intensity of

8%. In the second place, it cannot be excluded that there is a substantial

change in the transferred hyperfine field, when changing from ferromagnetic to

antiferromagnetic order. For the Fe-1 and Fe moments this change may be of

opposite sign, leading to a decrease in the total hyperfine field for the Fe 1 1

moments (see below), but to an increase for the Fe1 moments. Consequently, the

corresponding two subspectra might not show a large difference in hyperfine

field splitting at all, and the Fe* subspectrum could then be undetectable. As

can be seen from Fig.3.18, the drop in the mean-effective hyperfine field at

the magnetic phase boundary is not reflected in a jump in the isomer shift.

This means that the s-electron density at the Fe nuclei does not change, which

suggests that the drop in the mean-effective hyperfine field is mainly

associated with a change in magnitude and/or sign of the transferred hyperfine

field when passing the magnetic phase boundary.

The model B that we propose for the antiferromagnetic structure of

La(FexAl^_x)^3 may certainly not be interpreted as a determination of the

exact magnitude and direction of each individual magnetic moment. This model

is limited by the above assumptions of clusters and by the fact that we are

treating a pseudo-binary compound leading to various surroundings of the Fe

atoms by both Fe and Al atoms. Rather, exact magnitude and direction of the

moments are determined by the local magnetic environment of each Fe moment,

which may be concluded from the distribution of hyperfine fields in the

51

Mossbauer measurements [63]. However, we believe that our model reflects the

basic symmetry of the magnetic order, in view of the rather good reliability

factor Rmagn» the fulfilment of the extinction conditions, and the occurrence

of spin-flip transitions in relatively low magnetic fields (see below). This

means that the magnitude of the moments as obtained from the refinement

analysis (2.14|ig/Fe) must be considered as an averaged moment. However, as the

magnetisation also yields an averaged moment (2.13uB/Fe), the excellent

correspondence of the results further supports our model.

These results can be summarized as follows. We have found a new type of

metamagnetic compound, where ferromagnetic (1,0,0) planes of clusters

(icosahedra plus central atom) are formed and coupled antiferromagnetically.

Therefore, it is possible to spin-flip the system in relatively low magnetic

fields (H<15T) to an induced-ferromagnetic state[12]. The La(Fe,Al)13 compound

can thus be compared with other metamagnets with layered structures like

Au2Mn[27,28], HoNi[30], Pt3Fe[36], etc. Here there are also ferromagnetic

interactions within a layer and antiferromagnetic interactions between the

layers. However, for the latter compounds the layers are sheets of single

atoms, whereas in La^e.Al)-^ the layers are planes of clusters. Furthermore,

the layers in La(Fe,Al)i-> are not separated but directly adjacent to each

other, whereas in compounds like Pt3Fe and Au2Mn the ferromagnetic layers are

separated by another kind of atoms, either magnetic or nonmagnetic.

Finally, a confirmation of the reduction of the magnetic moments on the Fe*

atoms (l.lu /Fe) requires more specific information. No conclusive evidence

can be obtained from our neutron measurements, unless the cluster assumption

can be justified. Still, calculations of the magnitude of the Fb-moment have

indicated an instability of the magnetic moment, in an fee lattice, leading to

a moment reduction [67,68]. Thus, it was found that the Fe moment decreases

with decreasing atomic radius of the Fe atom in an fee lattice[68]. In

La(Fe,Al)j^ the Fe atoms have an fcc-llke local environment and furthermore,

the smallest atomic volume of the Fe atoms is found at the highest Iron

concentration, where the antiferromagnetic state arises. Hence, the moment

reduction of the Fe1 atoms Is likely to occur.

52

3.7 The critical behaviour of La(Fe,Si)jy

3.7.1 Introduction

La(FexSi1_x)13 can be stabilized in the NaZn^-type crystal structure in a

much smaller concentration regime than La(FexAl^_x)^3> viz. 0.8<x<0.9. It

will be shown that La(Fe,Si)j3 has similar Invar characteristics as

La(Fe,Al)13. In addition La(Fe,Si)j3 exhibits a pronounced critical behaviour

in ac susceptibility and electrical resistivity. Finally, the substitution by

Si instead of Al makes it possible to compare both systems. Here, no anti-

ferromagnetic phase is found, although the iron concentration is higher than

in La(Fe,Al)^3 at the ferrofagetic-antiferromagnetic phase boundary.

3.7.2 Experimental results

In the entire concentration regime of La(FexSii_x)13 ferromagnetic

behaviour was found. The transition from ferromagnetic to paramagnetic

behaviour is clearly observed by a steep decrease in the ac susceptibility. In

Fig.3.20 we show an x=0.862 sample as a typical example. Again, deviations

from the inverse demagnetizing factor at low temperatures were observed below

50K for all samples. However, this anomaly can easily be suppressed by

applying small magnetic dc fields. From these measurements the Curie

3ua

0.

1.0

0.8

O.6-

0.4(- L a (FexSii-x">|3X= 0.862

0.2-

0

' *i

100 200T(K)

300

Fig. 3.20. Temperature dependenee of the aa susceptibility in

with x=0.862.

53

280

260-

24O-

220

200-

180O.8O O.90

Fig* 5.21. Concentration dependence of the Curie temperature Tg and the

saturation moment \ig for ha(Fe^i^_x)23.

La(FexSi, Jx J ' i-x'i3

J i_100 200 300

T(K)

Fig. 3.22. Temperature dependence of the electriaal resistivity p of

54

temperature can be accurately determined. In Fig.3.21 we plot the iron

concentration dependence of the Curie temperatures and the saturation magnetic

moments. The Curie temperatures have the same temperature dependence, but are

higher, when compared to La(Fe,Al)^.j, whereas the saturation magnetic moments

lie on the same line (c.f. Fig.3.12).

The results of the electrical resistivity measurements p(T) are shown in

Fig.3.22. Particularly, in the compounds with x=0.854 and 0.862 there is a

pronounced cusp at the ferromagnetic-paramagnetic transition. The extreme

sharpness of this transition can be observed when plotting the temperature

dependence of dp/dT in the region near Tc(see Fig.3.23). The Curie

temperature, determined by ac susceptibility, is always higher then the

minimum of the slope, dp/dT, and is indicated by arrows in Fig.3.23- In

Fig.3.24 we show the the temperature dependence of dp/dT of one particular

compound (x=0.862) in a larger temperature regime.

0.12

0.08

0.04

0-

-1 r - [ - -

-0.04;-

- 0.08 -

-0.12150

T(K)

La(FexSi,.x)I3 H

a 0.862b 0.B54 ;c 0.846 -*d 0.838 |e 0.831 I

1_. I X l..J_.._L. J250 300

Fig. Z.2Z. Temperature derivative of the electrical resistivity dp/dT of

several La(FexSi2^x)23 compounds near Tff. The position of Ta is

indicated by arrows.

55

0.15-

100 200T(K)

300

Fig. 3.24. Temperature dependence of dp/dT between 4 and 300K. The position

of Ta ie indicated by an arrow. The inset shoue the calculated

temperature dependence of dp/dT of the phonon part p . of the

electrical resistivity in the oompound Fe^Pt (taken from Viard and

Gavoille [51]).

-4

-6

La(FexSi,_x)

X= 0.86213

-6.6 -5.8 -5.0 -4.2 -3.4 -2.6 -1.8In (T-Tc) / Tc

Fig. 3.25. Log -plotted versus log(T-Tc)/Ta for La(Fe3Si1_x)13 withx=0.862.

56

3.7.3 Magnetic properties

It is surprising that the transition from the ferromagnetic to paramagnetic

state is so extremely sharp. Namely, we may expect a broad distribution of

exchange fields due to the various local environments of the 3d-atoms, leading

to a smearing out of the transition (see e.g. Fig.3.20 and 3.23). Yet, it

turns out that these compounds behave like textbook-type ferromagnets where

for T>TC the susceptbility can be represented by[69]

X ~ (T-Tc)~Y .

It can be observed from Fig.3.25 that this power law behaviour is observed

over 1^ decades of reduced temperature. The slope of the straight line

corresponds to y=1.38(2) for x=0.862 and y=1.37(2) for x=0.831. The value of

y for <x-(bcc)-Fe equals 1.33. These experimental values of the critical

exponent y may be compared with the theoretical values of y=1.24 for the

three dimensional Ising model and y=1.38 for the isotropic Heisenberg model.

The excellent agreement between the experimental valaes and the value derived

for the isotropic Heisenberg model demonstrates the isotropic exchange, which

can be expected for these compounds with high Fe-Fe coordination number and

cubic crystal structure.

Nevertheless, this critical behaviour was not observed for the LaCFe.Al)^

compounds. This might be due to a reduced critical regime of LaCFe.Al)-^ with

respect to LaCFe.Si)-^, or to the latent antiferromagnetism in the ferro-

magnetic state of La(Fe,Al)j-j which is less in La(Fe,Si)^j>

The Fe concentration dependence of the Fe magnetic moments in La(Fe,Si)-L-j

is equal to that observed in La(Fe,Al)13 and the moment increases with

increasing Fe concentration. This behaviour reflects the fact that a substi-

tution of Fe by either Si or Al reduces the exchange splitting between the

majority and minority band by the same amount. However, the increasing moments

are accompanied by a decrease of the Curie temperature. This peculiar

behaviour is also observed in Invar alloys, and has been associated with a

suppression of the spin-fluctuations near the instability of the ferromagnetic

state. We will show that this Invar behaviour is reflected in the critical

behaviour of the electrical resistivity.

57

3.7.4 Electrical resistivity.

It was shown In Fig.3.22 that a sharp cusp in p(T) develops with increasing

Fe concentration in La(Fe,Si)^3, leading to a negative divergence in dp/dT at

the highest iron concentration (see Fig.3.23). Such a negative divergence was

also observed in LaCFe.Al)^. Therefore, it must again be concluded that the

critical behaviour is dominated by a lattice softening near T c associated with

the Invar effect.

Viard and Gavoille[51] calculated the phonon part of the resistivity p of

the Invar compound Fe3?t. They used the experimental values of the bulk

modulus B to calculate p via the relation p , ~B (l-gw)T. Here g is a

constant near unity and u the lattice expansion. Neglecting the effect of the

lattice expansion, they used dp . /dT~B • Although the compound Fe-jPt is

different from the compounds La(Fe,Si)^-j, there are also similarities such as

the high Fe concentration and the cubic symmetry. Due to lack of more

appropriate data, we have reproduced the results of Viard and Gavoille in the

Inset of Fig.3.24. Comparison with the data shown in the main part of the

figure illustrates that the dp h/dT behaviour obtained by these authors has

essentially the same features as those in the La(Fe,Si)^3 compounds. First,

the negative divergence is well reproduced, and second, the Curie temperature

is a bit higher than the temperature of the divergence. The latter property is

in excellent agreement with our experimental results and Is in contrast with

the calculations of the spin scattering part of the resistivity of de Gennes

and Friedel[47], Fisher and Langer[49] and Kim[48].

A final remark must be made on the critical behaviour of the electrical

resistivity of the La(Fe,Al)^3 compounds. Here it was found that the critical

behaviour is dependent upon the thermal history of the sample. The largest

critical behaviour was found when measuring the resistivity with decreasing

temperature through Tc< Also a larger critical behaviour was observed when

heating through Tc, when the initial temperature of heating was higher, i.e. a

larger citical behaviour was found by starting the experiment at liquid

nitrogen temperature than by starting it at liquid helium temperature. These

differences of the resistivity relative to the value in the paramagnetic state

can easily amount to a factor of two. The resulting changes in the absolute

value of the resistivity are, however, small (less than 0.6%). A time

dependence was excluded (less than 0.03% in 40 hours). These cooling/heating

measurements have not been performed on the La(Fe,Si)^3 system and are at

present not understood.

58

3-8. Summary

Iron-based magnetism and the related Invar problem are a long-standing but

fruitful area of research, which still retains a topical interest. We have

added two new intermetallic compounds La(Fe,Al)j3 and La(Fe,Si)^3, to the list

of such Materials by studying them via a wide variety of experiments. The

former compound has a most unusual magnetic phase diagram, consisting of a

mictomagnetic, ferromagnetic and antiferromagnetic regime. The ferromagnetic

state can be recovered from the antiferromagnetic state, by applying

relatively low magnetic fields- This unique proptrty gives insight into how

fundamental properties, like electrical resistivity and magnetostriction,

probe the magnetic state of the compounds. The electrical resistivity is

discussed in terms of the two spin-current model. The magnetostriction is

analysed with a combined band and local-moment model, from which was concluded

that the local-moment term is dominant. Finally, neutron scattering

experiments have revealed the symmetry of the long-range ordered

antiferromagnetic state, which was described with ferromagnetic sheets of

clusters, coupled antifeiromagnetically. Thus, these new materials have not

only been characterized, but they offer themselves as test systems for future

comparisons with the theory of iron-based magnetism.

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62

Magnetic Properties and Electrical Resistivity

of Several Equiatomic Ternary U-Compounds

Abstract

The magnetic properties and electrical resistivity were studied for several

equiatomic ternary (1-1-1) intermetallic compounds of formula RTX with R=Hf,

Th and U, with T a transition metal (Co, Ni, Ru, Rh, Pd, Ir, Pt and Au) and

X=A1, Ga, Sn and Sb. These compounds crystallize in three different crystal

structures: the cubic MgAgAs-type, the hexagonal Fe2P- and Caln2-types of

structure. All U-compounds exhibit magnetic moments of about 3 ja /U at higha

temperature and encompass U-U distances from 3.51 to 4.68 A. For the compounds

with the largest U-U distances, Kondo-lattice behaviour was observed. However,

these compounds have an electrical resistivity up to 3 orders of magnitude

larger than that expected for U-based intermetallic compounds. The Hf- and Th-

based compounds serve as nonmagnetic reference materials, in which also

anomalously large resistivities were observed.

4.1. Introduction

The magnetism of U-based compounds has recently attracted great interest,

especially since the discovery of the strongly interacting, heavy-fermion

systems. Here, anomalous metallic behaviour was found resulting in

enhancements of the specific heat, magnetisation, etc. due to hybridisation of

the conduction electrons with the 5f-electrons.

In the present investigation we have studied the equiatomic ternary RTX-

compounds where R is Hf, Th, U and T a transition metal and X a group

(III,IV,V) element (Al,Ga,Sn and Sb). Both local-moment magnetism and Kondo-

lattice effects were observed for these compounds, depending on the V-V

separation. Interestingly, for the compounds with the highest U-U separation,

semiconducting-like behaviour was found in the electrical resistivity, whereas

the magnetism exhibits Kondo- lattice properties.

63

4.2. Experimental procedures and results

The samples were prepared by arc melting the constituent elements of at

least 99.9% purity under purified argon gas. After arc melting the samples

were wrapped in Ta foil and vacuum annealed at 800°C for 2-3 weeks. The

crystal structure was determined by X-ray diffraction and the atomic positions

were obtained by an intensity analysisfl]. The ternary compounds were found to

crystallize in three crystal structures: the cubic MgAgAs-type and hexagonal

Caln2- and Fe2P-types of crystal structures. The distinction of these three

catagories of structures will be used throughout this chapter.

4.2.1. Crystal structure

The compounds (U,Th)NiSn, (U,Th,Hf)RhSb and (U.Th.Hf)PtSn crystallize into

the cubic. MgAgAs-type structure with F43m space group symmetry (No. 216) shown

in Fig.4.1. The lattice parameters, a, and R-R distances, d, are indicated in

table 4.1. The intensity analysis of ThNiSn yielded the best reliability

factor when placing the atoms in the following positions: Th at (\, \, \), Ni

at (0,0,0) and Sn at (I, \, % ) . The complete crystal structure is constructed

out of three interpenetrating face-centered cubic sublattices, with the above

positions as the sublattice origins.

Fig. 4.1. Crystal structure of the MgAgAs-type compounds as observed for

UliiSn. Filled oiroles U; larger open airolee N-i; smaller open

airales Sn.

The compounds UPd(Sn.Sb) and UAuSn crystallize in the hexagonal Caln2-type

crystal structure with space group symmetry P63/HHHC (No. 194) which is shown in

Fig.4.2. The U-atoms occupy the 2b-sites (0,0,^) and Pd and Sn the 4f-sites

(1/3, 2/3, z) with z»0.045. The lattice parameters a,c and R-R separation

d(*%c) are given in table 4.1. The U-atoms form trigonal prisms which are

slightly up and down centered by the Pd and Sn.Sb atoms.

64

Fig. 4.2. Crystal struature of the Caln2~type compounds as observed fov

VPdSn. Filled airoles U; open circles Pd and Sn.

The third group of compounds crystallizes in the Fe2P-type crystal

structure with space group symmetry P62m (No.189). This group comprises the

compounds UNiAl, (U,Th)NiGa, (U,Th)CoSn, URuSb and U(Ru,Rh,Ir)Sn, and is one

frequently encountered for equiatomic ternary compounds[2]. An intensity

analysis of the X-ray pattern of ThCoSn gave the following atomic positions:

Th at (x,0,*0, Co at (0,0,5j) and (1/3, 2/3, 0) and Sn at (y, 0, 0) with

x=0.583 and y=0.255. This results in a crystal structure as shown in Fig.4.3.

The lattice parameters and R-R distances, using this value of x are given in

table 4.1. The U-atoms are stacked in layers perpendicular to the c-axis.

Fig. 4.3. Crystal structure of the FesP-type compounds as observed for UCoSn.

Filled airoles U; larger open circles Sn; smaller open circles Co.

4.2.2. Magnetic properties

The magnetic properties are closely related to the different crystal

structures and will thus be separated in'io three groups. As Hf and Th do not

carry a magnetic moment, these compounds can be disregarded and only the U-

and Co-based compounds will be discussed here. In the MgAgAs-type compounds,

UNiSn, URhSb and UPtSn all are magnetic. The high temperature susceptibility

measurements yield an effective moment of 3.08, 3.25 and 3.55 n /f.u. and

Curie-Weiss temperatures of -75, -111 and -100K for UNiSn, URhSb and UPtSn,

65

respectivelyfl]. In spite of these large antiferromagnetic interactions at

high temperature, no standard local-moment antiferromagnetic ordering is

observed at low temperature. UNiSn has a change of slope in the M-T curve,

URhSb a broad maximum at 40K and UPtSn only shows a leveling off of the Curie-

Weiss increase of the magnetic susceptibility below about 75K. These effects

are illustrated in Fig.4.4. The two step-like anomalies in the M-T curve of

UPtSn at 25 and 5K can probably be ascribed to a segregation of 0.3% of the

Calii2 UAuSn

UPdSb

(JPdSn

Fe2P UIMA1

UNiCa

ThNICa

UCoSn

ThCoSn

URhSn

URuSn

UlrSti

URuSn

MgAgAs UNISn

ThNlSn

LaNiSn

URhSb

ThRhSb

HfRhSb

UPtSn

ThPtSn

HfPtSn

d

A

3.60

3.61

3.65

3.51

3.51

3.67

3.72

3.84

3.83

3.S3

3.84

3.85

4.51

4.63

a

A

4,717

4.587

4.608

6.733

6.733

7.057

7.145

7.383

7.365

7.345

7.375

7.385

6.385

6.544

(E-TlNlSt)

4.62

4.71

4.41

4.68

4.77

It.lib

6.534

6.66

6.238

6.617

6.749

6.310

7

7

7

4

4

4

3

c

A

.208

.215

.310

.035

.022

.019

.994

4.057

3

3

4

3

.993

.947

.012

.915

raagn.

a.f.

ferro

a.f.

a.f.

a.f.

p.p.

ferro

H.ferro

ferro

ferro

ferro

ferro

Ko

p.p.

p.p.

Ko

p.p.

p.p.

Ko

p.p.

p.p.

TN,CK

35

65

29

21

38

85

43

25

58

25

35

47

40

"75

9CWK

-4

+70

-10

+2

+28

+25

+8

+55

+20

+30

-75

-111

-100

"eff

3.06

2.92

3.16

1.70

2.71

3.0

3.43

2.61

2.86

3.04

3.08

3.25

3.55

0

1

1

1

1

0

0

"B

.70

.30

.28

.37

.13

.62

.60

H,

T

2

0,

0.

0.

0.

0.

C(4K)

.40

.38

.02

25

58

58

P(4K)

HQcm

650

3500

430

215

95

32

170

47

50

120

105

262

400

5700

25

72000

2640

385

19000

2600

28000

p(300)

610

5300

1500

255

325

110

300

200

320

420

295

302

1325

2770

360

68000

3000

850

36000

4800

14500

pmax

Mficm

650

5300

1500

255

325

110

300

200

320

420

295

302

7000

5700

360

80000

3000

850

40000

4800

28000

flp/p

10-3

-82

-6.5

-620

+10

-13

+4.2

-28

-20

-27

+3.3

+8.1

+5.0

+13

+2.7

y

mJ

molK2

62

4.3

160

59

53

3.7

IB

1.5

12

2.1

11

2

SDK

179

-

215

228

198

214

185

-

Table 4.1. Salient properties of the (1-1-1) compounds: structure, nearest

aatinide separation d, lattice parameters a and a, type of mag-

netism, Curie and fleet temperatures Tc and T$s Curie-Weiss

temperature 6 , effective moment \x „„, saturation moment(sW ejj

(i . eoeraive field Hg at 4K, eleatriaal resistivity p at 4K and

300K and the maximum value p ^ the relative resistivity change

Ap/p at 4K and 5T, linear specific heat coefficient \ and Debye

temperature 6^.

66

binary compound UPt, assuming a saturation magnetic moment of 0.4 u /f.u. for

UPt[3]. Namely, the magnitude of the step-like anomalies is independent of the

applied magnetic field, whereas the ac susceptibility diverges at 25K and 5K.

The magnetisation loops (M-H) yield a nearly linearly 'icrease of the

magnetisation in magnetic fields up to 5T for all three compounds.

For the Caln2~type compounds, UPdSb orders ferromagnatically and UPdSn and

UAuSn antiferromagnetically. The magnetisation curves (M-T) are shown in

Fig.4.4 and 4.5. UPdSb has its Curie temperature at 65K and a remanent

magnetisation of 0.65 n /f.u. The magnetisation loop at 1.57K exhibits very

sharp transitions at the coercive field (see inset Fig.4.5). This is

indicative of narrow domain wall ferromagnets, or equivalently, a very large

magnetic anisotropy. UPdSn and UAuSn order antiferromagnetically at 29K and

35K, respectively. Additionally, UPdSn exhibits a spin-flip transition at 4T

at 1.58K which is not completed at the maximum available magnetic field of 5T.

30

~5

3

I

A

++ +

+ ++ •

++

- n \

+ '

i

1 '

* UNi Sno URhSb* UPtSn

* UPdSn 1x0.75)* UAuSn(xO.75)'

++•

+V +

i i

100T (K)

200

Fig. 4.4. Temperature dependenoe of the da susceptibility of the U-based

compound with the MgAgAs-type avystal structure: USiSn, UHkSb and

UPtSn and u-ith the CaXn^-type crystal structure: UPdSn and UAuSn.

67

0.6

CD

0.2

oo

X> °o oo o

o'J 1

poo

cx»bo o o o o oiqoooooo^ ^

oo o

ooo

1T

2 0 2h,H IT)

UPdSb

o o o po o O | o o O[ 0

100 200T (K)

300

Fig. 4.5. Temperature dependence of the magnetisation in a field of IT and

remanenoe of UPdSb. The inset shows a reotangulav hysteresis loop

at 1.57K.

0 50 100T(K)

Fig. 4.6. Temperature dependence of the magnetisation of several FesP-type

eompotnde measured in various magnetic fields: UNiGa in 2T, UCoSn

in 0.ST and URulSn,Sb) in IT. The ineet shows a whasp-tailed

magnetieation loop for UNiGa at 4.SK.

68

The U-based compounds with the Fe2P~type structure all order

ferromagnetically except for the antiferromagnets UNiAl and UNiGa, and the

magnetisation curve of several compounds is shown in Fig.4.6. The Curie

temperatures Tc vary from 25K for URhSn and UlrSn to 85K for UCoSn. The values

of T„ are given in table 4.1, as well as the Curie-Weiss temperatures, the

saturation magnetisation, the coercive field and the effective moment. There

is no obvious relation between the lattice parameters and the parameters

describing the ferromagnetic state. All ferromagnetic compounds exhibit

standard ferromagnetic hysteresis loops (M vs. H). For UCoSn it is not clear

whether Co also carries a (small) magnetic moment. The value of the effective

moment (3.0 \i /f.u.) is comparable to the values of the U-moment of the otherD

compounds. Still, it might explain the larger value of Tc in this series of

compounds. The related compound ThCoSn exhibits very weak magnetism, and here

only 1.4xl0~2 p,„/f.u. can be induced with 5T at 4K. It is not clear whethera

ThCoSn exhibits an (itinerant) ferromagnetic ordering, since an Arrot-plot

analysis (see Fig.4.7) yields straight lines indicating a magnetic ordering at

43K. However, the straight lines are only observed at high magnetic fields

where the free-energy expansion, which is the basis of this analysis, is no

longer valid[4]. The negative slope of M vs H/M indicates a metamagnetic

transition at low temperature and these observations might indicate an

Fig. 4.7. Arvot-plot (Ms ve H/M) of ThCoSn.

69

1 >

/ URhSb %i

- YJSmsnX

j \\sHfptSn \ ^

•

2

8 -

vf§6O!

0 200 400 600 800 1000T IK)

Fig. 4.8. Temperature dependenae of the eleotriaal resistivity of the MgAgAs-

type aompounds (U,Th)NiSn, (U,Hf)PtSn and URhSb. The inset shows

log p vs T1 between 500 and 1000K.

I*— 3

JhNiSn

ThRhSb

100 200T(K)

2000

1500

UPdSb(/3)

UAuSn

-i 1 . L100 200

T (K)300

Fig. 4.9. Temperature dependenae of the eleatriaal resistivity of the MgAgAs-

type aompounds (La,Th)NiSn, (Hf,Th)RhSb and ThPtSn.

Fig. 4.10. Temperature dependenae of the electrical resistivity of the Calns-

type aompounds UPdSn, UPdSb and UAuSn.

70

induced-type of ferromagnetic ordering. UNiAl and UNiGa are the only

antiferromagnets with the Fe2P~type structure. For UNiAl the magnetisation

increases linearly with magnetic field up to 5T. However, UNiGa exhibits a

sharp metamagnetic transition in relatively low magnetic fields. The small

remanence can be ascribed to an impurity phase. Previously, this "whasp-

tailed" magnetisation loop was ascribed to the domain wall pinning of a

ferromagnetic state[5], as is observed for the Perminvars (Fe-Ni-Co)[6J.

Neutron diffraction measurements are required to solve this discrepancy in

interpretation.

4.2.3. Electrical resistivity

The electrical resistivity of the MgAgAs-type compounds is shown in Fig.4.8

and 4.9. The resistivity is high for most compounds and reaches a maximum

value of 8xlO^uRcm for URhSb at 150K, about three orders of magnitude larger

than expected for typical intermetallic compounds[7]. At high temperature the

resistivity decreases and in order to investigate the high temperature

behaviour, we have extended the measurements for some compounds up to 1000K.

Here, an exponential decrease of p(T) is observed as is illustrated in the

inset of Fig.4.8. This behaviour is characteristic for semiconductors and

therefore we have applied the formula appropriate for intrinsic

semiconductors: p~exp (E /2kgT). This yields an energy gap of 0.12eV for

UNiSn, 0.44eV for URhSb and 0.34eV for UPtSn. Such behaviour is not only

characteristic for the U-based compounds, but is also observed for the Th and

Hf-based compounds, as is clearly illustrated by the behaviour of ThNISn and

HfPtSn (see Fig.4.8). Below room temperature there are substantial deviations

from the exponential behaviour, which must be ascribed to non-intrinsic

behaviour. For comparison, the behaviour of LaNiSn is given as an example of

normal metallic behaviour. However, this compound has a totally different

crystal structure (e-TiNiSi)[8]. The maximum in resistivity of UNiSn at 55K

does not coincide with the anomaly in the magnetisation but is 8K higher. On

the other hand, URhSb and UPtSn do not exhibit any pronounced anomaly in the

electrical resistivity of magnetic origin.

The compounds with the Caln2~type structure also have a large resistivity

and are shown in Fig.4.10. The magnetic phase transition marks for all three

compounds a change of slope in the resistivity. The resistivity of UPdSb might

be overestimated because the enormous brittleness of the sample and the

suspected existence of micro-cracks. Still, the magnitude of the resistivity

of UPdSn and the shape of the temperature dependence of the resistivity of

71

— 200oa200

100

100 200T (K)

100 200T (K)

300

Fig. 4.11. Temperature dependence of the electrical resistivity of the Fe^p-

type compounds (U,Th)NiGa, (U,Th)CoSn and UltiAl.

Fig. 4.IS. Temperature dependence of the eleatriaal resistivity of the Fe2P-

type compounds V(Ru,RhjIr)Sn and URuSb.

of- O'o

oa.1

S -40I

X

-80

•

'o 1

• o

1

**§

UNiSn

- A

d'

)

, T

n n r

\

50(KI

1

-

\

1001

o—o T =

\\

1

100K

-

t>50 ~toiOD20

-

b

IT)Fig. 4.13. Magnetic field dependence of the reeietivity ahange Ap/p for UNiSn.

The ineet shows the temperature dependence of the magnetoreeistanae

coefficient, a(T) (eee text).

72

UAuSn, arouse the suspicion of the existence of an energy gap also for these

compounds •

The compounds with the Fe2P-type structure have large resistivities up to

430|iQcm, but do not exceed the limits of metallic behaviour- The ferromagnetic

transitions are clearly discerned by a change of slope in the resistivities

(see Fig.4.11 and 4.12). For two U-compounds the contribution of the non-

magnetic scattering processes can be deduced from the behaviour of the

corresponding Th-compounds, viz. UNiGa and UCoSn. The compound URuSb deviates

from all other ferromagnetic compounds by having a negative temperature

coefficient of p(T) below Tc- The antiferromagnet UNiAl has a maximum in the

resistivity below T^ and has not reached its residual resistivity value at 2K.

4.2.4. Magnetoresistivity

The magnetoresistance of several compounds was measured at fixed

temperature between 4 and 100K. In Fig.4.13 and 4.14 we plotted the relative

resistivity change of UNiSn and UPtSn, respectively, both of the MgAgAs-type

structure. UNiSn has a negative magnetoresistance at all temperatures, which

varies almost quadratically with the magnetic field. This H2-dependence is

especially accurate up to 7T for temperatures above 40K. Therefore, we show in

the inset of Fig.4.13 the temperature dependence of the coefficient a(T)

defined as p-p =-a(T)H2 in the low magnetic field limit. We observe a maximum

in the magnetoresistivity coefficient a(T) at about 40K. At this temperature

there also is a sharp maximum in the resistivity and an anomaly in the

magnetisation. Above this temperature the magnetoresistivity decreases

rapidly. For UPtSn we observe a positive magnetoresistivity at low

temperature, which turns negative for T>20K. The inset of Fig.4.14 shows the

temperature dependence of the magnetoresistivity coefficient a(T) which has a

maximum for T»30K.

For URhSb a negative magnetoresistance was observed at all temperatures. At

T=10K and \i H=7T, we found Ap/p=-O.O3 which then rapidly decreased for

T*30K. Above 30K the relative resistivity change is less than 5x10"^ in fields

up to 7T. ThPtSn exhibits a positive magnetoresistivity and nicely obeys the

quadratic field dependence in the entire temperature regime from 4 to 100K.

The coefficient a(T) varies linearly with temperature from -7xlO~4T~2 for T=0

to 0 for T=100K. The remaining compounds in the MgAgAs structure have a

magnetoresistivity as indicated in table 4.1.

The magnetoresistivity of the compounds with a hexagonal structure is also

indicated in table 4.1. Here, it is worth mentioning that UNiGa has a

73

resistivity decrease of 60% at 1.4T. At higher fields the resistivity changes

are much smaller. This enormous resistivity change must obviously be related

to the antiferromagnetic •+• ferromagnetic phase transition at 1.4T (c.f.

Fig.4.6).

4.2.5. Hall resistivity

The Hall resistivity was measured on three samples, UNiSn, URhSb and UPtSn.

For all three samples the Hall voltage increases linearly with magnetic field,

except for URhSb where low field deviations were observed below 30K. Here, a

slope dV/dH~10 V/T, was extracted at moderately high fields (between 2 and

5T) where the linear behaviour was observed. From these slopes the electron

density, n, was calculated using the lattice parameters as obtained by the X-

0

Fig. 4.14, Magnetic field dependence of the resistivity change Ap/p for UPtSn.

The ineet shows the temperature dependence of the magnetove si stance

coefficient, a(T) (eee text).

74

ray analysis. For all three samples the dominant carriers are holes. In

Fig.4.15 the temperature dependence of the carrier density n is shown. From

this plot it follows that for all three compounds the conduction electron

density is at least a factor 100 less than expected for metallic behaviour,

viz., 3 conduction electrons per formula unit, and a unit cell of

(6.5xl0~10m)3 yield an expected density of 4xl028aT3.

We observe for all three compounds a rather constant carrier density above

100K. For UNiSn the increase of the carrier density below 40K reflects the

resistivity decrease in this temperature regime. For URhSb the carrier density

is rather constant at low temperature, and the resistivity exhibits no

pronounced changes, accordingly. However, for UPtSn the decrease of

resistivity below 50K Is accompanied with a decrease in the carrier density.

Fig. 4.1 S. Temperature dependenee of the aarviev concentration n for UNiSn,

VRhSb and UPtSn, ae calculated from the Hall resistance

measurements.

75

200

1100-

o

1

4 O

o°°(P ° xxt

a

1

A °O

a

a

o0 x

0 •o * *

X

1

1

O

9

• o

+A

O

o

X

V

1

a

O

+

OX

X

UPdSnUPdSbUCoSnUNiSnURhSbUPt Sn

100T2 (K 2 )

200

Fig. 4.16. Temperature dependenee of the specific heat plotted as C/T ve T2 of

several U-based aompounds.

200

"O

100-

0

X

0

a

•

c

1

ThCoSnTh Ni SnThPtSn

LaNiSn

i r *

ao

x+ 4-

1

Q

O x

• *O O 4

X +

1

0X

°4

+

D x "

0

+

-

o 100

T2 (K2)

200

Fig. 4.17. Temperature dependenae of the speoifia heat plotted as C/T Veseveral Th-based compounds.

of

76

4.2.Ó. Specific heat

We have studied the specific heat of several compounds in order to obtain

more information about the electronic properties. The specific heat of several

U-based compounds is shown in Fig.4.16 plotted as C/T vs T^ from which the

electronic specific heat term y(~N(E )) can be extracted. For comparison,

some Th-based compounds are shown in Fig.4.17. The Y~val»ies vary from 2mJ/mol

K for URhSb up to 62mJ/mol K^ for UPdSb for the U-based compounds. An even

larger value of Y=160mJ/mol K 2 (a "middle weight" heavy-fermion) was reported

for UNiAl[9]. The Th-based compounds all have a yvalue of about 2mJ/mol K2.

4.3. Discussion

4.3.1. Magnetic properties

The magnetism of the investigated compounds must be ascribed to the U-

moments, because of the large magnetic anisotropy in these systems. It has

been argued that the U-magnetism is dominated by the width of the U 5f-band

and only to a lesser extend by its hybridisation with the d- and p-

electrons[9,10]. In other words, the U-bandwidth is a measure for the Coulomb

repulsion between the two spin-bands, which must be sufficiently large to

carry U-moments. The U-bandwidth is critically dependent on the U-U distance.

This concept was introduced by Hill, who found a critical U-U separation of

about 3.5A below which no magnetism occurred and above which U-moments were

found[ll].

In the present investigation all compounds have a U-U separation larger

than the Hill-limit, and a magnetic moment was found accordingly. However, it

appears to be rather difficult to indicate some trends in the magnetic

behaviour, e.g. the influence of the U-U separation or the dependence on the

number of d-electrons of the transition metal element. This is probably

because three different crystal structures are formed. Indeed, the crystal

structure influences the magnetic properties because the U-U interaction goes

via an indirect exchange mechanism, which can be strongly structure dependent.

The U-U separation is too large for a considerable direct exchange mechanism.

The compounds with the smallest U-U separation are found in the Fe2p

structure, viz., UNiAl and UNiGa. These compounds are very near the Hill

limit, which might explain the relatively low values of the effective moment

of 1.7 and 2.7 (i_/U, respectively. The former value is even lower than the

smallest moment calculated from Russel-Saunders coupling: 2.54|j. /U for 5fl,

3.58uB/U for 5f2, 3.62|*B/U for 5f3 and 2.68uB/U for 5f4. Such a small

value of the effective moment indicates a broad U-band due to the small U-U

77

separation- In contrast, the specific heat coefficient y is very large,

Y =160mJ/mol K2, which points to a high density of states at the Fermi level

or alternatively, to a narrow 5f-band. It is not clear at present how to

resolve this contradiction.

The compounds with the largest U-U separation of about 4.6A are found in

the MgAgAs-type crystal structure, viz., UNiSn, URhSb and UPtSn. The magnetism

of these compounds is similar to that observed in the Kondo-lattice systems

e.g. CeAl3 and CeCug[12]. Namely, at high temperature a good U-moment is found

of about 3u_/U with large negative Curie-Weiss temperatures of about -100K,

indicating large antiferromagnetic interactions. Still, at lower temperature

no clear antiferromagnetic ordering is observed and only weak anomalies are

present. For UNiSn a kink-like anomaly is observed at 47K, for URhSb a broad

maximum around 39K, and for [JPtSn no intrinsic anomaly is observed but only a

"levelling off" of the susceptibility to a constant value. The anomaly of

UNiSn at 47K is probably related to a band structure effect as will be

discussed below. Finally, we note that the susceptibility of these three

compounds is very large at helium temperature with a value about 100 times

larger than the value of Pd. All features have also been observed in the

Kondo-lattice systems (see also section 5.5). The remarkable difference with

the Kondo-lattice systems is, however, the reduced number of conduction

electrons in our systems whicli means that the interactions must be mediated by

a superexchange mechanism.

In addition to the U-U separation, also the nonmagnetic group (III,IV,V)

elements play a role in determining the magnetic properties. Substitution of

Sb by Sn in UPdSb preserves the Caln2 crystal structure and lattice

parameters, but the magnetic order changes from ferro- to antiferromagnetism,

the macnetic ordering temperature decreases by a factor of two, and

y decreases by a factor of fifteen. Likewise, URuSb and URuSn differ in Curie

temperature and saturation moment a factor two. As a final example we observe

that substitution of Ni by Ga in UNiAl preserves the crystal structure and

lattice parameters, but causes an increase of the ordering temperature by a

factor two and a decrease of the y value by a factor three. In conclusion, the

type of magnetism is dependent upon both the group (III,IV,V) element and of

the crystal structure. For example, Sn favours a ferromagnetic U-U coupling in

the Fe2P structure, but an antiferromagnetic coupling in the Caln2 structure.

Similar conclusions can be drawn for Al, Ga and Sb.

The dependence of the magnetic properties on the number of d-electrons of

the transition metal element is difficult to trace, because the crystal

78

structure also changes rapidly. E.g., with increasing number of 5d-electrons

we go from Ir via Pt to Au. Here, the crystal structure changes from Fe2l"~ via

MgAgAs- to Cal^-type for UlrSn, UPtSn and UAuSn, respectively.

In conclusion, we can summarize our experimental findings. The magnetism of

the ternary (1-1-1) compounds is dependent on the U-U distance. For U-U

separations less than 4A local moment magnetism was observed and the type of

magnetic order was critically dependent of the crystal structure, the

transition metal element (determining also the U-U separation) and the group

(III,IV,V) element. For U-U separations larger than 4.5A, magnetic properties

were observed similar to those in Kondo-lattice systems, in spite of the

reduced number of conduction electrons-

4.3.2. Resistivity

The electrical resistivity behaviour of the ternary (1-1-1) intermetallic

compounds is critically dependent on the crystal structure. The compounds with

the Fe2P~type structure exhibit normal metallic behaviour. At high temperature

the resistivity is dominated by spin disorder scattering (in case of magnetic

U-compounds). The mean free path is in the order of the interatomic distances

and, therefore, the resitivity cannot increase much further[13]. At the Curie

temperature the spin disorder starts to decrease resulting in a change of

slope of p(T) and a rapid decrease of p(T) with decreasing temperature. At

helium temperature the spin disorder has ceased for all compounds except for

UNiGa. In this case the resistivity can be decreased further, = 60%, by

applying a magnetic field of 1.4T. This contribution to the resistivity must

probably be ascribed to a metamagnetic phase transition. Besides the spin-

disorder scattering, the residual resitivity and phonon scattering contribute

to the resistivity, as can be observed from the behaviour of the Th-based

compounds •

In contrast to the metallic behaviour of the Fe2P-type compounds, the

MgAgAs-type compounds exhibit semiconducting-like behaviour in the electrical

resistivity. Since a semiconducting behaviour Is rather unique for ternary

intermetallic compounds, we will focuss the discussion on this unusual

property in the remainder of this saction.

In spite of the rather high measured resistivity of the compounds with the

Caln2~type structure, it is not completely clear whether this property is due

to intrinsic semiconducting behaviour or is an experimental artifact caused by

many microcracks in the samples. Such suspicions are aroused especially

because no semiconducting behaviour has ever been observed in this crystal

79

structure. In the following we will discuss only the MgAgAs-type compounds.

The discovery of the semiconducting III-V compounds has resulted in the

availability of new and dramatic different semiconductors. A basic requirement

for semiconductivity is the filled valence band of the anions with 8

electrons, viz., "the ionic criterion for semiconductivity". These anions

frequently occupy a face-centered cubic lattice. Then, one or two tetrahedral

holes or the octahedral holes of the fee lattice, or any combination of these

three possibilities, can be filled with the cations, leading to five basic

combinations[14]. The simplest crystal structure is obtained when filling the

octahedral holes, resulting in the NaCl structure. By filling of one of the

tetrahedral holes, the ZnS structure results, in which e.g. GaAs crystallizes.

The CaF2 structure is obtained when filling both tetrahadral holes. When the

two different F-sites of the CaF2 structure are severally occupied by

different atoms, the MgAgAs structure is obtained. This structure can also be

constructed by three interpenetrating fee lattices, with the anion and the two

tetrahedral holes as sublattice origin. For compounds in this crystal

structure, semiconductivity was observed when a group V element occupies the

Ca-sites of the CaF2 structure, e.g. AsAgMg and SbAgMg[14]. Note that these

compounds also obey the ionic criterion for semiconductivity. However,

metallic behaviour was found when the anion occupies the Ca site, e.g. CuSbMg.

Very recently, bandstructure calculations have revealed the phenomenon of

half-metallic ferromagnetism for a MgAgAs-type compound: NiMnSb[15]. Here it

was argued that owing to the loss of inversion symmetry on the Mn-site (i,i,i)

and owing to the large exchange splitting of the Mn d-band, a different

interaction exists between the electrons in the majority spin band with

respect to the minority spin band. This, it was argued, results in metallic

behaviour for the majority band and semiconducting behaviour for the minority

band, where an energy gap was found around the Fermi level.

We conclude from our resistivity measurements that due to the absence of

exchange splitting for both the U- and (Th.Hf)-compounds, there are no spin-

split bands and an energy gap appears around the Fermi-level in the energy

spectrum of all electrons. It is not clear what causes the opening of the band

gap. The occurence of the gap for the Hf- and Th-based compounds indicates

that the gap probably results from an interaction from the d-electrons with

the Sb p-electrons, rather than from the 5f-electrons with the Sb p-electrons.

Nevertheless, at low temperature deviations from the exponential

resistivity behaviour were observed for all MgAgAs-type compounds. These can

be ascribed to impurity states or, more likely, to a temperature dependence of

80

the energy gap, probably induced by the magnetic behaviour.

In order to check the existence of a band gap in these materials, we have

measured the Hall resistivity of three compounds: UNiSn, URhSb and UPtSn.

Assuming there are only electrons or holes, a density of carriers was

calculated of at least a factor 100 less than expected for metallic behaviour.

This further confirms the presence of a band gap. For UNiSn we observe at low

temperature an enormous increase of the carrier density, which explains the

decrease in the resistivity. Probably, the narrow band gap of 0.12eV at high

temperature closes at about 50K, resulting in metallic behaviour at helium

temperature. For URhSb and UPtSn the resistivity decreases at low temperature

with decreasing carrier density. This effect is rather unclear but could be

explained with a decrease of the gap below 100 K, influenced by the magnetic

behaviour.

The suggestion of a band gap is opposed by the non-zero values of the

linear term of the specific heat, y, usually proportional to the density of

states at the Fermi surface- For some compounds we found values for y

comparable to normal metals in spite of the observed high resistivities at low

temperature. For instance, the compound UPtSn has a residual resistivity of

19O0O|i2cm, where a Y=l°*9mJ/ino:1- R 2 w a s observed (in Cu y=0.7mj/mol K^).

Recently, XPS-measurements of UNiSn, URhSb and UPtSn have revealed that a

narrow 5f-band is located just below the Fermi-level[16J. Consequently, the

value of y resulting from the valence electrons, could be enhanced enormously

by the same interactions, present in heavy-fermion systems[12]. Here, y is

enhanced by hybridisation of the conduction electrons with the 5f-electrons,

which are located in a very narrow band (see section 5.5). This effect must be

absent for the Th- and Hf-based compounds, ar. these compounds have no 5f-

electrons. Accordingly, the compounds UPtSn and ThPtSn have y~values

of Y=11 and 2mJ/mol K2, respectively, whereas UPtSn has a much larger residual

resistivity of 19000pQcm than ThPtSn with 26O0[iQcm. Thus in spite of a

significantly smaller conductivity by a factor 7, the value of y is still a

factor 5 larger for UPtSn with respect to ThPtSn. Unfortunately, the accuracy

of the XPS-measurements is not sufficient to reveal the existence of a band

gap-

Finally, it is difficult to check the ionic criterion for semiconductivity

in these compounds, since the valency of the constituent elements is unknown.

Still, the general rule that semiconductivity occurs in this crystal structure

when the group V elements occupy the (0,0,0) sites (with respect to Fig.4.1)

is violated[14]. It is interesting to note that for UNiSn, URhSb and UPtSr, the

81

total number of d-electrons of the unfilled shell of the transition metal

element and p-electrons of (Sn, Sb) is constant. However, a check of the ionic

criterion for semiconductivity is made difficult because compounds with a

different value for the total number of d- and p-electrons adopt another

crystal structure. Here, optical methods or accurate band structure

calculations are more appropriate to study the semiconducting properties.

4.4. Conclusions

The investigated ternary (1-1-1) compounds crystallize in the hexagonal

Fe2P- and Caln2-, and cubic MgAgAs-type crystal structure. The U-based Fe2P~

type compounds order ferromagnetically between 25K and 85K, except for the

antiferromagnets UNiAl and UNiGa. The resistivity is dominated at high

temperature by spin-disorder scattering. For the Cal^-type compounds

ferromagnetic (UPdSb) and antiferromagnetic (UPdSn, UAuSn) behaviour was

observed.

The resistivity of the MgAgAs-type compounds is controlled by an energy gap

around the Fermi level, leading to semiconducting behaviour. The linear

specific heat coefficient y of the U-based compounds is enhanced, with respect

to the value expected from the resistivity measurements, due to hybridisation

of the valence electrons with a narrow 5f-band just below the Fermi level. The

enhancement of the magnetisation gives further support for this picture of a

strongly interacting fermion system, even though these compounds are semi-

conducting. Our experiments indicate that strong, many-body interactions in

the f-band can be present in a semiconductor. This is a most intriguing possi-

bility that warrents further study.

References

Parts of this chapter have been published and can be found in references 1 and

7. This chapter will be revised for future publication.

1. K.H.J. Buschow, D.B. de Mooij, T.T.M. Palstra, G.J. Nieuwenhuys and J.A.

Mydosh, Philips, J. Res. 40 (1985) 313.

2. D.J. Lam, J.B. Darby, Jr., and M.V. Nevitt in The actlnldes: electranic

structure and related properties vol.11, edited by A.J. Freeman and J.B.

Darby, Jr. (Academic Press, New York, 1974) pg. 119-184.

3. P.H. Frings and J.J.M. Franse, J. Magn. Magn. Mater. 51 (1985) 141.

•4. A. Aharoni, J. Appl. Phys. 56 (1984) 3479.

82

5. A.V. Andreev, M. Zeleny, L. Havela and J. Hrebik, Phys. Stat- Sol. 81A

(1984) 307.

6. R.M. Bozorth in Ferromagnetism (D. van Nostrand, Toronto, 1955) pg.171.

7. T.T.M. Palstra, G.J. Nieuwenhuys, J.A. Mydosh, and K.H.J. Buschow, J.

Magn. Magn. Mater. 4-57 (1986) 549.

8. J.L.C. Daams and K.H.J. Buschow, Philips J. Res. 39 (1984) 77.

9. V. Sechovsky, L. Havela, L. Neuzil, A.V. Andreev, G. Hilscher and C.

Schnitzer, J. Less Comm. Met. (preprint).

10. L. Havela, L. Neuzil, V. Sechovski, A.V. Andreev, C. Schmitzer and G.

Hilscher, J. Magn. Magn. Mater. 54-57 (1986) p.551.

11. H.H. Hill, in Plutonium and other actinides, edited by W.M. Miner (AIME,

New York, 1970) pg.2.

12. See e.g. G.R. Stewart, Rev. Mod. Phys. 56 (1984) 755.

13. J.H. Mooij, Phys. Stat. Sol. 17A (1973) 521.

14. W.B. Pearson, in The Crystal Chemistry and Physics of Metals and Alloys

(Wiley, New York, 1972) pg.207.

15. R.A. de Groot, F.M. Mueller, P.G. van Engen and K.H.J. Buschow, Phys. Rev.

Lett. 50 (1983) 2024.

16. H. HSchst, K. Tan and K.H.J. Buschow, J. Magn. Magn. Mater. 54-57 (1986)

545.

83

fffriXD' --o- o

---u-1,o ..O'

OT «x Ca

Fig. 5.1- Crystal etvuituree of the WSySi^ compounds. Theavyetal struature is body-centered whereas thestructure is primitive.

type

84

Magnetic and Superconducting Properties of

Several RToSi2 Intermetallic Compounds

5.1. Introduction.

The ternary (1-2-2) compounds ^2X2, with R a rare earth or actinide, T a

3d-, 4d- or 5d- transition metal and X=Si, Ge, Sn or Pb, have attracted much

interest, because of the great variety in their magnetic and superconducting

properties. This chapter treats both some superconducting and magnetic (1-2-2)

compounds as well as the magnetic superconductor URu2Si2 and is organized as

follows. The first section discusses the metallurgical aspects of the

fabrication of the compounds, as a detailed knowledge of the metallurgy is

indespensible for a correct interpretation of the experimental results. The

next section will treat the superconducting properties of some nonmagnetic

compounds (R=Y,La,Lu). Section 5.4 describes the magnetic behaviour of the

compounds with R=Ce, U and here a guideline for the location of heavy-fermion

behaviour is offered. Finally, in section 5.5 the superconducting and magnetic

properties of the recently discovered heavy-fermion system URu2Si2 are

presented. This compound exhibits a magnetic phase transition at 17.5K and a

superconducting transition at 0.8K, both originating from the heavy electron

system.

5.2. Structure and crystal growth.

The ternary RT2X2~compounds crystallize in two allotropic modifications of

the tetragonal BaAl^-type structure[l]. Most compounds were found in the body-

centered tetragonal ThCr2Si2-type structure[2], and some in the primitive

tetragonal CaBe2Ge2-type structure[3J (see Fig.5.1). LaIr2Si2 even adopts both

structures as a low-temperature and high-temperature modification,

respectively[4]. For the compounds with T»Pt an even lower symmetry than the

CaBe2Ge2~type structure was found, characterized by the absence of an diagonal

glide plane[5].

85

The polycrystalline samples were prepared by arc-melting the pure elements

in a stoichiotnetric ratio in an argon atmosphere. After arc-melting the

samples were vacuum annealed for about 7 days at 900°C. All polycrystals are

contaminated by second phases, sometimes not detectable by standard X-ray

techniques (<5%). However, light microscopy and microprobe analyses can

clearly indicate their presence, in the form of precipitates on the grain

boundaries as well as in a subgrain structure. The origin of these

precipitates is twofold. First, the R and T elements as well as their

silicides, will always contain several percents of their oxides. Second, the

acccuracy of the stoichiometric ratio is limited by weighing accuracy and

melting losses. The occurrence of R-oxides leads to an excess of T-silicides

which may form a three-dimensional network along the grains. This formation of

precipitates can lead to a certain periodicity in the concentration gradients

from grain to grain or to off-stoichiometry in the vicinity of grain

boundaries. The experience is that a heat-treatment at low temperatures (below

1200°C) does not Improve the quality of the polycrystalline samples with

respect to the total amount of precipitates, but only improves the formation

of a larger three-dimensional network of the precipitates on the grain

boundaries. Nevertheless, the heat treatment may on atomic scale result in a

more ideal site occupancy of the T and Si atoms, i.e. a reduction of the site

interchange between the T and Si atoms. When annealing at higher temperatures,

there is the danger of contamination of the samples by the crucible material,

owing to the high reactivity of the rare earth or uranium.

All powder diffractograms were indexed on basis of the tetragonal ThC^Sio-

type structure. This structure is body-centered tetragonal and thus has the

reflection condition that the sum of Miller indices £(h,k,l) must be even.

This condition was fullfilled for all compounds except for CePt2Si2 and UT2Si2

with T«Ir, Pt aiid Au. Here additional lines were observed that could be

indexed with an odd sum of Miller indices. This means that these compounds

either adopt the primitive tetragonal CaBe2Ge2-type structure, or that the T

and Si atoms randomly occupy the 4(d) and 4(e) sites[6]. Powder diffractograms

cannon distinguish these possibilities as both give an identical intensity

distribution. However, recent calculations by Hiebl and Rogl[5] indicated that

the degree of disorder in CePt2Si2 was less than 10%, leading uniquely to the

CaBe2Ge2~£ype crystal structure. This preferential site occupation can also be

expected from the size difference of the T and Si-atoms. Additionally, these

authors found reflections (h,k,0) with £(h,k)»odd, which are symmetry

forbidden in the CaBe2Ge2-type structure. This means that the symmetry is

86

lowered from P4/nmm (CaBe2Ge2> to P4mm (CePt2Si2), with the absence of a

diagonal glide plane. We cannot confirm these latter observations because the

intensity of the (h,k,0) lines in the powder diffractogram is too weak with

respect to our experimental resolution. In all our powder diffractograms we

found a disagreement between the measured and calculated intensities. This

descrepancy likely arises from the preferential orientation in the powder, due

to the easy cleavage in the basal plane-

In addition to the polycrystals, several single crystals were prepared[7].

There are three main reasons to grow bulk single crystals of these compounds.

First, there are large anisotropies in the physical properties, which make an

interpretation of the experimental results on polycrystalline samples

difficult or even impossible. Second, some experimental techniques are only

possible on single crystals, e.g. de Haas-van Alphen measurements. Finally,

the formation of precipitates in the matrix during the crystal-growth

procedure with near-equilibrium conditions Is substantially suppressed. Here,

precipitates are only deposited on the surface and not built into the crystal,

and they can easily be removed by polishing or etching. The single crystals

were prepared with an adopted "tri-arc" Czochralski method[8]. The physical-

chemical properties are favourable to grow single crystals with this method.

Namely, these compounds form congruently from the melt, have a high melting

temperature, are formed by a strong exothermic reaction, and form facets when

cooling the melt. The larger facets were formed when the growth direction was

closer to the a-axis. Finally, the weight losses during the arc melting were

negligible.

5.3. Superconductivity of the RT7Si?-ternary compounds (R=Y, La, Lu).

5.3.1 Introduction

In this section we focus on the superconducting properties and the related

metallurgical problems of the nonmagnetic compounds with R=»Y, La, I.u and T=Rh,

Pd and X»S1. It was found that all RPd2Si2 compounds are type I

superconductors below IK. The superconductivity of the RRh2Si2 compounds has

been a controversial issue. Two investigations of " <?Rh2Si2 have reported a

superconducting temperature at about AK[9,1O]. . , ver, a more detailed

investigation ascribed this superconductivity to second phases[11]. We have

determined that single-phase LaRh2Si2 is a type I superconductor, but with T c

at a much lower temperature, 74mK. Furthermore, we will show that che

87

on r

y— i—

LaRh2Si2 ' .YPd2Si2 •'

LaPd2Si2" • _"LuPd2Si2

O 0.2 0.4 0.6T(K)

0.8 1.0

Fig. 5.2. Temperature dependenoe of the aa susceptibility of RPdsSi2 andLaFh2Sis at the superconducting transition (F=Y,La,Lu).

o°o

o o

• o

-3

o

ooo

1 / 1

-3 - 2

- 1

\

- l

C

OOM

N

(arb.units)

i

) 1

M(arb.units)

Ssv 1

8°

o oo

3. (i0H(mT)

o

o

/

YPd2 Si2T=Q35 K

M-oH(mT)

2 / 3

V

5.3. Magnetio field dependence of the aa eueaeptibility andmagnetisation of

88

stability regime of the LaRh2Si2 stoichiometry is very small, leading to an

easy formation of second phases. Two of the second phases are superconductors,

one at 4.OK and the other at 0.36K, and this can explain the conflicting

results [9-11J.

5.3.2 Experimental results.

The three RPd2Si2 compounds become superconducting at transition

temperature of TC=O.67K for LuPd2Si2, Tc=0.39K for LaPd2Si2 and Tc=0.47K for

YPd2Si2 (see Fig.5.2). To check whether the superconductivity is a bulk

property, we prepared single crystals, which are completely single-phase.

These single crystals become superconducting at identical temperatures as the

polycrystalline samples. The dc-field dependence of the ac-susceptibility

below Tc is shown in Fig.5.3 and exhibits a pronounced positive peak. This

peak can be understood in terms of the fully reversible hysteresis-loops on

the magnetisation curve, also shown in Fig.5.3. This magnetisation curve

demonstrates that these compounds are type I superconductors. A parabolic fit

to the temperature dependence of the critical field HC(T) versus T

yields u H (O)=7.OtnT for LuPd2Si2, H H (0)=3.1mT for LaPd2Si2 and

u H (0)=5.4mT for YPd2Si2» as is illustrated in Fig.5.4.

0.2 0.4T(K)

Fig. 5.4. Supeveondusting phase diagram of

lu.

0.6

i2 and %2 with R=Y, La,

89

For LaRh2Si2 the situation is more complicated. We prepared three

stoichiometric, polycrystalline samples. Sample 1 was measured with ac

susceptibility down to 20mK and the other two down to 330mK. Sample 1

contained the least segregations of these three samples as observed by

microprobe analysis and became superconducting at 74mK (see Fig.5.2). The

field dependence of the ac susceptibility exhibits positive peaks, similar to

those of RPd2Si2, indicating a type-I behaviour. Sample 2 was measured before

annealing and became superconducting at 360mK. After annealing we found only a

weak onset of superconductivity at this temperature. Sample 3 did not become

superconducting down to 33OmK.

In order to resolve the intrinsic superconducting properties of LaRh2Si2>

we also prepared nonstoichiometric samples of formula Laj+xRh2Si2 and

LaRh2+xSi2-x. These samples lie along the two heavy lines through LaRh2Si2 in

the ternary phase diagram given in Fig.5.5. We observed that the La1+xRb.2Si2

samples with excess La became superconducting at 0.36K and the samples with La

deficit did not become superconducting (Tc<0.33K). For the compounds

1 La Rh Si3 2.32 La2Rh Si3 -3 La Rh Si2 3.34 La2Rh3Si5 4.45 La Rh2Si2 0.0746 La Rh Si 0.36 S'7 La Rh3Si2 -8 La3 Rhj Si i 4.4

LaSi

La La4Rh3 LaRh LaRh2 RhLa5Rh4 LaRh3

Fig. 5.5. Isothermal section of the ternary La-Rh~Si phase diagram after

Broun [111.

90

2-x we found a superconducting transition at 4.OK for the Si rich

samples but no superconductivity for the Rh rich samples. Finally, we measured

the ac susceptibility of the LaRh2Si2 single crystal which should reveal the

intrinsic superconducting behaviour because of the total absence of all second

phases. The single crystal became superconducting at 74mK.

For YRh2Si2 and LuRh2Si2 n o superconductivity was observed down to O.33K.

In addition, we have performed very accurate magnetisation measurements on all

the variously prepared samples of LaRh2Si2- There were no indications for any

magnetic phase transitions as were reported earlier[10]. The magnetisation had

little temperature dependence and a value of 1.5x10 emu/mol, indicating a

weak Pauli-paramagnetism.

5.3.3 Discussion

The La-Rh-Si system is one of the few ternary systems for which an

isothermal-section phase diagram has been established[ll]. Here, eight ternary

compounds were identified, five of which were found to be superconductors

[11]. In contrast to these results, the compounds LaRhSi and LaRh2Si2 have

also been claimed to be superconductors[9,10]. We have concentrated our

efforts on the compound LaRh2Si2 not only to resolve the question of

superconductivity, but also to in"sstigate the causes of the metallurgical

difficulties which have led to these contradictory results.

All previous results were obtained on arc-melted samples with a subsequent

heat treatment on 900°C or 950°C. During arc melting the temperature is so

high that all possible ternary phases are in the liquid state. The fast

quenching procedure, created by the water-cooled copper crucible, will freeze-

in not only LaRh2Si2 but also some of the adjacent phases. These second phases

are not only due to the off-stoichiometry caused by weighing errors, oxides in

the starting materials and melting losses, but also due to small concentration

fluctuations in the melt. Accordingly we found both La-rich and La-poor

precipitates in an as-quenched stoichiometric LaRh2Si2 sample. Consequently,

an annealing procedure is necessary, although we think that the usual

annealing temperature of 900°C is quite low with respect to the estimated

melting temperature of 1600°C

Ttu. basic problem of the metallurgy of LaRh2S±2 is the extremely small

range of stoichiometry. This property leads to the formation of second phases

already for off-stoichiometric preparation of samples of order of 1%.

Furthermore, the aforementioned weigl.ing errors, oxides in the starting

materials and preferential melting losses will also result in errors in the

91

stoichiometry of the same order of magnitude. During the solidification

process all second phases will precipitate along the grain boundaries. During

the subsequent rapid cooling of the solid, the range of stoichiometry will

decrease and eventually additional segregations will be formed on preferential

planes, probably the a-b basal plane. Further heat treatment increases the

mobility of the atoms and the segregations will be mainly directed to the

grain boundaries. Here, the concentration fluctuations can be smeared out

leading to a decrease of the amount of segregations. Additionally the

crystallites will increase enormously In size.

It is evident that the remaining precipitates along the grain boundaries

can Influence the determination of superconductivity. First, the precipitates

can form easily a network and may short-circuit the resistance of the sample-

Secondly, the precipitates on the grain boundaries may shield magnetic fields,

and thus ac susceptibility results must be interpreted with caution. There are

two other frequently used techniques for establishing bulk superconductivity,

namely, specific heat and Meissner effect measurements. However, it is rather

difficult to accurately estimate the superconducting volume fraction from

these methods, especially if the transition is smeared out in temperature.

Furthermore, these measurements are quite difficult below 1 K. Meissner effect

measurements may lead to systematic errors for type II superconductors due to

the complicated flux-pinning behaviour[12].

We have approached the question of bulk superconductivity via two

metallurgical techniques. First, we used off-stoichiometric samples to

indicate the intrinsic properties. Here, the results for Tc from the ac

susceptibility need closely be related to the detailed analysis of the sample

quality and segregations. This method has the additional advantage that it

also provides information about the neighbouring phases. Second, we have

studied "ideal" samples by preparing single crystals with a specially adopted

"tri-arc" Czochralski method. These single crystals grow under near-

equilibrium conditions which is highly suitable if the range of stoichiometry

is small. This method has the further advantage of the purifying effect of the

Czochralski method.

With our detailed knowledge of the ternary La-Rh-Si phase diagram, we

conclude from the observed behaviour of the polycrystals and single crystals

that (i) stoichiometric LaRh2Si2 is a type-I superconductor with Tc=74 mK.

(11) the superconductivity at 0.36 K must be attributed to segregations of

LaRhSi. (ill) the observed superconductivity[9,10] at 4.0 K must be ascribed

to segregations of

92

In our opinion, the different transition temperatures must be caused by

different ternary phases and not by a range of transition temperatures over

the range of stoichiometry[13]. The latter would require that T c could vary by

a factor 50 over the extreme small range of stoichiometry less than 1%. The

former is supported by the fact that both the single crystal and the purest

polycrystal have the same Tc value of 74 mK.

The contradictory results reported on LaRh2Si2 can neither be explained

with a high-temperature, low-temperature modification of the ThCr2Si2~" atld

CaBe2Ge2~type crystal structure, as reported for LaIr2Si2[4]> nor with a mixed

site occupancy of the Rh- and Si-sites. For in both cases, powder diffrac-

tograms should show Miller-indices with an odd sum, which was not the case

with annealed samples nor with rapidly quenched samples.

In order to check the superconducting properties of LaRhSI, we have

prepared a polycrystalline (1-1-1) sample. This sample became indeed

superconducting at 0.36 K. This result is in agreement with the observations

of Braunfll] who found no superconductivity down to 1.2 K. However, Chevalier

et al.[9] report a superconducting transition temperature Tc=4.35 K. A

detailed metallurgical analysis by Braun and likewise by ourselves attributes

this result to the formation of second phases. We conclude that the intrinsic

transition temperature of LaRhSi is 0.36 K.

Consistent with our results type-I superconductivity ( K „ < 0 . 7 ) had earlier

been reported for LaPd2Ge2[14]. This behaviour stands in total contrast to the

type-II superconductivity of the isostructural heavy-fermion compounds

CeCu2Si2 <<GL»22) [15] and URu2Si2 (<GL«33) (see section 5.5.2). The

distinction between type-I and type-II behaviour seems to be critically

dependent on whether the R-atoms are nonmagnetic (Y, La, Lu) or magnetic

(Ce.U).

The Ginzburg-Landau parameter K-, is defined in the pure limit as

K =0.96 \ (0)/£ with X. (0) the London penetration depth and Z, the coherenceO L O Ij O

length[16]. ^ ( 0 ) can be calculated from the London equation

\?(0)=m /n.ne2 with m* the effective electron mass, u the permeabilityLi O O

constant, n the conduction electron density and e the electron charge. In BCS-

theory the coherence length £ is given by £ »0.18hv_/k„T with h Planck'sO O F O C

constant, vF the Fermi velocity, kg Boltzmann's constant and T c the super-

conducting transition temperature. This leads to the universal relation :K =3.21xlO22«T -(m*/m ^^'n'^-k'1.O C c r

93

Assuming a spherical Fermi-surface n=k|/3ii2 and setting TC=O.5K the equation

can be reduced to K =8.72xlO22(m*/me) /kp5 . For the (1-2-2) compounds

there are 6 conduction electrons per two formula units per unit cell

(4x4xlO=160A3) yielding a Fermi vector kF=1.04A . Thus, we obtain a relation

between the Ginzburg-Landau parameter < and the effecti :e r.>ass of the° -i 3/2

conduction electrons for these compounds, viz., < =7.9x10 " (m'/ai ) . For

CeCu2Si2 a value of < =10 was calculated, resulting our mod.il in a mass

enhancements of 118, and in close agreement with other calculations[17].

The distinction between type-I and type-II superconductivity can be

calculated to take place at a mass enhancement m*/me=20. As this mass

enhancement is unlikely for the compounds presently investigated, type-I

behaviour may be expected as a general property for the nonmagnetic RT2Si2~

type compounds. We stress that this analysis assumes a spherical Fermi surface

and thereby leads to only a rough estimate of kp. Nevertheless, a factor of 2

error in kp would not invalidate our conclusion of the type-I behaviour for

this type of compounds. Furthermore, this analysis neglects mean free path

effects, which have been shown of minor importance in case of the heavy-

fermion superconductors. Here, this requires that the additional term to the

Ginzburg-Landau parameter K2=I<:GL~K =2.4X10 y p is also less than %/2 (with

y in J/m^K2 and p in Qm), or that y pO.OxlO . This has, unfortunately, not

yet been verified, but is acceptable if the residual resistivity is of order

of luQcm. Still, the definite observation of type-I superconductivity imposes

this requirement.

The superconducting transition temperature T c is obviously strongly depen-

dent on the actual electron-phonon interaction, and for the RPd2Si2 compounds

there is a relation between Tc and the unit-cell volume V (see Table 5.1).

Finally, we note that Hc(0)/Tc for all four compounds is nearly constant. As

a(A) c(A) V(A3) TC(K) Hc(o)(mT)

YPd2Si2

LaPd2Si2

LuPd2Si2

YRh2Si2

LaRh2Si2

LuRhoSio

4.129

4.283

4.089

4.031

4.112

4.090

9.84

9.88

9.85

9.92

10.29

10.18

167.8

181.2

164.7

161.2

174.0

170.3

0.47

0.39

0.67

<0.33

0.074

<0.33

5.43.1

7.0

-

0.7

-

Table S.I. Lattice parameters a and a, and unit-aell volume V of the ternary

(1-2-2) compounds RPdsSi2, with R=Y, La, Lu with the super-

conducting transition temperature Tg and the critical field Bg(o).

94

H2/T2~y~N(E ) this means that the density of states at the Fermi surface raust

be nearly the same for these four compounds• Hence, superconductivity for

YRhoSio and LuRhoSi2 might likewise be expected in the millikelvin range-

In conclusion, we have found bulk superconductivity for single-phase

RPd2Si2 with R=Y,La,Lu and for LaRh2Si2- The observed type-I behaviour may be

regarded as a general property of this type of nonmagnetic R compounds and

serves as a simple reference for the heavy-fermion compounds, CeCu2SÏ2 and

URu2Si2, with respect to their superconducting properties[18]-

5.4 Magnetic properties of the RT?Si?-ternary compounds (R=Ce,U).

5.4.1 Introduction

This section describes the magnetic properties of the CeT2Si2 and UT2Si2

compounds, as the transition metal T is varied through the 3d-, 4d- and 5d-

transition metal series. The behaviour of some individual compounds will turn

out to be very interesting. Moreover, from this study we have determined a

systematic trend in the magnetic properties, which enabled us to locate heavy

fermion behaviour. So far, in this series of compounds, heavy-fermion

materials were found for CeCu2Si2, CeRu2Si2 and URu2Si2. The latter compound

will be described in detail in the next section, since it exhibits both an

antiferromagnetic ordering and a superconducting transition.

5.4.2 Crystal structure

In Fig.5.6 the crystal structure parameters of the CeT2Si2 and UT2S12

compounds are presented, i.e. the lattice parameters a and c, the unit-cell

volume V and the c/a ratio. The parameters a, c and c/a do not show a clear

correlation with the number of d-electrons. Still, these parameters exhibit

features in the CeT2Si2 compounds similar to those in the UT2Si2 compounds,

e.g. the maxima in the c/a ratio in the Co-series and the minima in the c/a

ratio in the Ni-series. The only continuous parameter is the unit-cell volume

V, which follows closely the atomic volumes of the transition metals[19]. In

the transition metal series the 3d-elements are smaller than the corresponding

4d- and 5d-elements, whereas corresponding 4d- and 5d-elements have similar

atomic volumes. Furthermore, the transition metals have a parabolic-like

behaviour of their volumes when scanning the periodic system from the

IIIB-(Sc-group) to the IIB-group (Zn-group), with minimum values at the Fe- or

Co-group. Both observations agree with our findings. However, it is not clear

what determines the parameters a, c and c/a. The two different crystal

structures seem to have no effect on all four parameters.

95

5.4.3 ExperiKeatal results

In order to systematically treat all the investigated compounds, we will

separate them into 6 series. Each series contains either CeT2Si2 or UT2Si2

compounds with T either a 3d-, 4d- or a 5d- transition metal. Table 5.2 and

5.3 give the values of some important parameters.

2.33d4d5d

Mn Fe Co Ni CuTc Ru Rh Pd AgRe Os I f Pt Au

Mn Fe Co Ni CuTc Ru Rh Pd AgRe Os I r Pt Au

Fig. 5.5. Structural parameters of the flZ^Sig compounds with. R=Ce,V: thelattice parameters a and a, the unit aell volume V and the ratioa/a.

96

CeT2Sl2 T=3d-»etal.

In this series we investigated T=Co, Ni, Cu- CeCo2Si2 is a Pauli-paramagnet

with a temperature independent susceptibility and a linear magnetisation up to

5r. Ac low temperature 1.4K<T<100K a small increase of the susceptibility was

observed, which we ascribe to some impurity phase. CeNi2Si2 was prepared as

single crystal[7] and exhibited a temperature-independent, Pauli-paramagnetic

behaviour down to 1.4K with a linear magnetisation up to 5T. For CeCu2Si2 w e

found the well known Kondo-lattice behaviour[15] at high temperature and a

superconducting transition temperature of 0.59K.

T=4d-»etal.

2i2 has two different transition temperatures. This is most clearly

seen in the resistivity behaviour shown in Fig.5.7. Here, p exhibits anomalies

at T=37K and T=12K. In the three regimes the resistivity has a different power

law dependence on temperature p-p =Ta, where a=2.44 for T<12K, a=3.67 for

12K<T<37K and a=0.85 for T>37K. The dc susceptibility curve, shown In Fig.5.8,

only displays an anomaly at 37K, whereas the lower transition temperature only

marks the increase of the susceptibility with decreasing temperature. However,

only below 12K the magnetisation versus magnetic field curves show a small

metamagnetic-like increase at about 3T, which confirms two different magnetic

T (K)

?u

CX

(

100

80

6 0

4 0

2O

n

3I

J

" -<

' f /1 <f- V

ut : /IJ'

1001

\/ \

f'

TLN

1 r

2001 i

"sA

r -ce Rn?s,2 -

ioJ

10n

1O° 10'T (K)

Fig. 5.7. Temperature dependence of the eleatrioal resistivity of CeRh2Si2 ona double logarithmic and double linear scale.

97

. 20

o

'g 10

H

°oL

• C<2Rn,Si8

_J A

100T (K)

Fig. 5.S. Temperatur'e depen-

dence of the da susaeptibili-

ty and inverse susceptibility

o/ CeTgSig with f a 4d-metal:

200

3 Rh, Pd, Ag.

200-

300

600

100T (K)

"200

4OO

2OO

300°

. 5.5. Temperature depen-

dence of the da susceptibili-

ty and inverse susceptibility

\ of single crystalline CePdgSig

o along several axes. The inset

£_ shows an enlargement of the

3 low temperature behaviour.

1.O

0.81-

0.6 -

0.4 -

0.2 -

o£

C<2Pd2Sis• // (1,0,0)'//(0.0,1)«#(1.1,0)

10 20 30H>H (T)

40

Fig. 5.10. Magnetic field de-

pendence of the magnetisation

of single crystalline CePdgSig

along several axes in fields

up to S8T.

98

structures. This lower transition temperature seems to be very sample

dependent as Grier et al.[20] report a lower transition temperature of 27K.

CePd2Si;, was prepared as single crystal [7] and the anisotropic

magnetisation curve, shown in Fig.5.9, is consistent with magnetic moments

parallel to the (1,1,0)-axis[20]. The magnetisation parallel to several axes

was measured up to 40rC and is shown in Fig.5.10. It Increases linearly with

magnetic field up to 10T and changes slope at about 30T reaching a value of

0.9 n_/(f.u.). CeAg2Si2 also exhibits two magnetic phase transitions. The

upper one shows an anomaly in the dc susceptibility at 9.5K[20], but can only

be observed in large enough magnetic fields. In low magnetic fields only a

small ferromagnetic component shows up at 4K as is discerned by hysteresis in

magnetisation loops (Hc~10mT) and a cusp in the ac susceptibility at 3K. For

the compounds discussed in this series no superconductivity was found for

CeRh2Si2, CePd2Si2 and CeAg2Si2 down to 40 mK.

CeT2Si2 T=5d-aetal,

Fig.5.11 shows the temperature dependence of the dc susceptibility of both

polycrystalline and single crystalline CePt2Si2 measured parallel to the a-

and c-axis. This figure clearly shows the discrepancy between polycrystal and

single crystal samples[7] although the X-ray powder diffractograms only

contained hardly detectable traces of impurity phases. It is obvious that the

single crystal results show no indication of magnetic ordering down to 1.6K,

600

3OO

Fig. 5.11. Temperature dependence of the da susceptibility and inverse

susceptibility of polyarystalline and single-crystalline CePt3Sis.

99

4O

3 3 0

ö

§ 20

"o

Ce PL,Si.

Ce Au2Si2

100T ( K )

200

"

600 FÏ3' 5 > i 2 . rewper»atur>e depen-

dence of the da susceptibili-ty and inverse eusaeptibilityof CeT2Si8 with T a Sd-metal:

° ^ Pt, Au.o

200^3

3 0 0

6O

E 4 0 -

o

"o" 20

; /

URh2Sis

ure2si:

100

4 0 0

300 jp.

2 0 0

100

3 0 0

Fig. 5.13. Temperature depen-denee of the de susceptibili-ty and inverse susceptibilityof UTsSis vith T a 4d-metal:Rh, Pd.

T (K)

4 0

o

§20a?

ol /V".Ti +

400

1OO

xn

2OO

2 0 0

1- 5.14. Temperature depen-

dence of the dc susceptibility

and inverse susceptibility of

Re, Os, Ir, Pt, Au.

100

despite the relatively large Curie-Weiss temperature intercept 9_ ~-100K

[21]. Still, the polycrystal results, exhibiting a small peak at 6K, were

previously misinterpreted as evidence for magnetic ordering[22]. The broad

maximum at 60K both parallel to the a- and c-axes is only observable in the

single-crystal data. CeAu2Si2 exhibits a clear antiferromagnetic phase

transition[23] at 10.IK, as evidenced from the dc-susceptibility shown in

Fig.5.12. The magnetisation increases linearly with magnetic field up to 5T.

OT2Si2 T=3d-netal.

No compound in this series was prepared, but Ref.24 contains a neutron

scattering study for T=Co, Ni, Cu. The three compounds were found to order

magnetically at 85, 103 and 107K, respectively.

UT2Si2 T-4d-«etal-

The first compound studied in this series, URu2Si2, w a s v e ry recently found

to order antiferromagnetically at 17K, and surprisingly becomes super-

conducting at 0.8K. The magnetisation curve shown in Fig.5.18 indicates that

the moment is very anisotropic, with only a component along the c-axis. At

high temperature (T>150K) an effective moment of 3.51 u/l.u. is measured

which is close to the value expected for an f or f* ground state. A full

description of this compound is reserved for the next section. The two other

compounds studied in this series, URh2Si2 and UPd2Si2> are shown in Fig.5.13

and have the highest ordering temperatures of the variously studied CeT2Si2

and UT2Si2 compounds. URti2Si2 n a s a rather low value for the susceptibility,

but clearly orders antiferromagnetically at 130K[25]. The small upturn below

20K, accompanied with a small hysteresis loop (H ~50mT), is ascribed to

impurity phases. UPd2Si2 orders antiferromagnetically at 97K. A hysteresis

loop at 1.66K exhibits a large coexercive field of 0.8T and this hysteresis

remains present up to the ordering temperature.

UT2Si2 T-5d-Ktal.

In Fig.5.14 we show the temperature dependence of the dc susceptibility of

the five polycrystalline samples, investigated in this series. The first two

compounds URe2Si2 and UOs2Si2[26] are Pauli-paramagnets, as may be concluded

from their temperature independent magnetic susceptibility of 1.4x10"^ emu/mol

f.u. for both compounds. UIr2Si2 is an antiferromagnet, with a Nêel

temperature of 5.5K. This may be concluded from the magnetic field dependence

of the magnetisation, being linear up to IT, then showing a small

101

raetamagnetic-llke transition at IT, and the large negative Curie-Weiss

temperature of -156K. The estimated saturation magnetisation is about

0.3 \x-/f.u. which is about 60% reached at 5T. It is peculiar that the dc

susceptibility does not decrease below the ordering temperature. This could be

attributed to a preferential growth direction during the rapid cooling, or

more likely, during the annealing procedure. UPt2Si2 has an antiferromagnetic

ordering temperature of 36K. Fig.5.15 shows the anisotropy of the

susceptibility parallel to the a-and c-axes. The anisotropy behaviour is not

consistent with a magnetic moment parallel to the c-axis as reported earlier

[27]. Furthermore, this curve shows the anisotropy of the moments (3.39 and

2.87 u /f.u. parallel to a- and c-axes) and of the Curie Weiss temperaturesD

(-98 and -31K parallel to the a- and c-axes). The magnetisation increases

linearly with magnetic field up to 5T at 1.7K, without any indication for

metamagnetic behaviour[27]. UAu2Si2 exhibits two transition temperatures. It

orders antiferromagnetically at 78K with a reordering at 27K. This compound

exhibits small hysteresis loops with a remanent magnetisation of

0.20|i /f.u. and a coexercive field of about 0.1T at 4.4K. Zero-fieldjj

measurements of the field-cooled state indicate that ferromagnetic component

changes from 0.09 |i /f.u. above 27K to 0.20u_/f.u. below 27K. Still, in a

magnetic field of 5T the magnetisation does not exceed 0.43u^/f.u.

1400

Fig. 5.IS. Tempevatuve dependence of the da susaeptibility and inversesusceptibility of single crystalline UPt2Si2 along several axes.

102

5.4.4 Discussion

It is known that the magnetic behaviour of Ce-compounds can be dominated by

valency fluctuations between Ce and Ce with corresponding moment

fluctuations between 2.54 (4f*) and 0.0a /Ce (4f°). This explains why

CeC£>2Si2 and CeNi2Si2 can be nonmagnetic. Co and Ni never carry a magnetic

moment in these (1-2-2) compounds as is inferred by magnetic measurements of

other (1-2-2) Co and Ni compounds. CeCu2Si2« being the first discovered heavy

fermion system[15], is on the borderline between Pauli-paramagnetism and

antiferromagnetism. Its low temperature state can be described by the

formation of a so-called Kondo-lattice. Here, magnetisation measurements yield

the normal Ce effective moment at high temperature. However, the moments are

screened so completely at lower temperature, that at about 0.6K even a

transition into the superconducting state was found[15]. At present the origin

of the superconducting state is not understood, as there is a lack of

knowledge about the microscopic interactions in the heavy electron system.

However, not all heavy fermion systems become superconducting as is

encountered for CeRu2Si2' This system also exhibits heavy fermion

behaviour[28], but no superconductivity was found down to 40mK[29].

The magnetic ordering of CeRh2Si2 *s also not well understood. Neutron

scattering studies revealed a complicated magnetic structure either consisting

of two magnetic structures spatially separated or a magnetic structure with

two modulation vectors[20]. The ordering temperature is remarkably higher than

those found In the other CeT2Si2 compounds, and is one of the highest known

for Ce-compounds. It has been argued that the high ordering temperature

results from an Itinerant moment due to the Rh-4d-band, but an analysis of the

magnetic form factor and of the magnetic structure eleminates this

possibility. However, the high ordering temperature might be related to the

small lattice parameter a, which is considerable smaller than in the other 4d-

compounds, and which indicates a stronger d-f hybridization. The upper

transition temperature T„ is consistently found at 37K on various samples with

various measuring techniques. Nevertheless, the lower transition temperature

T„ seems to be sample and/or technique dependent. Neutron scattering

experiments found an T„ =27K, whereas the resistivity measurements Indicate a

transition at 12K. Finally, the susceptibility yields a transition temperature

Th=5K[30]. It is not clear how these findings can be related to each other.

CePd2Si2 orders antiferromagnetically at 10.5K (see Fig.5.9). The

anisotropy in the magnetisation shows that (1) the moments are parallel to the

(1,1,0) axis, (2) the moments are not isotropic Heisenberg spins, and (3) the

103

exchange Is larger within the basal plane than along the c-axis. Statement (1)

is proven by a constant susceptibility below TN along the (1,1,0) and (0,0,1)

axis. The different maxima of both curves indicates statement (2) and

statement (3) is based on the different Curie-Weiss temperatures being -63K

and -21K parallel to the a- and c-axis, respectively. This difference results

obviously from the different geometry with Ce atoms being directly adjacent in

the basal plane, but separated by two Si- and one Pd-layer between Ce atoms in

T=3d- Mn Fe Co Ni Cu

a (A)

c (A)

T=4d- Tc Ru Rh Pd Ag—

pp

3.953

9.776

PP

4.0369.575

Ko+sc4.1059.934

a

c

TNecwPeff

(A)(A)(K)

(K)

GO

af

4.098

10.19

3 7 .

-163.

2.43

ay

4.2309.873

10.5

-57.

2.55

ca af4.250

10.66

9 .5

-36 .

2.54

T=5d- Re 0s Ir Pt Au

PP

a

c

TNecwPeff

(A)(A)

(K)

(K)

GO

Ko4.253

9.798

-

-85.2.42

af4.310

10.20

10.1

-18.

2.43

Table 5.2. Structural and magnetic parameters of the CeTgSig compounds, a and

o ave the lattice parameters, TN the magnetic ordering temperature,

Qrv the Curie-Weiss temperature and peff the effective moment per

formula unit, pp denotes Pauli-paramagnetiem, Ko a Kondo-lattiae

system, se eupera ondua tivity and (aa) af (canted) antiferro-

magnetiem.

104

different basal planes. Previously,.neutron scattering experiments[20] found a

commensurate magnetic structure with moments of 0.62|i /Ce along the (1,1,0)

axis, and a modulation vector (^,^,0). This is consistent with the constant

susceptibility below TN along the (1,1,0) and (0,0,1) axis and a reduction of

%/2 along the a-axis. The high-field-magnetisation experiment (Fig.5.10)

yields magnetic moments of 0.9^/Ce exceeding the value 0.62ji /Ce in the

neutron scattering result. The increase of the magnetisation in fields beyond

T=3d-

a

c

TN

ecwPeff

T=4d-

a

c

TN

ecwPeff

T=5d-

a

c

TN0cwPeff

(A)(A)(K)

(K)

(,B)

(A)(A)(K)

(K)(V

(A)(A)(K)

(K)

<V

Mn

Te

Re

PP

Fe

Ru

Ko+sc

4.127

9.610

17.5

-160

2.86

Os

PP4.121

9.681

Co

af

3.917

9.614

85

-285

4.85

Rh

af

4.012

10.06

130.

-40.

2.65

Ir

af

4.088

9.790

5.5

-156.

3.03

Ni

af

3.958

9.504

103

-56

2.91

Pd

af

4.121

10.19

97.

-10.

2.88

Pt

af

4.217

9.704

36.

-57.

3.22

Cu

fe

3.988

9.953

107

-11

3.58

Ag

Au

ca af

4.228

10.26

78.

-36.

3.11

Table 5.3. Structural and magnetic parameters of the VT^Si^ compounds. The

parameters are defined as in table 5.2. The data for T=3d-metal

have been taken from Ref. 24.

105

30T, means that a simple local moment picture is not appropriate, since then a

saturation field being twice the exchange field (in molecular field theory) is

expected. An explanation can be given in terms of a crystal-field picture

where the large magnetic fields can excite states with larger magnetic moments

than the ground state. A more likely explanation is in terms of spin

fluctuations, considering the resistivity results of Ref.23. Then the local

magnetic Ce moment is suppressed at low temperature by spin-fluctuations and

these spin-fluctuations can be suppressed in turn by applying large magnetic

fields.

For CeAg2Si2 two magnetic transitions were observed. The upper transition

occurs at 9.5K and can only be observed in relatively large applied magnetic

fields (n H>0.1T). In low fields this transition is indiscernible from the

Curie-Weiss background. On the other hand, the lower transition is only

observable in relatively low fields- This lower transition also marks the

onset of a small hysteresis in the magnetisation loops. Zero-field ac

susceptibility measurements display a rounded maximum at 3K and with

decreasing temperature x goes towards zero. However these ac measurements

show no anomaly at 9.5K. Neutron scattering experiments[20] indicated an •

incommensurate magnetic structure below 10K., which could be interpreted as a

modulation of the moments either with a sine-wave or with a square-wave, with

the moments pointing along the a-axis.

The CePt2Si2 intermetallic compound exhibits several remarkable properties.

First, it is the only Ce-compound that does not adopt the ThCr2Si2~type

structure, but a variant of the CaBe2Ge2-type structure (see above). Second,

there is a remarkable discrepancy between the measurements on polycrystalline

and single crystalline samples. Nevertheless, hardly any additional

impurity lines were observed in the X-ray pattern. This difference is ascribed

to impurity phases of antiferromagnetically ordered Ce-Pt intermetallics.

Finally, no magnetic ordering is observed down to 1.5K, in spite of a good Ce-

moment (2.42(i /Ce) at high temperatures and a large (negative) Curie-Weiss

temperature. This indicates that there are at high temperature both moments

and large interactions. The absence of magnetic ordering could be ascribed to

the same mechanisms as in CeCu2Si2, where the formation of a Kondo-lattice

leads to a nonmagnetic ground state. The broad maximum is the dc

susceptibility at about 60K might be ascribed to spin-fluctuation properties.

The analogy with the heavy-fermion compound CeCu2Si2 is further emphasized by

the large specific heat coefficient Y=100mJ/mol K2, we have measured for

CePt2Si2'

106

In contrast, CeAu2Si2 has a smaller Curie-Weiss temperature and yet orders

antiferromagnetically at 10.IK. This clearly demonstrates that In these (1-2-

2) compounds no normal systematic behaviour Is manifested, e.g. a larger

(absolute) value of the Curie-Weiss temperature resulting in a larger ordering

temperature. Such anomalous behaviour is also found for the compounds with

T=4d-metal and will be discussed below. Neutron scattering experiments[20]

determined an antiferromagnetic ordering for CeAu2Si2 at 10K with

ferromagnetically coupled basal planes with the spins

(1.29(j.o/Ce) perpendicular to the planes and alternating in sign along the c-

direction.

Summarizing, we have found in the CeT2Si2-compounds three Kondo-lattice

systems, viz., when T=Cu(3d-), Ru(4d~) and Pt(5d-). Four compounds order

antiferroiaagnetically, viz., T=Rh, Pd, Ag(4d-) and Au(5d-), two of which have

an incommensurate magnetic structure (T=Rh,Ag). The remaining compounds

exhibit no magnetism and are weak Pauli-paramagnets.

The magnetism of the UT2Si2 compounds is in some respects similar to that

of the CeT2Si2 compounds as the magnetism of Ce and Ü is both carried by f-

electrons, and both Ce and U can be magnetic or nonmagnetic. However, the 4f-

electrons (Ce) are very localized, whereas the 5f-electrons (U) are more

itinerant. Thus, Ce-Ce interactions can only be carried via an indirect

exchange mechanism, like the RKKY-exchange. The U-U interactions, on the other

hand, are very dependent on the U-U distance. Here, a good U-moment can be

expected at large U-U separation, when this separation is too large for

overlap of the 5f-wave functions. However, at small U-U distance a 5f-band

will be formed, which is too broad to support magnetism and results in a

Pauli-paramagnetic state. An empirical criterion was formulated by Hill[31]

with a critical separation of about 3.5A. Yet, we find for the (1-2-2)

compounds both Pauli-paramagnetic and antiferromagnetic systems and there is

no correlation between the U-U separation (= lattice parameter a) and the

magnetic ordering temperature. Thus the Hill criterion is violated. Hence, the

magnetism is not only governed by the U-U separation, but other parameters

have to be taken Into account. For most heavy fermion systems the separation

is so large that no direct exchange is possible and any interaction between

the moments must be caused by a different origin.

For all the investigated UÏ2Si2 compounds, with T a 4d-metal, we found an

antiferromagnetic ordering[32]. In addition URu2Si2 exhibits a superconduction

transition (see Section 5.5). URti2Si2 has the highest ordering temperature ot

all our compounds, TN"130K. The magnetic structure was reported[25] to be like

that of CeAu2Si2« For UPd2Si2 an antiferromagnetic structure was found below

97K. The hysteresis in the magnetisation loops is, 0.9T at 1.66K and remains

visible up to TN. Furthermore, it is rather peculiar that the remanent

magnetisation increases with increasing temperature from SxlO"-')! /f.u. at 1.66

K via UxlO~3u /f.u. at 30K to 60xlO~3(L/f .u. at 80K. This effect might be

related to the incommensurate magnetic structure which was reported to have

two modulation vectors each having a different temperature dependence[25].

In the UT2S12 compounds with T=5d-metal, Fauli-param2gnetism was

encountered for T=Re,Os, and UIr2Si2 orders antiferroraagnetically at 5.5K.

lere, we observe that Q^ is about 25 times TN- For UPt2Si2 a magnetic

structure was proposed as found for CeAu2Si2, with moments along the c-axis.

Jur magnetisation measurement along the (1,0,0), (0,0,1) and (1,1,0) axes are

incompatible with the neutron scattering results[27]. Furthermore, our

neasurements cannot be interpreted with magnetic moments along one crystal

axis. Hence, a more detailed investigation is required. Similar to CePd2Si2,

the moments are anisotropic above T N with Peff=3-39 and 2.87 a /f.u. along the

a- and c-axes respectively, with again the Curie-Weiss temperature larger in

the basal plane (-98K) than along the c-axis (-31K), as discussed before,

'inally, UAuoSi2 orders with a canted antiferromagnetic structure. The canting

ingle changes at 27K, where a distinct change of slope of the remanent

lagnetisation versus temperature (not shown) is observed.

Summarizing, in the UT2S12 nine antiferromagnetic systems were found, of

/hich one (T-Ru) has properties related to the dense Kondo system and is

surprisingly a superconductor. Two systems are Pauli-paramagnets (T=Re,Os).

From tables 5.2 and 5.3 we can detect several similarities in magnetic

jehaviour, if we compare the different series of compounds- First, we see that

he effective moment is almost constant within a series. For the Ce-compound

chis moment corresponds with the 4f -state with 2.54(i„/Ce. The U-moraents are,

lowever, between the values expected for the 5f^ and 5fz-states having an

effective moment of 2.54 and 3.58n /U, respectively. This does not require

'alence fluctuating behaviour but is rather a result of the inadequacy of the

'ussel-Saunders coupling or of 5f-band effects. Second, we observe an

trengthening of magnetism within a series from Pauli-paramagnetism via

ntiferromagnetism to canted antiferromagnetism with increasing number of d-

lectrons. This trend is reflected in an increase of the ordering

emperatures. In some series these three magnetic possibilities are not

bserved, because the limits for Pauli-paramagnetism or antlferromagnetisn

ould not be reached. These limits are due to intrinsic properties, like band

108

structure effects (see below), or to metallurgical problems like the high

volatility of Zn, Cd during preparation of the samples or the inavailability

of technetium for experiment. There is one notable exception of the rule viz.

the RRh2Si2-compounds, which have unusually higher ordering temperatures than

expected by this systematics. Finally, we note there is always a decrease of

the Curie-Weiss temperatures with decreasing number of d-electrons within a

series. This leads to absolute values of 0_. up to 25 times the Nêel

temperature Tjq at the Pauli-paramagnetic antiferromagnetic phase boundary.

Thus far, four compounds of the (1-2-2) series were found to exhibit heavy-

fermion behaviour, viz- CeCu2Si2, CeRu2Si2, CePt2Si2 and ORu2Si2- All four

compounds lie on the borderline between Pauli-paramagnetic and antiferro-

magnetic behaviour. In general, this trend suggests that heavy-fermion

behaviour should be sought on the borderline between the Pauli-paramagnetic

and antiferrocagnetic systems. CeCu2Si2 and URu2Si2 even become

superconducting, whereas CeRu2Si2 and CePt2Si2 do not become superconducting

nor magnetically ordered. However, it is not clear what relation exists

between the heavy-fermion behaviour and the superconductivity, as the

microscopic interactions have not yet been resolved.

In order to physically explain the trend that indicates the heavy-fermion

behaviour, we need a driving mechanism that (1) decreases the

antiferromagnetism with decreasing number of d-electron, which in turn leads

(2) to a reduction of the U-moments beyond a certain limit and (3) to more

negative Curie-Weiss temperatures with decreasing number of d-electrons. Such

a mechanism can in general be created by a local-moment model or by a band

model-

In a local-moment model various contributions have to be taken into

account. First, the ratio of the Curie-Weiss temperature and the Néel

temperature is dependent of the magnetic structure. Furthermore, crystal-field

splitting and spin-orbit coupling have to be taken into account. Finally,

many-body effects have to be incorporated, associated with the Kondo screening

of the moments and spin-fluctuating properties. This results in many

parameters to describe the observed trend and it is very difficult to indicate

the driving mechanism.

A clearer picture can be offered by band structure considerations. As the

U-U separation is larger than the Hill-limit, there is not too much overlap of

the 5f-wave functions, resulting in a very narrow 5f-band. However, as was

noticed above, there are many exceptions from the Hill criterion. This means

that other parameters should be taken into account to properly describe the

109

one 5f-spin band is completely filled, leading to good U-moments. Then, heavy-

fermion behaviour originates when the Fermi-level is at or near the top of the

5f-band. It is clear that this particular location of the Fermi-level has a

unique position for the given series of compounds. Nevertheless, heavy-fermion

behaviour can, in principle, be generated in all six series by alloying.

Consequently the behaviour of the pseudo-ternary compounds like U(Os,Ir)2SÏ2

might be very interesting in this respect.

It must be stressed that this picture is a simplification and requires

confirmation by detailed band structure calculations. First, it is a priori

not allowed with increasing number of d-electrons only to shift the Fermi-

level, as the band structure itself can change dramatically with, e.g., a

shift of the relative d- and f-band positions. Moreover, band structure

calculations of other heavy-fermion compounds were unable to fully reproduce

the anomalous properties. Finally, it is extremely difficult to extract the

interactions between the moments from the band structure. Here, a local moment

picture is more adequate. Still, the proposed band structure gives a basic

understanding of the trend observed In the (1-2-2) compounds. Additionally,

the trend of the Nêel and Curie-Weiss temperatures can also be explained in

terms of this band structure model. With decreasing number of d-electrons in

the antiferromagnetic state, the 5f-band will be nearer to the Furmi-ltvel.

This leads to an increase of the hybridisation of the f-electrons with the

conduction electrons and thereby to a broadening of the f-band. Thus, the

Kondo-screening of the 5f-moments increases with a corresponding increase in

the Kondo temperature. Consequently, we observe (1) a decrease of the Curie-

Weiss temperatures to more negative values, (2) a reduction of the 5f-moments

at low temperature, and (3) a weakening of the magnetism. All is in

qualitative agreement with the observed trends.

In conclusion, we have observed a trend in the magnetic properties of the

CeÏ2Si2 and UT2SI2 compounds, which located the heavy-fermion behaviour on the

borderline between Pauli-paramagnetism and antiferromagnetism. This trend was

explained with an ad hoc assumption of the band structure, in which with

increasing number of d-electrons the Fermi-level crosses the f-band. Heavy-

fermion behaviour arises when the Fermi-level is located at or near the top of

the f-band and seems a rather general property for these compounds. The

magnetic properties of all (1-2-2) compounds are governed by the proximity

of the f-band to the Fermi-level. Sometimes it results in spin-fluctuating and

Kondo behaviour. However, the heavy-fermion behaviour itself is not explained

nor its relation to the heavy-fermion superconductivity.

110

band structure. Particularly, in these compounds the hybridisation with the d-

electrons is of importance. To describe the properties of the (1-2-2)

compounds a band structure like that shown in Fig.5.16 can be postulated. This

figure shows the UT2Si2~compounds with T a 5d-metal and Ru. Similar ones can

be constructed for the other series. This band structure picture assumes a

broad band for the d-electrons in which a very narrow band for the f-electrons

is fixed. Furthermore, it is assumed that the spin-degeneracy of the f-states

is lifted by the Coulomb repulsion, which shifts one 5f-spin band far above

the Fermi level whereas the other one remains in the d-band. In the Pauli-

paramagnetic systems (URe2Si2 and UOS2S12) there is a considerable charge

transfer from the 5f-band to the d-band, leading to the absence of a 5f-

moment. However, with an increased number of d-electrons (UIr2Si2 and UPt2Si2)

UT2Si2

LU

d-bancl!

5f-bandiA

00

inO

ii

i

i

00• CM CNI

DCEZ>

BMIIË

C-1—1

z>

sJ

00i

Q.Z)iiii

i

Fig. 5.IS. Sehematie band structure model of the VT2Si2 compounds with T a Sd-

metal and URU2SV2 showing the density of states as a function of

energy. The dashed lines indicate the position of the Fermi level

for the corresponding aompowtde.

Ill

5.5. The heavy-fermion compound URU2S12

5.5.1 Introduction to heavy-feraion behaviour

In the preceeding sections the term "heavy-fermion" has often been used

without a proper definition or characterization. In this introduction some

basic concepts will be illuminated[33,34].

The heavy-fermion systems are characterized by large values of the

effective mass of the conduction electrons (m /me~100-200). Although the

origin of this mass enhancement is not fully understood, it is related to

hybridization of the conduction electrons with a very narrow f-band and to

many-body interactions of these hybridized electrons. Therefore, the Fermi-

level must be located in this f-band. This mass enhancement results in an

enhancement of the dressed density of states, thus influencing many physical

properties.

- specific heat. The anomalously large values of the electronic contribution

to the specific heat y, reaching values of 1000mJ/mol K2 and more, have

started the interest in the heavy-fermion systems. This value can be compared

to 0.8mJ/mol K^ for a "normal" metal Cu. Such enormous values arise because

the electronic contribution to the specific heat is proportional to the

dressed electronic density of states N(O)(l+\), with N(0) the bare (or band

structure) density of states and \, an interaction parameter. In these

systems both N(0) and \ are large since the Fermi-surface is located in the

f—band and because of the considerable interactions between the various

electrons (see below). There are enormous entropy changes at low temperature

of the electron system, e.g. S«Rln2 per U at 20K in UBe-j^. This suggests

localized excitations of the heavy electrons. However, such effects are in

contrast to the metallic behaviour observed in the resistivity and the

occurrence of superconductivity.

- Magnetisation. The magnetisation of the heavy-fermion systems is

characterized by Curie-Weiss-like behaviour at high temperature (T~IOO-1000K).

This indicates the existence of local moments in this temperature regime with

values of ~2.6u /Ce, in agreement with a 4fl-state (2.54ji /Ce) and

2.5-4.5u /U which has to be compared to 2.54, 3.58 and 3.62n /U for the Sf1-,

5f2- and 5f^-states, respectively. The Curie-Weiss temperature is large and

negative (ecw~~^°—25OK) indicating large antiferromagnetic interactions in

this temperature regime. Yet, not all compounds order antiferromagnecically,

but instead the magnetic moments can disappear at low temperature. Still, the

magnetic susceptibility of the nonmagnetic systems is enhanced at low

temperature having a value of "10 emu/mol. This enhancement has the same

112

origin as in the specific heat which results in a parameter characterizing the

heavy-fermion compounds: the Wilson-ratio. This parameter is defined as the

ratio between the specific heat and the susceptibility and is unity for free

electron systems. Still, similar values are also found for heaviest systems,

like CeCu2Si2 and UBe^- Compounds with a smaller mass enhancement however,

have all larger values than unity. Unfortunately, the exact physical meaning

of this parameter has not yet been resolved.

The disappearance of the magnetic moments at low temperature has

theoretically been associated with the problem of a dilute magnetic impurity-

For this problem Anderson has proposed a model which takes into account the

Coulomb repulsion U between the two electron spin states on the impurity atom,

the energy difference E between impurity state and the Fermi-level, and the

hybridization V between the impurity level and the conduction band- Then, a

magnetic moment is obtained when the Coulomb repulsion is larger than E,

unless the hybridization with the conduction band is too strong. For this

problem Kondo obtained a logarithmic increase of the resistivity with

decreasing temperature. Thereafter the dilute magnetic impurity problem has

been called the Kondo problem. The basic understanding of the Kondo problem

has encouraged theorists to evolve the dilute system into a non-dilute system,

i.e. a Kondo-lattice. Here a periodic array of magnetic impurities forms a

"Kondo-lattice". The basic idea of the Kondo problem is that the magnetic

moments are screened at low temperature by a cloud of conduction electrons

forming a nonmagnetic many-body singlet ground state at zero temperature. The

magnetic moments dressed with their conduction electron cloud give rise to the

logarithmic increase of the resistivity. The Kondo-lattice problem Is made

difficult first by the orbital degeneracy of the f-electrons and second by the

fact that there are not sufficient conduction electrons in the Kondo system to

screen the moments. How the formation of a singlet ground state occurs only

from the f-electron states, is an issue which has not yet been theoretically

resolved.

- resistivity. For nearly all heavy-fermion systems this logarithmic increase

of the resistivity associated with the screening of the moments, has been

observed. However, at low temperature (6-50K) the resistivity does not level

off, as expected from the dilute case, but exhibits a dramatic decrease from

100-250pQcm to values sometimes less than luQcm. This phenomenon has been

attributed to a coherency effect, where the magnetic atoms coherently scatter

the conduction electrons. Such a coherent state at low temperature indicates

the large interactions between the f-atoms at low temperature. These large

113

interactions must be mediated by less localized (s-,p-,d-) electrons, since

the f-f-atom separation is larger than the Hill iimit, excluding a

considerable f-wave function overlap. This low temperature coherent state,

although not well understood, seems of crucial importance for the description

of the heavy-fermion system. In this coherent state a quadratic temperature

dependence of the resistivity, p-p =AT2, is frequently observed. The

parameter A is enhanced, relative to "normal" metals, and values up to

A=35y£2cm/K2 have been reported. Unfortunately, a T -behaviour has been

predicted by many theories, e.g. Fermi-liquid theory, paramagnon theory,

antiferromagnetism, spin-fluctuation theory.

- Feral liquid theory. The heavy-fermion systems are frequently described by

Landau's theory of Fermi-liquids at low temperature (T«T F). The main

difference with normal metals is the temperature scale since here TF"10-100K

is much lower than in ordinary metals (E =k„T =h2k|/2in ). This theory takesF o r B

account of the large electron-electron interactions present in these systems

by a set of parameters, the Landau parameters F, and an effective mass m . The

major advantage of this theory is that it requires no knowledge of the origin

of tht microscopic electron-electron interactions in order to relate and

calculate macroscopic quantities. A basic result is an enhancement of the

specific heat by m relative to the non-interacting electron system

m =ft oE/ök|, =k_/v_. Among other results are an enhancement of the magnetic

susceptibility by m /(1+F ), and a quadratic temperature increase of theresistivity, p-p =AT2, with the coefficient A~T„ .

O F

- Superconductivity. The occurrence of superconductivity in the heavy-fermion

systems is probably the most puzzling aspect. Meissner effect measurements

have proven it to be a bulk property and the magnitude of the discontinuity at

the superconducting transition in the specific lieat AC/yT ~1 has been taken as

evidence that indeed the heavy-electron system goes superconducting.

Experimentally, the heavy-fermion systems are characterized by a large initial

slope of the critical field -p dH 2^dTlT=T w i t h v a l u e s UP t 0 ~4^T/K- This

large slope arises, in BCS-theory, because tne slope is related to the (large)

specific heat coefficient y (see below). Theoretically, the situation is

complicated because the Fermi-temperature is of order of the Debye temperature

(or the Fermi velocity is of order of the sound velocity), which makes so-

called strong-coupling corrections very important. Further, spin-orbit

interactions and band structure effects must be incorporated. Still, nearly

all experiments on the superconducting state could be explained within

standard BCS-theory, though some parameters had anomalous values. In spite of

114

this success of the BCS-theory, many approaches have taken the electron-

electron interactions, present in the normal state, as the basic mechanism for

superconductivity. Here, the analogy with JHe has suggested an odd-parity spin

pairing mechanism. However, thus far no decisive experiment has been thought

of and a description of the superconducting state in terms of electron-

electron interactions is very incomplete.

5.5.2 MagnetIs» and Superconductivity of the heavy-fermion system URu2Si2

Despite an intense theoretical interest in heavy-fermion systems,[35,36]

there are no predictions as to which ground state will develop at low

temperatures. Experimentally, three possibilities have been demonstrated: (i)

the "bare" heavy-fermion materials characterized by their very large

Y coefficients, e.g., CeAl3[37] and CeCu6,[38] (ii) the heavy-fermion

superconductors such as CeCu2Si2,[15] UBe13,[39] and UPt3,[40] (ill) the

antiferromagnetically ordered heavy-fermion systems like U2Zn-L7[41] and

UCd11[42]. A fourth possibility exists, namely systems with both magnetic and

superconducting order.

During a systematic study of the magnetic properties of CeT2Si2 and UT2Si2

compounds[22] (T is a transition metal) it was found that one particular

system, URu2Si2, exhibited a magnetic transition at 17.5K and a very sharp

superconducting one at 0.8K. The measurements include susceptibility,

magnetisation, and specific heat and were performed on high-quality, single-

crystal samples[43]. Both the magnetic and superconducting properties are

observed to be highly anisotropic. In this section experimental evidence is

presented for the existence of anisotropic magnetic and superconducting order

in URu2Si2- The interpretation is limited to a phenomenological description of

the experimental effects.

We have prepared and studied one polycrystalline and two single-crystalline

samples of URu2Si2- The purity of the elements was better than 99.8% for U,

99.96% for Ru, and 99.9999+% for Si. The polycrystalline sample (»6g) was

fabricated by arc melting and was vacuum annealed for 7d at 1000°C. The single

crystals (>»5 and lOg) were grown with a specially adopted Czochralski "tri-

arc" method[8] and no further heat treatment was performed. The high quality

of these samples was established by X-ray analysis - only lines corresponding

to the ThCr2Si2-crystal structure were observed - and microprobe and

raetallograph: No_ indications for inhomogenities or second phases were found.

The lattice parameters were a=4.121 A, c=9.681 A for the polycrystal at 294K;

115

600

u

800

3010 20T (K)

Fig. 5.1?. Specif ia heat of URu3Sis plotted as C/T ve "fi (above) yielding y

and 9_, and as C/T vs T (below) showing the entropy balance.

0,0 100 200

T(K)

Fig. 5.18. do susceptibility and inverse susceptibility of UR^Sig, measured

in a field of 2T, parallel to the a- and a-axes. The crosses

represent the inverse sueaeptibility and yield 9 =-6SK.

116

a=4.1279(1) A, c=9.5918(7) A at 294K; and a=4.1239(2) A, c=9.5817(8) A at 4.2K

for the single crystals. Consequently, there are no distortions or changes in

symmetry between 300 and 4.2K.

Specific heat was measured on the polycrystalline sample with an adiabatic

heat-pulse method, using a sapphire substrate, an evaporated heater, and a

bare—e.leui.'nt glass-carbon thermometer. Magnetisation was measured with a Foner

vibrating-sample magnetometer in magnetic fields up to 5T and from 1.4K up to

300K on two oriented single-crystalline cylinders, shaped by spark erosion, ac

susceptibility was measured on an oriented sphere, shaped by spark erosion,

down to 0.33K with a standard mutual-inductance bridge operating at a

frequency of 87Hz. The ac driving field was 50uT and a dc magnetic field

parallel to the driving field could be applied up to 3T. Experiments in the

different orientations were performed by cementing the sphere, after fixing

the orientation, to an epoxy cylinder which fitted exactly into the primary

coils. The Meissner effect and magnetisation below IK were determined in the

same manner as described in Ref. 61-

In Fig.5.17 we show the specific heat of annealed polycrystalline URu2Si2

plotted as C/T vs T and C/T vs T^. The magnetic transition (see below) is

clearly discerned by a \-like anomaly at 17.5K. The superconducting transition

exhibits a peak at 1.1K. Extrapolation of the high-temperature regime yields a

value for y=180mJ/mol.(formula unit).K2 and a Debye temperature 9D=312K. Use

of these values in the entropy plot (C/T vs T) results in a negative entropy

balance of -O.166R. This value is comparable to the values obtained for U^Zn^

and UCd u, -O.165R and +0.196R, respectively, [34]. In addition the relative

change in y between the extrapolated and observed valu?s at OK,

(Yext;-Yobg)/Ye =72% for URu2Si2, is very similar to the 70% for U2Zn17 and

the 63% for UCd n[34].

Figure 5.18 shows the dc magnetisations measured in a magnetic field

u H=2T (x, =M/(i H) parallel to the a-and c-axes. The magnetisation is clearly

very anisotropic and the c- axis is the easy axis with very little

magnetisation parallel to the a-axis. The Nêel temperature, if the transition

is considered to be antiferromagnetic-iike, can be defined as the maximum of

d(xT)/dT and occurs at 17.5K[44]. This value corresponds exactly with the

anomaly in the specific heat. The high-temperature data along the c-axis yield

an effective moment u »3.51(i / (formula unit) and a Curie-Weiss temperatureerr B

9 "-65K. Note, however, the deviations from Curie-Weiss and the reduced

\x already beginning at «150K. The room temperature dc susceptibility of

URu2Si2 is about 30 times larger than for ThRu2Si2[32].

117

2 -

-'.71

I i

Bi!-". ".".".•

O.d 1.0T(K)

O i ± L _ _O 0.2 0.4 0.6

T(K)

U Ru3 Si2

o a-axisA c-axis

1.0

Fig. S.I9. Upper aritiaal field \i E „ of URu.gSi8 ^s temperature parallel tothe a- and a-axes. The inset shows three aa susceptibilitysupersonduating transitions measured parallel to the a-axis inapplied mxgnetia fields of 0, 0.62 and 0.81T.

Fig. 5.20. Recorder trace of a magnetisation loop (M vs H) with a virgin aurveat 657mK. The field H was applied in an arbitrary direction.

1 1 8

In Fig.5.19 we plot the superconducting transition temperature, defined as

the 50% point of the transition in the ac susceptibility (see inset of

Fig.5.19), as a function of the magnetic field, parallel to the a-axis and

parallel to the c-axis- For strong-pinning, type-II superconductors this

represents a determination of H^. No corrections were made for the

demagnetising effects [D(sphere)= •«•] f°r both directions. The transitions are

all very sharp: AT between the 10% and 90% points is 0.015K. This further

demonstrates the homogeneity of our samples. We have very carefully corrected

for the magnetic field dependence of the thermometer. The initial slope

-(j. dH „/dT as T>T is the same in both directions, viz. 4.4T/K. However, as To cZ c

is reduced the slope decreases parallel to the c-axis (as is usual), but it

increases strongly reaching 14T/K parallel to the a-axis. Note that it is the

hard-magnetic a-axis which exhibits the largest and most atypical HC2(T)

behaviour.

Figure 5.20 displays one of a series of curves of magnetisation (M) versus

magnetic field (H) in the superconducting state. The initial slope represents

a superconducting volume fraction of more than 80£. This, we argue below, is

convincing evidence that the superconductivity must be ascribed to the bulk.

The |iH , value (1.4mT) obtained from this magnetisation loop compared with

the a H 2=0.86T determined from the ac susceptibility in the same direction

yields a very large Ginzburg-Landau parameter K»33. Note in Fig.5-20 the

typical "type-II" shape of M vs H curves which are fully reproducible upon

cycling and independent of the reversing field amplitude. Other standard

features are the nice overlap of the virgin curve with the field-cycled curves

and that the initial and maximum- and minimum-field slopes are all equal.

Although the magnetisation and specific-heat experiments indicate a

magnetic phase transition at 17.5K, nevertheless the exact mechanism for

magnetism is not clear. The magnetisation curve in 2T shows a broad transition

indicative of an antiferromagnetic ground state. In contrast, we observe a

very sharp transition in the specific heat which cannot be explained simply by

a standard type of magnetic phase transition. The negative entropy balance and

the large relative change in y suggest that the transition must be

accompanied by other effects of electronic or magnetostrictive origin.

Neutron-scattering measurements are required to resolve this problem.

Very similar features have been observed for the heavy-fermion system

Ü2Zn1y[41], Here also a broad magnetisation curve was found accompanied by a

\-like anomaly in the specific heat, a similar relative change in y, and a

small, negative entropy balance. Although an ordinary magnetic phase

119

transition cannot alone explain all these observations, y t neutron

scattering[45] has verified the existence of a long-range ordered

antiferromagnetic state. The close similarities in the specific heat of U^Zn^y

and URuoSio suggest'that the magnetic phase transition should be of the same

origin.

Additional information about the magnetism in URu2Si2 is obtained from our

systematic study[22] of the CeT2Si2 and UT2Si2 compounds. Here we have

determined a trend from antiferromagnetism to Pauli paramagnetism with

decreasing number of d electrons. This trend was explained by an increasing

Kondo-type compensation of the U moments as the number of d electrons is

decreased and it eventually leads to a disappearance of the moment. Two

systems, namely CeCu2Si2 and CeRu2Si2. lie on the borderline between

antiferromagnetism and Pauli paramagnetism and they are usually described with

a Kondo-lattice model. As URu2Si2 also lies close to this border, the general

trend suggests a "confined-moment" behaviour[36], although less severe than in

CeCu2Si2 where the moments completely disappear. Still for URu2Si2 it is not

immediately clear to what extent this moment confinement proceeds at low

temperatures before the superconductivity sets in or whether the

superconductivity coexists with the magnetic order. Again, neutron scattering

should be able to illuminate these questions.

We now will establish from our observations that the superconductivity must

necessarily be a bulk property. The magnetisation measurements were performed

on a high-quality single crystal, with no contaminations or precipitations

observable on the scale of light microscopy and microprobe analysis (lOuro).

Besides being a bulk property, the superconductivity might be ascribed to very

small filaments or a thin surface layer. Superconducting filaments can be

ruled out immediately because of the large initial slope of M vs H (Fig.5.20).

In the case of a superconducting surface layer there are two

possibilities[46]: (i) If the applied field is large enough to penetrate

through the layer, then the magnetisation would collapse at that field by an

amount H-Hc^ for very strong flux pinning or to a value corresponding to the

superconducting volume fraction of the surface for the case of weak pinning

(ii) If the applied field is not large enough, no observable drop in the

magnetisation would be detected. Both possibilities are clearly in

contradiction with our observation in Fig.5.20. Thus the superconductivity

must be a bulk property. Moreover, the specific-heat data below 2K on the

annealed polycrystal, shown in Fig.5.17, confirm bulk superconductivity. Here,

we observe a discontinuity at 1.1K with (Cs-Cn)/Cn»1.3. The normal-state

120

specific heat between 2 and 17K can accurately be fitted with

C=yT+aT3+6e where A»115 K. This exceptional behaviour suggests the opening

of an energy gap at 17.5K over at least part of the Fermi surface.

The anisotropy in HC2 is different from that observed for CeCu2Si2 and

UPt3[34]. Now the initial slope (-|i dH 2/dT) is, within our measuring

accuracy, the same for the a- and c-axes- However, whereas the c axis has the

usual convex behaviour, the a-axis displays a very anomalous, concave

dependence of HC2<T). Nevertheless, the HC2(T) behaviour shows some

resemblance to the HC2 diagrams calculated by Fisher[47] for superconductors

with local magnetic moments.

In conclusion, we have demonstrated the existence of most unusual magnetic

and superconducting transitions in URu2Si2- The magnetism is related to a

confined-moment type of antiferromagnetism, while the superconductivity is

bulk and exhibits abnormal critical-field behaviour. The experimental

properties are highly anisotropic with the c-axis strongly magnetic and the

a-axis favourable for superconductivity. A full theoretical description of

these results is certainly warranted.

5.5.3 Anisotropic electrical resistivity of URu2Si2

In order to gather additional information about this highly unusual heavy-

fermion behaviour the electrical and magnetoresistivity p(T,H) of URu2Si2 was

studied[48]. All measurements were performed on high- quality single crystals

between 0.33 and 300 K in magnetic fields up to 7 T. The electrical

resistivity is highly anisotropic with its room temperature value parallel to

the a-axis almost twice as large as parallel to the c-axis. The magnetic and

superconducting transitions are clearly illustrated by a sharp jump in p at

17 K and p+0 at 0.8 K, respectively.

The single-crystal samples were grown with a specially adopted Czochralski

tri-arc method[8]. No further heat treatment was given. Cylindrical samples of

typical dimensions $ = lmm, X = 5mm were spark cut, parallel to the a- and c-

axes, out of the same single crystal, on which magnetisation measurements were

measured. The electrical resistivity was measured with a standard four-point

method using a dc current of 5mA. The absolute value of the resistivity was

determined at room temperature to better than 2% by measuring the diameter of

the cylinders and the voltage drop at various distances over the entire length

of the sample. The temperature was measured with calibrated carbon-glass and

platinum thermometers. A dc magnetic field up to 7 T could be applied

perpendicular to the current direction via a superconducting solenoid.

.121

4 0 0

200

'I'

I//Q-QXI5

I//OQXIS

URu2Si2

1 _ i. . 1 _.J . J100 200 300

T(K)

Fig. C.21. Temperature dependenoe of the eleetriaal resistivity of unannealed,

single-arystalline URU2Si-2 parallel to the a- and a-axes.

200

S.22. £ou temperature resistivity of single-erystalHne URu2Sis parallelto the a- and o-axee, showing the magnetic (Tjf) and superconducting(T ) phaee transitions. The solid lines illustrate a best fit toEq.(l)' The inset shows an enlargement of the euperoonduating phasetransition.

122

Fig.5.21 shows the overall temperature dependence of the electrical

resistivity parallel to the a- and c-axes. The room temperature resistivity is

330(i!2cm parallel to the a-axis and 170iiQcm parallel to the c-axis. The

temperature coefficient dp/dT is negative in both directions down to 80 K, but

much "larger" along the a-axis. Below 50 K the resistivity decreases rapidly

to a residual resistivity of 32uQcm — the same for both a and c directions.

Two distinct anomalies are observed in the resistivity behaviour at low

temperatures. In Fig.5.22 we show these anomalies on an expanded scale. The

inset in Fig.5-22 clearly elucidates the superconducting transition p-K) . The

50% point of the resistivity transition is at 0.70 K with a transition width

between the 10% and 90% points AT =0.2K. The second anomaly which is strongly

anisotropic in magnitude occurs around 17 K and is reminiscent of the Nêel

temperature anomaly for p(T) in pure Cr[49], a spin density wave

antiferromagnet. To better describe this critical behaviour we have computer

calculated the temperature derivative dp/dT and present our results in

Fig.5.23. Note the negative divergence of dp/dT at 17 K.

30

-T 20

a 10

0

-10-T5

o.-20

-30

URu2Si2

. I//a-axis_ x I //c-axis

_

-

i

je •

X

1 1

t

>

_

-

1

10 15T(K)

20 25

Fig. 5.23. Temperature dependence of the temperature aoeffioient dp/dT ofVRu^Sï^ parallel to the a- and o-axes.

123

The temperature dependence between 1 and 17 K can accurately be described

by using che formula appropriate for an energy gap (A) antiferromagnet[50]

with an additional T -term appropriate for Fermi-liquid behaviour

p - PO = bT[l+2T/A] exp(-A/T) + cT2(1)

Best fitting (see Fig.5.22) gives A = 90(68) K, b = 800(52) n£3cm/K,

c = 0.17(0.10) tiflcm/K2 and p0 = 33 (iQcm, parallel to the a-(c-) axis,

respectively. Just above TN, the resistivity has a power law behaviour

p-po = cT2 with c = 0.35(0.126) pöcm/K2 parallel to the a- (c~) axis.

0.08

0.04

0.00

0.08

0.04

O.OO

'T ?Cl

•'oo

r\

-

°0

OJ p

o

°C)

- • "

i

l//c-axis

\' " " •2OT(K)

-

i

40...-'

• • • ' . • - ' * '

p.-:;|i;i;|;::^Ï3;--.-J«f-vtr-'r.---|i--

i

l//a-axis

* •20

T(K)

1

4 0' «'

*" '• - * *" *

i

• r

- - • • , __IiZ5. . !" 25 40

T=4K.i'

. * - ' . • • ;

I5"*' ~

.....-- •".":

i i

O 4(T)

5.24. Magnetic field dependenae of the resistivity ohange Ap/p ofUR^Sig parallel to the a- and a-axee at several fixedtemperatuve8. The dashed lines ave a fit to parabolic fielddependences. The inset shows the temperature dependenae of the fitaoeff-iaiente a(T) defined ae p-p =a(T)B2.

124

In Fig.5.24 we plot the relative resistivity change,

[p(T,H)-p(T,0)]/p(T,0), versus magnetic field parallel to the a- and c-axes at

several fixed temperatures. Below about 20 K a large, positive magneto-

resistivity emerges in both directions. As the temperature is reduced to 4 K,

Ap/p becomes larger reaching 10% in fields of 7T. Above 25 K, the relative

resistivity change is much smaller (<\X). By fitting these curves to a

parabolic field dependence, Ap/p = aH2, a temperature dependent coefficient

a(T) is obtained and shown in the insets of Fig.5.24. From this coefficient, a

characteristic temperature T o can be extrapolated (see Fig.5.24) resulting in

T Q = 15 and 18 K parallel to the c- and a-axis, respectively. T Q is in close

correspondence with the magnetic transition temperature TN = 17.5 K determined

from other measurements-

Combining these resistivity results with the other measurements, we now can

calculate some microscopic parameters. Using the BCS relations given in

Ref.51, we need four independent parameters to form a self-consistent

description of the superconducting state. We have chosen these parameters as— ft

the isotroplc residual resistivity p =31xl0~ Sm, Y=50mJ/mol K2, Tc=0.78 K

and the isotropic initial slope of the upper critical field-u (dH »/dT)_ _ =4.4 T/K. All were measured on various unannealed singleo c<£ I**i

crystal samples. Accordingly, the relation

-UQ(dHc2/dT)T+T = 1.26xl035Y2Tc/S

2 + 478Oypo (2)c

yields a Fermi surface area S=1.88xl0^m~ . The "dirt parameter"

\ =0.52 indicates that we are neither in the pure nor dirty limit. This

results in a Fermi velocity vF=8.84xl03m/s, a mean free path £cr=2.62xl0~

8m, a—ft

BCS coherence length Z, =1.56x10 m, a London penetration depth

\L(0)=8.60xl0~ m and a Ginzburg-Landau parameter K =73[51].

Thus far no anisotropy is involved in the above calculation since (I) the

initial slope of the upper critical field and the residual resistivity are

isotropic and (ii) we have used formulas [51] which are valid independent of

the shape of the Fermi surface, i.e., they depend only on the total area S.

The anisotropy does indeed affect the determination of the Fermi momentum kp

because the spherical Fermi-surface approximation, S=4nk2, is not valid for

this highly anisotropic compound. Furthermore, we cannot even estimate kp from

S because of the anisotropically gapped Fermi surface due to the antiferro-

magnetic ordering at 17.5K (see below). This gap will reduce S drastically

without necessarily inducing large changes in kp.

125

Therefore, in order to proceed a bit further, we have attempted two other

approaches, which are frequently used in heavy fermion systems [34], to

evaluate k-p. According to Friedel [52], kp can be determined by the number of

conduction electron per formula unit Z

Q ,1/4 ( 3 )

2e2p 3*2

ma,'

Here the angular momentum is A=3,the fraction of U-atoms is x = 1/5, p is-29 q maX

the maximum resistivity and Q = 8.17x10 nr is the volume per U-atom. Using

maximum resistivities parallel to the a- and c-axes of 4O0 j£2cm and 17O(i£2cm, we

calculate Z = 2.02 and 3.83, respectively. This gives a Fermi momentum

k =(3Tt2Z/Q)X^3 being 0.90A"1 parallel to the a-axis and 1.12A"1 for the

c-axis. These values are reasonable when compared to our second approach, the

fully-isotropic, free-electron case of three conduction electrons per U-atom

(Z=3), yielding k l.COA"1 and S=13.3xlO2Om"2. This value of S, a high

temperature one, is much larger than the value calculated above from the BCS

relation which gives a low temperature limit. The difference suggests that

only about 15% of the Fermi surface area contributes to the superconductivity

and is not removed by the antiferromagnetic order. Our result of «15%

remaining Fermi surface area is somewhat smaller than the estimate based on

the ratio of the electronic specific heat coefficients

(y). . /(Y).r-».T "28%. Similarly the Ginzburg-Landau parameter K =73 obtainedj (jij

above is larger than K =33 measured in an arbitrary direction. The

enhancement of the effective mass m* relative to the bare mass mo can be

determined by m /mo=hk„/v_m . As this enhancement is governed by the actual

value of kF, we cannot use the BCS-relations to calculate kp, as only a minor

part of the Fermi surface is involved with the superconductivity and so no

conversion can be made from the Fermi surface area S to the Fermi momentum kp.

Here the estimates for kF based upon the approaches of Friedel or the free-

electron gas are perhaps more appropriate, providing there are no dramatic

changes of the conduction electron density (naki) in the high- and low-

temperature limits. Thus, using an average value of k *1.0A , we obtain

m*/m -130.o

As a phenomenological description of our experimental effects, we propose

the following scenario for the temperature dependence of the magnetic

properties of UIU^S^. At high temperatures (T > 150 K) the U-atoms are in the

local moment regime. Here an anisotropic effective moment of 3.51 n_/f.u. was

measured parallel to the c-axis. The negative dp/dT found in this temperature

126

regime is a rather general property for the heavy fermion systems. Except for

UPtj, it has been found in the magnetic, nonmagnetic and superconducting

systems. This logarithmie-like increase of the resistivity with decreasing T

suggests the formation of a Kondo-like state. However, at * 75 K a broad

maximum appears in p(T) and signals interaction effects between the magnetic

ions[53]. As the temperature is further reduced (T < 70 K) the resistivity

decreases dramatically. Now, due to many-body and hybridization effects, there

is an overlap of the 5f-U wave functions which creates a long-range coherence

to couple the Kondo scatterings among the U ions. This causes the local U

moments to decrease, as can also be concluded from the decrease of the dc-

susceptibility in the same temperature region.

At 17.5K a magnetic phase transition occurs whose exact nature is not

fully clear. We suggest that the phase transition can be described by an

antiferromagnetic type of order with greatly reduced moments. These moments

might be of the induced type with a singlet ground state and a large exchange

interaction!54]. Preliminary neutron scattering results on single crystalline

samples have revealed magnetically ordered moments along the c-axis of order

of O.Olp, /U. These moments were found to coexist with the superconducting

state[55].

The behaviour of the specific heat and resistivity below TJJ can be

ascribed to the opening of an energy gap at TJJ (see above and Ref.56). Here

parts of the Fermi surface with appropriate symmetry conditions will form an

energy gap due to the symmetry of the antiferromagnetic state. This leads to

two conduction channels as expressed in Eq.(l): one for the gapped part of the

Fermi surface, and a second for the remainder of the Fermi surface. The T

term of Che latter channel is a general property of Fermi liquids. Since m*

and kF are similar to UPt3[57], but only «15% of the Fermi surface is involved

with the transport properties, we expect a reduction by about an order of

magnitude for the coefficient c in Eq.(l)[58]. This is in agreement with

experiment[59]. Correspondingly, there should also be a reduction of the

magnetoresistivity coefficient a(T) by the same amount with respect to UPt-j.

However, we find experimentally similar values for the magnetoresistivity up

to 7T for URu2Si2 as for UPt3[59]. Therefore, the magnetoresistivity cannot

simply be attributed to Fermi liquid behaviour, but must, in part, be caused

by the antiferromagnetic ordering[60].

Below 5K the contribution of the gapped part of the Fermi surface to the

resistivity is frozen out leaving only out the T^-behaviour. Similarly the

electronic part of the specific heat is reduced with respect to its value

127

above TN. Still, no fully coherent state arises as is inferred by the large

residual resistivity, (c.f.(Ce,La)Pb3)[33]. This could be caused by the

presence of (reduced) magnetic moments which remain down to at least 0.5K.

Finally, superconducting order sets in at 0.8K. The discontinuity in the

specific heat at Tc with (Cg-CN)/CN»l-3 suggests that the heavy electrons

themselves go superconducting. This is also indicated by the high values of

-HodHc2/dT. In addition, the f-electrons, hybridized with the conduction

electrons, further participate in the magnetic transition at 17.5K. This is

illustrated by the U-form factors found in the neutron measurements[55]. Hence

it would seem that part of the Fermi surface is involved with the magnetic

ordering and part with the superconductivity, with a coexistence of

superconductivity and magnetic ordering below about IK. However, both parts

are characterized by the same hybridized 5f-electrons.

References

Parts of this chapter have been published or have been submitted for

publication and can be found in references 7, 18, 22, 43, 48, 55. Section 5.4

will be revised for publication in Phys. Rev. B.

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2. Z. Ban and M. Skirica, Acta Cryst. 18 (1965) 594.

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1155.

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5. K. Hiebl and P. Rogl, J. Magn. Magn. Mater. 50 (1985) 39.

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7. A.A. Menovsky, C E . Snel, T.J. Gortenmulder, H.J. Tan and T.T.M. Palstra,

J. Cryst. Growth, (1986).

8. A.A. Menovsky and J.J.M. Franse, J. Cryst. Growth 65 (1983) 286.

9. B. Chevalier, P. Lejay, J. Etourneau and P. Hagenmuller, Mat. Res. Bull.

18 (1983) 315.

10. I. Felner and I. Nowik, Solid State Comm. 47 (1983) 831.

11. H.F. Braun, J. Less Comm. Met. 100 (1984) 105.

12. T.T.M. Palstra, P.H. Kes, J.A. Mydosh, A. de Visser, J.J.M. Franse and A.

Menovsky, Phys. Rev. B30 (1984) 2986.

13. M. Ishikawa, H.F. Braun and J.L. Jorda, Phys. Rev. B27 (1983) 3092.

128

14. G.W. Hull, J.H. Wernlck, T.H. Geballe, J.V. Waszczak and J.E. Bernardini,

Phys. Rev. B24 (1981) 6715-

15. F. Stegllch, J. Aarts, C D . Bredl, W. Lieke, D. Meschede, W. Franz and H.

Scha'fer, Phys. Rev. Lett. 43 (1979) 1892.

16. M. Tinkham, in Introduction to Superconductivity, (McGraw-Hill, New York,

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17. U. Rauchschwalbe, W. Lieke, C D . Bredl, F. Steglich, J. Aarts, K.M.

Martini and A.C. Mota, Phys. Rev. Lett. 49 (1982) 1448.

18. T.T.M. Palstra, L. Guo, A.A. Menovsky, G.J. Nieuwenhuys, P.H. Kes and J.A.

Mydosh, submitted to Phys. Rev. B.

19. W.B. Pearson, The Crystal Chemistry and Physics of Metals and Alloys,

(Wiley, New York, 1972) p. 156.

20. B.H. Grier, J.M. Lawrence, V. Murgai, and R.D. Parks, Phys. Rev. B29

(1984) 2664.

21. K. Hiebl and P. Rogl, J. Magn. Magn. Mater. 50 (1985) 39.

22. T.T.M. Palstra, A.A. Menovsky, G.J. Nieuwenhuys and J.A. Mydosh, J. Magn.

Magn. Mater. 54-57 (1986) 435.

23. V. Murgai, S. Raaen, L.C. Gupta, and R.D. Parks, in Valence Instabilities,

edited by P. Wachter and H. Boppart, (North-Holland, Amsterdam, 1982) p.

537.

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529.

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1225.

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211.

27. H. Ptasiewicz-Bak, J. Leciejewicz and A. Zygmunt, Sol. State Comm. 55

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28. J.D. Thompson, J.O. Willis, C Godart, D.E. McLaughlin and L.C. Gupta,

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29. L.C. Gupta, D.E. McLaughlin, Cheng Tien, C. Godart, M.A. Edwards and R.D.

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31. H.H. Hill, in Plutonium and other Actinldes, edited by W.N. Miner (AIME,

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32. K. Hiebl, C. Horvath and P. Rogl, J. Magn. Magn. Mater. 37 (1983) 287.

33. An overview of some theoretical aspects of heavy-fermion systems is given

129

by P.A. Lee, T.M. Rice, J.W. Serene, L.J. Sham and J.W. Wilkins, Comm.

Sol. State Phys.

34. An overview of experimental data on heavy-fermion systems is given by G.R.

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35. See, for example, the collection of papers in Moment Formation in Solids,

edited by W.J.L. Buyers (Plenum, New York, 1984).

36. C M . Varma, Comm. Solid State Phys. 11 (1985) 221.

37. H.R. Ott, Physica 126B (1984) 100.

38. G.R. Stewart, Z. Fisk and M.S. Wire, Phys. Rev. B30 (1984) 482.

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1595.

40. G.R. Stewart, Z. Fisk, J.O. Willis and J.L. Smith, Phys. Rev. Lett. 52

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1551.

42. Z. Fisk, G.R. Stewart, J.O. Willis, H.R. Ott and F. Hulliger, Phys. Rev.

B30 (1984) 6360.

43. T.T.M. Palstra, A.A. Menovsky, J. van den Berg, A.J. Dirkmaat, P.H. Kes,

G.J. Nieuwenhuys and J.A. Mydosh, Phys. Rev. Lett. 55 (1985) 2727.

44. The ac susceptibility X'CO exhibits a very weak magnetic response from 4

to 25K. Nevertheless a small is descernable at about 17.5K.

45. D.E. Cox, G. Shirane, S.M. Shapiro, G. Aeppli, Z. Fisk, J.L. Smith, J.

Kjems and H.R. Ott, to be published.

46. A.M. Campbell, and J.E. Evetts, Adv. Phys. 21 (1972) 199.

47. O.H. Fisher, Helv. Phys. Acta 45 (1972) 331.

48. T.T.M. Palstra, A.A. Menovsky and J.A. Mydosh, accepted for Phys. Rev. B.

49. 0. Rapp, G. Benediktsson, H.U. Aström, S- Arajs and K.V. Rao, Phys. Rev.

B18 (1978) 3665.

50. N. Hessel Andersen, in Crystalline Field and Structural Effects in f-

electron Systems, edited by J.E. Crow, R.P. Guertin and T.W. Mihalisin

(Plenum, New York, 1980) p.373.

51. T.P. Orlando, E.J. McNiff, S. Foner and M.R. Beasley, Phys. Rev. B19

(1979) 4545.

52. J. Friedel, Nuovo Cimento Suppl. 7 (1958) 287.

53. J.S. Schilling, Phys. Rev. B33 (1986) 1667.

54. B.R. Cooper, in Magnetic Properties of Rare Earth Metals, edited by R.J.

Elliot (Plenum, London, 1972) p.41.

55. C. Broholm, J. Kjems, W.J.L. Buyers, T.T.M. Palstra, A.A. Menovsky and

130

J.A. Mydosh, to be published.

56. M.B. Maple, J.W. Chen, Y. Dalichaouch, T. Kohara, C. Rossel, M.S.

Torikachvlli, M.W. McElfresh and J.D. Thompson, Phys. Rev. Lett. 56 (1986)

185.

57. C.J. Pethick, D. Pines, K.F. Quader, K.S. Bedell and G.E. Brown, to be

published-

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Press, New York, 1972) p.60.

59. A. de Visser, R. Gersdorf, J.J.M. Franse and A.A. Menovsky, J. Magn. Magn.

Mater. 54-57 (1986) 383,

60. In general antiferromagnetically ordered materials also have a quadratic

field dependence of their magnetoresistivity. See, for example, K.A.

McEwen, in Handbook of the Physics and Chemistry of Rare Earths, Vol.1,

edited by K.A. Gschneider, Jr. and L. Eyring (North-Holland, Amsterdam,

1978) p.479.

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A.A. Menovsky, Phys. Rev.B30 (1984) 2986.

131

Summary

In this thesis the magnetic and superconducting properties are discussed

for three novel types of intermetallic compounds- These compounds are studied

with methods probing the magnetism, electrical transport and super-

conductivity.

First, the LaFejj-type compounds were studied. We have established the

magnetic phase diagram of La(Fe,Al)^3, consisting of a mictomagnetic,

ferromagnetic and antiferromagnetic regime. The mictomagnetism and

ferromagnetism can be considered as analogues of the binary Fe-Al system.

Therefore, we have concentrated on the unusual antiferromagnetic phase. By

applying a magnetic field this phase exhibits sharp metamagnetic transitions

to the saturated ferromagnetic phase. This effect offers the unique

possibility to study how fundamental properties, such as the volume,

electrical transport, etc., probe the magnetic state. These measurements were

interpreted in terms of phenomenological models, which portray the basic

physics of these fundamental properties. Also the magnetic critical phenomena

have been studied. Finally, the symmetry of the antiferromagnetic structure

was revealed by neutron scattering experiments. Our main conclusion is that in

La(Fe,Al)23 the magnetic properties vary in a controlled way from a-Fe-like

ferroraagnetism to y-Fe-like antiferromagnetism. Therefore, this system can be

considered as a new and favourable model system for the study of Invar

phenomena.

Second, uranium-based compounds were studied. In several equiatomic ternary

(1-1-1) compounds we observed a broad variety of magnetic properties, ranging

from local-moment magnetism to Kondo-lattice behaviour. This study is

complicated by the three different crystal structures of these compounds. The

most interesting behaviour was observed for the cubic systems, where

Kondo-lattice behaviour was observed in the magnetic properties, and a

semlconducting-like behaviour in the electrical transport properties. The

semiconductivity is discussed in terms of the crystal structure. The

Kondo-lattice behaviour is ascribed to strong many-body interactions of the

5f-electrons in a narrow band near the valence or conduction band.

Finally, the magnetic and superconducting properties are described for

several RT2Si2 compounds, with T a transition metal. For R»Y, La and Lu type-I

superconductivity was observed, which is explained with BCS-theory. The study

of the magnetic properties of the compounds with R»Ce,U yielded a systematic

trend by varying the number of d-electrons and suggested a guideline for the

132

location of heavy-fermion behaviour. This trend was interpreted in terms of a

simple band structure model. This investigation resulted in the discovery of

the exotic behaviour of URu2Si2- This compound exhibits both an antiferro-

magnetic phase transition at 17.5K and a superconducting one at about IK, both

caused by the 5f-electrons. Such a coexistence behaviour is interpreted with

part of the Fermi surface carrying the magnetism and another part the super-

conductivity.

Samenvatting

In dit proefschrift worden de magnetische en supergeleidende eigenschappen

van drie nieuwe typen intermetallische verbindingen behandeld. Deze

verbindingen zijn bestudeerd met meettechnieken die inzicht geven in het

magnetisme, de supergeleiding en de electrische transporteigenschappen.

Ten eerste zijn de LaFejj-achtige verbindingen bestudeerd. Hierbij is het

magnetische fase-diagram bepaald van La(Fe,Al)13- Het bestaat uit een micto-

magnetisch, ferromagnetisch en antiferromagnetisch gebied. Het mictomagnetisme

en ferromagnetisme kunnen als analogie van het magnetisme in het binaire Fe-Al

systeem worden beschouwd. Daarom hebben we ons geconcentreerd op de ongebrui-

kelijke antiferromagnetische fase. Deze fase ondergaat een metamagnetische

faseovergang naar de verzadigd ferromagnetische toestand. Deze eigenschap

biedt de unieke gelegenheid om te bestuderen hoe fundamentele eigenschappen

zoals het volume, de electrische weerstand, enz., samenhangen met de

magnetische toestand. Deze metingen zijn geïnterpreteerd op basis van fenome-

nologische modellen, die de essentie van deze fundamentele eigenschappen

weergeven. Tevens is het kritisch gedrag bestudeerd. Ten slotte is de

symmetrie van de antiferromagnetische toestand opgehelderd door neutronen-

metingen. De belangrijkste conclusie is dat in La(Fe,Al)13 de magnetische

eigenschappen op een gecontroleerde manier veranderen van het ferromagnetisme

van a-Fe naar het antiferromagnetisme van y-Fe. Daarom kan dit systeem worden

beschouwd als een nieuwe en zeer gunstige verbinding voor de studie van Invar

verschijnselen.

133

Ten tweede zijn uranium verbindingen bestudeerd. In enkele equiatomaire

ternalre (1-1-1) verbindingen is een rijke schakering van magnetisch gedrag

waargenomen, variërend van lokaal-moment magnetisme tot Kondo-rooster gedrag.

De interpretatie is bemoeilijkt door de drie verschillende kristalstructuren

van deze verbindingen. Het meest interessante gedrag is waargenomen voor de

kubische verbindingen. Hier werd Kondo-rooster gedrag gevonden voor het

magnetisme, en halfgeleider gedrag bij de electrische transport eigenschappen.

Het halfgeleider gedrag is besproken in termen van de kristalstructuur. Het

Kondo-rooster gedrag wordt toegeschreven aan sterke veel-deeltjes interacties

van de 5f-electronen in een smalle band dicht bij de valentie of geleidings-

band.

Ten slotte zijn de magnetische en supergeleidende eigenschappen behandeld

van enkele RT2si2 v e r b i n d i n8 en, met T een overgangsmetaal. Voor R=Y,La en Lu

werd type-I supergeleiding gevonden, hetgeen verklaard is met de BCS-theorie.

De studie van het magnetische gedrag van de verbindingen met R=Ce,U leverde

een systematische trend op met veranderend aantal d-electronen, die een

leidraad verschaft voor het aantreffen van zwaar-fermion gedrag. Deze trend is

vertaald in een eenvoudig bandenstructuur model. Dit onderzoek resulteerde in

het ontdekken van de exotische eigenschappen van URu2Si2- Deze verbinding

vertoont zowel een antiferromagnetische faseovergang bij 17.5K en een super-

geleidende overgang bij ongeveer IK, beide veroorzaakt door de 5f-electronen.

Deze coëxistentie is geïnterpreteerd met een wodel waarbij een deel van de

electronen aan het Fermi oppervlak verantwoordelijk is voor het magnetisme en

een ander deel voor de supergeleiding.

134

Nawoord

Dit proefschrift is tot stand gekomen in intensieve samenwerking met vele

personen. Allereerst wil ik de metaalfysica groep Mt-4 noemen, waar ik mijn

promotie op een prettige manier heb kunnen uitvoeren. Hierbij waren de vele

discussies met Peter Kes onontbeerlijk, die me duidelijk heeft kunnen maken

dat, ondanks het feit dat de BCS-relaties algemeen geldig zijn, toch geen

enkele supergeleider hieraan voldoet. Alois Menovsky heeft me ingeleid in de

problemen van de metallurgie. Zijn uitstekende preparatieve faciliteiten waren

doorslaggevend voor het welslagen van enkele projecten. Soms blijkt namelijk

de supergeleidende overgangstemperatuur meer te schalen met de kennis van de

metallurgie dan met de natuurgegevens. Verder noem ik graag de prettige samen-

werking met Cor Snel, Ton Gortenmulder en Jan Tan, die op preparatief- en

analysegebied veel werk voor mij hebben verzet. Op Gerrit van Vliet kon ik

altijd rekenen bij problemen met de electronica. De collegae promovendi waren

altijd bereid hun experimentele mogelijkheden voor mij beschikbaar te stellen,

met name de mengkoeler van Detlev Hüser en Auke Dirkmaat, het sputteren van

Armand Pruymboom en de soortelijke warmte van Hans van den Berg. De doctoraal

studentan die bij mij (een deel van) hun experimentele stage hebben gedaan,

zijn goeddeels verantwoordelijk voor een nooit aflatende stroom meetgegevens:

Henri Werij, Ben van Tilborg, Frans van den Akker, Bernard Ouwehand en Marcel

Vlastuin. De heer W-F. Tegelaar heeft grotendeels de tekeningen gemaakt. Mevr.

J.M.L. Tieken heeft het type-werk gedaan, waarbij dit keer zorg is gedragen

voor de rechter kantlijn.

Ook buiten deze groep ben ik gesteund door velen, die meegewerkt hebben aan

het welslagen van mijn promotie-opdracht. De samenwerking net de Werkgroep

Metalen van het Philips Natuurkundig Laboratorium te Eindhoven heeft in

belangrijke mate vorm gegeven aan dit proefschrift. Verder wil ik met name Dr.

A.M. van der Kraan noemen met zijn bijdrage op het Mössbauer gebied, en Dr.

R.B. Helmholdt met neutronen verstrooiing. De metaalfysica groep in Amsterdam

heeft mij ingeleid in het gebied der "zware fermionen". De samenwerking met

Drs. A. de Visser aan zijn onderzoek aan UPt3 is voor mij zeer vruchtbaar

geweest. Dr. F.R. de Boer heeft daarbij nog de hoog-veld metingen voor zijn

rekening genomen.

I wish to acknowledge many stimulating discussions with Dr. K. Bedell on

the interpretation of our 'heaviest' results. Also the discussions with Drs.

C. Broholm and Dr. J. Kjems of Risrf National Laboratory and the use of their

neutron facilities are greatly acknowledged.

135

Curriculum Vitae

T.T.M. Palstra

geboren 12 september 1958 te Kerkrade

Na het behalen van het Gymnasium-p diploma op het RK Gymnasium

Rolduc te Kerkrade, ben ik begonnen met de studie Natuurkunde aan

de Rijksuniversiteit Leiden. Hier behaalde ik in maart 1981 het

kandidaatsexamen in de studievariant met hoofdvakken Natuurkunde

en Wiskunde en het bijvak Scheikunde (N2). In de doctoraalfase heb

ik mijn experimentele stage verricht in de Werkgroep Metalen onder

leiding van Prof-Dr. J.A. Mydosh. Hier werd ik begeleid door Dr.

J.C.M, van Dongen. Mijn afstudeerwerk betrof de bestudering van de

intermetallische verbinding Gd(Cu.Ga) met behulp van electrische

weerstandsmetingen en magnetische susceptibiliteitsmetingen. Het

doctoraal examen Natuurkunde legde ik af in november 1981.

In december 198X trad ik in dienst van de Stichting FOM te

Utrecht, gedetacheerd bij bovengenoemde Werkgroep Metalen op het

Kamerlingh Onnes Laboratorium. De resultaten van het hier

verrichte onderzoek staan grotendeels beschreven in dit proef-

schrift. Sinds januari 1982 was ik assistent bij het Natuurkundig

Practicum voor prekandidaten, waar ik ondermeer de röntgen-

opstelling en de soortelijke warmteproef beheerde.

136

magnetism, superconductivity and their interplay a …

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