MAGNETISM, SUPERCONDUCTIVITY AND 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 MAGNETISM, SUPERCONDUCTIVITY AND THEIR INTERPLAY A STUDY OF THREE NOVEL INTERMETALLIC COMPOUNDS:
La(Fe,Al)13 UNiSn URu2Si2 MAGNETISM, SUPERCONDUCTIVITY AND THEIR INTERPLAY A STUDY OF THREE NOVEL INTERMETALLIC COMPOUNDS:
La(Fe,Al)13 UNiSn URu2Si2
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN 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 1986 TE KLOKKE 16.15 UUR
door
THOMAS THEODORUS MARIE PALSTRA geboren te Kerkrade in 1958
NKB OFFSET BV — BLEISW1JK Samenstelling Promotiecommissie
Promotor : Prof.Dr. J.A. Mydosh Co-promotoren : Dr. K.H.J. Buschow Dr. G.J. Nieuwenhuys Referenten : Prof.Dr. E.P. Wohlfarth Dr. J.J.M. Franse Overige leden : 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 3.7.2 Experimental results 53 3.7.3 Magnetic properties 57 3.7.4 Electrical resistivity 58 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 4.2.2 Magnetic properties 65 4.2.3 Electrical resistivity 71 4.2.4 Magnetoresistivity 73 4.2.5 Hall resistivity 74 4.2.6 Specific heat 77 4.3 Discussion 77 4.3.1 Magnetic properties 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 5.3.1 Introduction 87 5.3.2 Experimental results 89 5.3.3 Discussion 91 5.4 Magnetic properties of the RT2Si2~ternary compounds (R=Ce,U) 95 5.4.1 Introduction 95 5.4.2 Crystal structure 95 5.4.3 Experimental results 96 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 as observed two decades lower in temperature for LaRh2Si2» 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, CD. 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 (
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 Vind 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 Cubic
La(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 Fe11, 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-
O 0.2 0.4 0.6 0.8 1.0
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
-2.50 Q.
-2.48
-2.46
-2.44 0.6 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 Fe11 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 Fe11 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 H and x=0.9 for I^(FexSi1_x)13. °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 La Fe si different composition becomes favoured. This limits ( x i_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 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 v e since several xFey and LuxFe„ compounds do exist. Still, YF i3 and LuFe^3 Fe and cannot be stabilized because Y2 17 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 0.1 5 2OO IOO (c) 0 100 200 3OO T(K) fig. 3.5. 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 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 0- La(FexAl,.x),3 200- f X = 0.58 X=0.73 190 160- 100 200 300 100 200 300 T(K) T(K) 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 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)13 100 200 300 TOO 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 0.5- = 0.73 a) I.Ol- l_a(FevAl.x) a. 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 1 1 1 1 1 ' ' i i La (Fe AL 4y x l-x),3 X= 0.877 es) 3 in 2 -° 5 • 1 's- 1 > i i i o. 50 100 T(K) Fig. 3.10. Tempevatuve dependence of the spin-flip fields for inaveaeing (open airalee) and deaveaeing fields (full eiveles) for I>a('Pe:lAl1_x)ls with x=0.877. 8.85 0.90 Pig. 3.11. Concentration dependence of the spin-flip fields observed in La(Fe;lAl^_x)2s a* 4.2K for insveasing (open airales) and decreasing 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 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 0.10 La(FexAl,.x)I3 ]7O X=0.88 ,0.05 E 16O- a. •a 150 - 0.05 - Lfl(FexAl,.x) X=0.88 140J— -0.10. 1 100 2OO 300 !OO 200 300 T(K) T(K) Fig. 3.13. Eleotriaal resistivity p vs temperature for an antifervomagnetia £ 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 TN 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 -3 uf=+7.2xl0 and the hysteresis width decreased from 3.ST at 4.2 K to 0.5T at 77K. 1 r La(Fe Al,_ ) x x 13 1.0 _ X = 0.89 T=4.2K 'o 3~ 0.5 Fig. 3.16. Forced volume magnetostriction u)*=hV/V)*=h as a function of mignetio field for an antiferromagnetia sample (x=0.89) at helium temperature. 35 3.5 Discussion 3.5.1 Magnetic properties. La can e The magnetic phase diagram of (FexAli_x)]L3 ^ constructed from the results of the susceptibility, resistivity, and magnetisation experiments. The first regime (I), 0.42 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. I a Fe Furthermore, we find a mictomagnetic phase in -' ( xAlx_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 La(FexAL,_x))3 200 100 micto- I magnetism 0.4 0.6 Fig. 3.16. Magnetic phase diagram of La^Fe^l}^)^. The freezing temperature ie indicated by A, the Curie temperature by 0, and the fleet temperatures 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 Fe^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 Tc 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 Fe in connection with y-Fe (fee) and xNi^_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 thermally a 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 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 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]. La Fe As a pseudobinary intermetallic compound, ( xAli_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. j Some striking metamagnetic properties of I a(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 Hgf 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 a anisotropy field Han, H f (2H H ) , since the exchange field Hex 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. ïja Fe The main features of the electrical resistivity of ( xAl^_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 6 l 1 ar=8i-xlQ~ K~ , p=182|iflcm for x=0.84 and C^ISAXKT^K" , 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«TC) 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. L F Such is in agreement with the observed behaviour of a( e3CAl^_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=0.89 sample, 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 S , 1UC L J where « is the compressibility, Cloc 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)s = KC.band ,£7 m?(Tiv ') 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. La Fe In order to explain the magnetostriction results of ( xAl^_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, 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 state s 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 fluctuations[61]. In spin-fluctuation theory Tc is proportional to T)(T )=u (T )/u (0) and in FeNi Invar ri(T ) has a minimum in the instability c 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. La Fe Neutron diffractograms of two ( xAl1_x)13 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 in t> 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 Fe11 sites does not seem possible, owing to the fact that for both sites various types of nearest-neighbour coordinations exist, differing in the 47 50 La(FexAl,_x)]3 ::::::! observed profile c X=0.91 calculated profile 8 "o cin 5 75 100 125 150 175 2-theta (degrees) 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, B o 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 Fe11 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~^^ ^or 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 x=0.69 x=0.91 300 K 4.2 K 300 K 4.2 K a A 11.7378(3) 11.7235(3) 11.5788(3) 11.5932(3) y 0.17720(7) 0.17738(6) 0.17869(6) 0.17938(6) z 0.11399(7) 0.11369(7) 0.11591(6) 0.11624(7) d A 2.470 2.440 2.466 2.478 2 B A 0.64(5) 0.22(6) 0•61(5) -0.04(5) M/Fe - 1.41(8) - 2.05(3) "Fe1 - - - 1.10(7) MFeII ^B - - - 2.14(3) RNucl % 2.2 1.8 1.3 1.3 RMagn % - 3.0 - 21.4 v 2 13.0 6.8 8.6 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 1 11 factor, mpel and the magnetic moment of Fe and Fe 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 2 2 l Xv is defined as XV =I W^[yJiobB)-y^aalc)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 that a 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 Fe11 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 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 La Fe In the entire concentration regime of ( xSii_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 1.0 ' *i 0.8 3 O.6- u a La Fe Si 0.4(- ( x i-x">|3 X= 0.862 0.2- 0. 0 100 200 300 T(K) Fig. 3.20. Temperature dependenee of the aa susceptibility in with x=0.862. 53 280 260- 24O- 220 200- 180 O.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(FexSiJ' ,i-x'i J 3 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. -1 r -[-- 0.12 0.08 0.04 0- -0.04;- La(FexSi,.x)I3 H a 0.862 b 0.B54 ; - 0.08 - c 0.846 -* d 0.838 | e 0.831 I -0.12 1_. I X l..J_.._L. J 150 250 300 T(K) 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- 100 200 300 T(K) 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]). La(FexSi,_x) 13 X= 0.862 -4 -6 -6.6 -5.8 -5.0 -4.2 -3.4 -2.6 -1.8 In (T-Tc) / Tc Fig. 3.25. Log -plotted versus log(T-Tc)/Ta for La(Fe3Si1_x)13 with x=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] Y X ~ (T-Tc)~ . 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 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 Tc 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. References Parts of this chapter have been submitted for publication or are already published. These publications can be found in references 3, 4, 5, 12, 62, 63 and 64. 1. R.W.G. Wyckoff, The Analytic Expression of the Results of the Theory of Space Groups (Carnegy Institution of Washington, 1922) pg 99. 2. P.I. Kripyakevich, O.S. Zarechnyuk, E.I. Gladyshevsky, and O.I. Bodak, Z. Anorg. Chem. 358 (1968) 90. 3. T.T.M. Palstra, J.A. Mydosh, G.J. 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Omata, H. Mollymoto, M. Motokawa and M. Date, J. Phys. Soc. Jpn 47 (1983) 675 and In High Field Magnetism (North-Holland, Amsterdam, 1983) pg.51. 38. A.B. Lidiard, Proc. Roy. Soc. A224 (1954) 161. 39. E.P. Wohlfarth, Phys. Lett. 4 (1963) 83. 40. M. Shimi2u, J. Magn. Magn. Mater. 50 (1985) 319. 41. J.H. Mooij, Phys. Status Solldi A 17 (1973) 521. 42. P.B. Allen, In Physics of Transition Metals 1980, edited by P. Rhodes (I0P, London, 1981), pg. 425. 43. J.W.F. Dorleijn, Philips Res. Rep. 31 (1976) 287. 44. I.A. Campbell and A. Fert, in Ferromagnetic Materials, edited by E.P. Wohlfarth (North-Holland, Amsterdam, 1982), Vol. 3, pg. 747. 45. N.F. Mott, Adv. Phys. 13 (1964) 325. 46. W. Bendick and W. Pepperhoff, J. Phys. F8 (1978) 2535. 47. P.G. de Gennes and J. Friedel, J. Phys. Chetn. Solids 4 (1958) 71. 48. D.J. Kim, Progr. Theor. Phys. 31 (1964) 921. 49. M.E. Fisher and J.S. Langer, Phys. Rev. Lett. 20 (1968) 665. 50. M.P. Kawatra and J.I. Budnick, Int. J. Magn. 1 (1970) 61. 51. M. Viard and G. Gavoille, J. Appl. Phys. 50 (1979) 1828. 52. Y. Suezaki and H. Mori, Progr. Theor. Phys. 41 (1969) 1177. 53. See, for example, S. Alexander, J.S. Helman, and I. Balberg, Phys. Rev. B13 (1976) 304. 54. The Invar Problem, edited by A.J. Freeman and M. Shimizu (North-Holland, Amsterdam, 1979). 55. E.C. Callen and H.B. Callen, Phys. Rev.A 139 (1965) 455. 56. E.P. Wohlfarth, J. Phys. C2 (1969) 68. 57. M. Shimizu, J. Magn. Magn. Mater. 20 (1980) 47. 58. M. Shiga, J. Phys. Soc. Jpn. 50 (1981) 2573. 59. J.F. Janak and A.R. Williams, Phys. Rev. B 14 (1976) 4199. 60. J.C.M. van Dongen, T.T. :. Palstra, A.F.J. Morgownik, J.A. Mydosh, B.M. Geerken, and K.H.J. Buschow, Phys. Rev. B27 (1983) 1887. 61. T. Morya and K. Usaml, Solid State Commun. 34 (1980) 95. 61 62. T.T.M. Palstra, G.J. Nieuwenhuys, J.A. Mydosh, R.B. Helmholdt and K.H.J. Buschow, J. Magn. Magn. Mater. 54-57 (1986) 995. 63. R.B. Helmholdt, T.T.M. Palstra, G.J. Nieuwenhuys, J.A. Mydosh, A.M. van der Kraan, Phys. Rev. B, to be published. 64. A.M. van der Kraan, K.H.J. Buschow and T.T.M. Palstra, Hyperfine Interact. 15/16 (1983) 717. 65. H.M. Rietveld, J. Appl. Cryst. 2 (1969) 65. 66. P.CM. Gubbens, J.H.F. van Apeldoorn, A.M. van der Kraan and K.H.J. Buschow, J. Phys. 4 (1974) 921. 67. D.M. Roy and D.G. Pettifor, J. Phys. F, 7 (1977) L183. 68. O.K. Anderson, J. Madsen, U.K. Poulsen, 0. Jepsen, and J. Kollar, Physica 86-88B (1977) 249. 69. E.P. Wohlfarth, in Ferromagnetic Materials, vol.1, edited by E.P. Wohlfarth (North-Holland, Amsterdam, 1980) pg.3. 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 high a 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 d a c raagn. T 9 H,C(4K) P(4K) p(300) p flp/p S N,C CW "eff max y D A A A K K "B T HQcm Mficm 10-3 mJ K molK2 Calii2 UAuSn 3.60 4,717 7.208 a.f. 35 -4 3.06 650 610 650 UPdSb 3.61 4.587 7.215 ferro 65 +70 2.92 0.70 2.40 3500 5300 5300 62 179 (JPdSn 3.65 4.608 7.310 a.f. 29 -10 3.16 430 1500 1500 -82 4.3 - Fe2P UIMA1 3.51 6.733 4.035 a.f. 21 +2 1.70 215 255 255 -6.5 160 UNiCa 3.51 6.733 4.022 a.f. 38 +28 2.71 1.30 95 325 325 -620 59 ThNICa 3.67 7.057 4.019 p.p. 32 110 110 +10 UCoSn 3.72 7.145 3.994 ferro 85 +25 3.0 1.28 0,.38 170 300 300 53 ThCoSn 3.84 7.383 4.057 H.ferro 43 47 200 200 3.7 URhSn 3.83 7.365 3.993 ferro 25 +8 3.43 1.37 0..02 50 320 320 -13 URuSn 3.S3 7.345 3.947 ferro 58 +55 2.61 1.13 0.25 120 420 420 +4.2 UlrSti 3.84 7.375 4.012 ferro 25 +20 2.86 0.62 0.58 105 295 295 URuSn 3.85 7.385 3.915 ferro 35 +30 3.04 0 .60 0.58 262 302 302 -28 MgAgAs UNISn 4.51 6.385 Ko 47 -75 3.08 400 1325 7000 -20 IB 215 ThNlSn 4.63 6.544 p.p. 5700 2770 5700 1.5 228 LaNiSn (E-TlNlSt) p.p. 25 360 360 12 198 URhSb 4.62 6.534 Ko 40 -111 3.25 72000 68000 80000 -27 2.1 214 ThRhSb 4.71 6.66 p.p. 2640 3000 3000 +3.3 HfRhSb 4.41 6.238 p.p. 385 850 850 +8.1 UPtSn 4.68 6.617 Ko "75 -100 3.55 19000 36000 40000 +5.0 11 185 ThPtSn 4.77 6.749 p.p. 2600 4800 4800 +13 2 - HfPtSn It.lib 6.310 p.p. 28000 14500 28000 +2.7 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.f or 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 I 1 ' A * UNi Sn + + + o URhSb + + + • * UPtSn + + * UPdSn 1x0.75) - n \ * UAuSn(xO.75)' ~5 3 + ' + +• + V + i i i 100 200 T (K) 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 poo 0.6 o o cx»bo o o o o oiqoooooo^ ^ X> ° o o 2 0 2 CD o o oJ' 1 h,H IT) o o o o 0.2 o o 1T UPdSb o o o po o O| o o O[ 0 100 200 300 T (K) 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 50 100 T(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 other D 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 whether a 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 > • 8 - vf/ URhSb %i §6 O! 2 - YJSmsnX j \\sHfptSn \^ 0 200 400 600 800 1000 T 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. 2000 JhNiSn UPdSb(/3) I* 1500 — 3 ThRhSb UAuSn -i 1 . L 100 200 100 200 300 T(K) T (K) 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 — 200 o a 200 100 100 200 100 200 300 T (K) T (K) 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. 1 1 n n r of- O o—o T =100K 'o **§ o • UNiSn - a.1 S -40 \ t>50 ~ I toiO X 'o 1 - A - D20 • o - d' \ \ ) 50 100 \ b T (KI -80 , 1 1 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 1 1 1 a O 9 A ° O O + a O X a •o a X o 1100- 4 O 0 x 0 • o * * + UPdSn X A UPdSb o o°° O UCoSn (P ° xxt o UNiSn X URhSb V UPt Sn 1 1 100 200 T2 (K2) Fig. 4.16. Temperature dependenee of the specific heat plotted as C/T ve T2 of several U-based aompounds. 200 1 1 X ThCoSn Th Ni Sn D x " 0 ThPtSn 0 "O a LaNiSn 0 X Q 100- O x ° + 4 • * + O O 4 a X + • o - x c + 4- ir* 0 1 o 100 200 T2 (K2) Fig. 4.17. Temperature dependenae of the speoifia heat plotted as C/T Ve of several Th-based compounds. 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 K2 (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, 2 3 4 3.58uB/U for 5f , 3.62|*B/U for 5f and 2.68uB/U for 5f . 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- R2 was 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 fffri XD' --o- o ---u-1 ,o ..O' OT «x Ca Fig. 5.1- Crystal etvuituree of the WSySi^ compounds. The type avyetal struature is body-centered whereas the structure is primitive. 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 " 87 n r o y— i— LaRh2Si2 ' .YPd2Si2 •' LaPd2Si2" • _"LuPd2Si2 O 0.2 0.4 0.6 0.8 1.0 T(K) Fig. 5.2. Temperature dependenoe of the aa susceptibility of RPdsSi2 and LaFh2Sis at the superconducting transition (F=Y,La,Lu). o °o 8° o o (arb. units) o o • o o i -3 -1 C) 1 3 . (i0H(mT) o o o o o o / OOM YPd2 Si2 M T=Q35 K (arb. \ units) M-oH(mT) 1 / 1 N Ss -3 -2 -l v 1 2/3 V 5.3. Magnetio field dependence of the aa eueaeptibility and magnetisation 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 0.4 0.6 T(K) Fig. 5.4. Supeveondusting phase diagram of i2 and %2 with R=Y, La, lu. 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 2.3 2 La2Rh Si3 - 3 La Rh Si2 3.3 4 La2Rh3Si5 4.4 5 La Rh2Si2 0.074 6 La Rh Si 0.36 S' 7 La Rh3Si2 - 8 La3 Rhj Si^i 4.4 LaSi La La4Rh3 LaRh LaRh2 Rh La5Rh4 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. no For YRh2Si2 and LuRh2Si2 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 Tc 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 < 93 2 Assuming a spherical Fermi-surface n=k|/3ii and setting TC=O.5K the equation 22 5 can be reduced to K =8.72xlO (m*/me) /kp . For the (1-2-2) compounds there are 6 conduction electrons per two formula units per unit cell 3 (4x4xlO=160A ) 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 =I<: K Ginzburg-Landau parameter K2 GL~ =2.4X10 yp 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 Tc 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 3 a(A) c(A) V(A ) TC(K) Hc(o)(mT) YPd2Si2 4.129 9.84 167.8 0.47 5.4 LaPd2Si2 4.283 9.88 181.2 0.39 3.1 LuPd2Si2 4.089 9.85 164.7 0.67 7.0 YRh2Si2 4.031 9.92 161.2 <0.33 - LaRh2Si2 4.112 10.29 174.0 0.074 0.7 LuRhoSio 4.090 10.18 170.3 <0.33 - 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. 2.3 3d Mn Fe Co Ni Cu Mn Fe Co Ni Cu 4d Tc Ru Rh Pd Ag Tc Ru Rh Pd Ag 5d Re Os If Pt Au Re Os Ir Pt Au Fig. 5.5. Structural parameters of the flZ^Sig compounds with. R=Ce,V: the lattice parameters a and a, the unit aell volume V and the ratio a/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=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 (K) (3 100 200 J I 1 1 i io 100 J \ /\ 80 " -< "s ? A u 60 CX ' f / 1 Fig. 5.7. Temperature dependence of the eleatrioal resistivity of CeRh2Si2 on a double logarithmic and double linear scale. 97 Fig. 5.S. Temperatur'e depen- dence of the da susaeptibili- . 20 ty and inverse susceptibility o o/ CeTgSig with f a 4d-metal: 3 Rh, Pd, Ag. • C<2Rn,Si 'g 10 8 200- H L _J A °o 100 200 300 T (K) 600 . 5.5. Temperature depen- dence of the da susceptibili- ty and inverse susceptibility 4OO \ of single crystalline CePdgSig o along several axes. The inset £_ shows an enlargement of the 2OO 3 low temperature behaviour. 100 "200 300° T (K) 1.O Fig. 5.10. Magnetic field de- C<2Pd2Sis pendence of the magnetisation 0.81- • // (1,0,0) '//(0.0,1) of single crystalline CePdgSig «#(1.1,0) along several axes in fields 0.6 - up to S8T. 0.4 - 0.2 - o£ 10 20 30 40 H>H (T) 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 5> > 4O 600 FÏ3' i2. rewper»atur e depen- dence of the da susceptibili- Ce PL,Si. ty and inverse eusaeptibility 30 3 Ce Au2Si2 ö of CeT2Si8 with T a Sd-metal: ° ^ Pt, Au. § 20 " o "o 200^ 3 100 200 300 T (K) 6O 400 Fig. 5.13. Temperature depen- URh2Sis denee of the de susceptibili- ure2si: 300 jp. ty and inverse susceptibility E 40- of UTsSis vith T a 4d-metal: o 200 Rh, Pd. "o " 20 100 ;/ 100 300 T (K) 40 400 1- 5.14. Temperature depen- dence of the dc susceptibility and inverse susceptibility of x o n Re, Os, Ir, Pt, Au. §20 2OO a? l /V". o Ti + 1OO 200 100 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- was ver The first compound studied in this series, URu2Si2, y 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 nas and UT2Si2 compounds. URti2Si2 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 temperatures D (-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-field jj 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 inverse susceptibility 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 pp PP Ko+sc a (A) 3.953 4.036 4.105 c (A) 9.776 9.575 9.934 T=4d- Tc Ru Rh Pd Ag — af ay ca af a (A) 4.098 4.230 4.250 c (A) 10.19 9.873 10.66 TN (K) 37. 10.5 9.5 ecw (K) -163. -57. -36. Peff GO 2.43 2.55 2.54 T=5d- Re 0s Ir Pt Au PP Ko af a (A) 4.253 4.310 c (A) 9.798 10.20 TN (K) - 10.1 ecw (K) -85. -18. Peff GO 2.42 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- Mn Fe Co Ni Cu af af fe a (A) 3.917 3.958 3.988 c (A) 9.614 9.504 9.953 TN (K) 85 103 107 ecw (K) -285 -56 -11 4.85 2.91 3.58 Peff (,B) T=4d- Te Ru Rh Pd Ag Ko+sc af af a (A) 4.127 4.012 4.121 c (A) 9.610 10.06 10.19 TN (K) 17.5 130. 97. ecw (K) -160 -40. -10. ( 2.86 2.65 2.88 Peff V T=5d- Re Os Ir Pt Au PP PP af af ca af a (A) 4.121 4.088 4.217 4.228 c (A) 9.681 9.790 9.704 10.26 TN (K) 5.5 36. 78. 0cw (K) -156. -57. -36. 3.03 3.22 3.11 Peff 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 TN 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) 5f-band iA UT2Si2 00 00 00 LU • CM CNI i in D C- O CE 1—1 Q. Z> z> Z) i i i B i M i d-bancl! i II sJ i i Ë 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 e negative ( cw~~^°—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«TF). 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 takes For 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 the resistivity, 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 dT with values U t0 4 T slope of the critical field -p dH 2^ lT=T P ~ ^ /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; 115 800 600 u 10 20 30 T (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 2 value for y=180mJ/mol.(formula unit).K 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 UCdu, -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 UCdn[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 temperature err 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 -'.71 U Ru3 Si2 o a-axis A c-axis I i 2- Bi!-". ".".".• O.d 1.0 T(K) O i ± L__ O 0.2 0.4 0.6 1.0 T(K) Fig. S.I9. Upper aritiaal field \i E „ of URu.gSi8 ^s temperature parallel to the a- and a-axes. The inset shows three aa susceptibility supersonduating transitions measured parallel to the a-axis in applied mxgnetia fields of 0, 0.62 and 0.81T. Fig. 5.20. Recorder trace of a magnetisation loop (M vs H) with a virgin aurve at 657mK. The field H was applied in an arbitrary direction. 118 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 T o 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 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. .121 400 I//Q-QXI5 200 I//OQXIS 'I' URu2Si2 1 _ i. . 1 _.J .J 100 200 300 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 parallel to the a- and o-axee, showing the magnetic (Tjf) and superconducting (T ) phaee transitions. The solid lines illustrate a best fit to Eq.(l)' The inset shows an enlargement of the euperoonduating phase transition. 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 URu2Si2 -T 20 je • . I//a-axis > a 10 _ x I //c-axis 0 X -10-_ _ T5 o.-20 - - -30 i 1 1 1 10 15 20 25 T(K) Fig. 5.23. Temperature dependence of the temperature aoeffioient dp/dT of VRu^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, 2 c = 0.17(0.10) tiflcm/K 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. i i l//c-axis • r 'T ? Cl 0.08 •'o - - o \ r\ °0 ' "2 "O • 40...-' 0.04 T(K) •••'.•-'*' p.-:;|i;i;|;::^Ï3;--.-J«f-vtr-'r.---|i-- --••, __IiZ5. .! 0.00 "^25 40 i OJ p l//a-axis T=4K.i' 0.08 o * • °C) 20 40 T(K) .*-' .••; 0.04 ' «' I5"*' ~ *" '• - * *" * .....--^•".": O.OO -•" 1 i i i O 4 (T) 5.24. Magnetic field dependenae of the resistivity ohange Ap/p of UR^Sig parallel to the a- and a-axee at several fixed temperatuve8. The dashed lines ave a fit to parabolic field dependences. The inset shows the temperature dependenae of the fit aoeff-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 To can be extrapolated (see Fig.5.24) resulting in TQ = 15 and 18 K parallel to the c- and a-axis, respectively. TQ 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 = 2 the isotroplc residual resistivity p =31xl0~ Sm, Y 50mJ/mol K , 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 single o c<£ I**i crystal samples. Accordingly, the relation 35 2 2 -UQ(dHc2/dT)T+T = 1.26xl0 Y Tc/S + 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 3 8 results in a Fermi velocity vF=8.84xl0 m/s, a mean free path £cr=2.62xl0~ m, 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) e2p 3*22 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 j"28% . Similarly the Ginzburg-Landau parameter K(ji j=73 obtained 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. 1. E. Parthe and B. Chabot, in Handbook on The Physics and Chemistry of Rare Earths, Vol.6, edited by K.A. Gschneidner and L. Eyring (North-Holland, Amsterdam, 1984) pp. 111-334. 2. Z. Ban and M. Skirica, Acta Cryst. 18 (1965) 594. 3. B. Eisenmann, N. May, W. Muller and H. Sch3fer, Z. Naturforsch. 27a (1972) 1155. 4. H.F. Braun, N. Engel and E. Parthé, Phys. Rev. B28 (1983) 1389. 5. K. Hiebl and P. Rogl, J. Magn. Magn. Mater. 50 (1985) 39. 6. I. Mayr and P.D. Yetor, J. Less Comm. Met. 55 (1977) 171. 7. A.A. Menovsky, CE. 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, CD. 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, 1975). 17. U. Rauchschwalbe, W. Lieke, CD. 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. 24. L. Chelmicki, J. Leciejewicz and A. Zygmunt, J. Phys. Chem. Sol. 46 (1985) 529. 25. H. Ptasiewicz-Bak, J. Leciejewicz and A. Zygmunt, J. Phys. Fll (1981) 1225. 26. K. Hiebl, C Horvath, P. Rogl and M.J. Sienko, Sol. State Comm. 48 (1983) 211. 27. H. Ptasiewicz-Bak, J. Leciejewicz and A. Zygmunt, Sol. State Comm. 55 (1985) 601. 28. J.D. Thompson, J.O. Willis, C Godart, D.E. McLaughlin and L.C. Gupta, Sol. State Comm. 56 (1985) 169. 29. L.C. Gupta, D.E. McLaughlin, Cheng Tien, C. Godart, M.A. Edwards and R.D. Parks, Phys. Rev. B28 (1983) 3673. 30. C. Godart, L.C. Gupta and M.F. Ravet-Krill, J. Less. Comm. Met. 94 (1983) 187. 31. H.H. Hill, in Plutonium and other Actinldes, edited by W.N. Miner (AIME, New York, 1970) p.2. 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. Stewart, Rev. Mod. Phys. J56_ (1984) 755. 35. See, for example, the collection of papers in Moment Formation in Solids, edited by W.J.L. Buyers (Plenum, New York, 1984). 36. CM. 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. 39. H.R. Ott, H. Rudigier, Z. Fisk and J.L. Smith, Phys. Rev. Lett. 50 (1983) 1595. 40. G.R. Stewart, Z. Fisk, J.O. Willis and J.L. Smith, Phys. Rev. Lett. 52 (1984) 679. 41. H.R. Ott, H. Rudigier, P. Delsing and Z. Fisk, Phys. Rev. Lett. 52 (1984) 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- 58. A.A. Abrikosov, in Introduction to the Theory of Normal Metals (Academic 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. 61. T.T.M. Palstra, P.H. Kes, J.A. Mydosh, A. de Visser, J.J.M. Franse and 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 verbindin8en, 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