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An Experimental Study of Praseodymium Intermetallic Compounds at Low Temperatures. F.J.A.M. Greidanus

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An Experimental Study of Praseodymium Intermetallic Compounds at Low Temperatures. F.J.A.M. Greidanus AN EXPERIMENTAL STUDY OF PRASEODYMIUM INTERMETALLIC COMPOUNDS AT LOW TEMPERATURES. F.J.A.M. GREIDANUS AN EXPERIMENTAL STUDY OF PRASEODYMIUM INTERMETALUC COMPOUNDS AT LOW TEMPERATURES. • i ; i L: I AN EXPERIMENTAL STUD Y OF PRASEODYMIUM INTERMETAIUC COMPOUNDS AT LOW TEMPERATURES» 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. A.A.H. KASSENAAR, HOOGLERAAR IN DE FACULTEIT DER GENEESKUNDE, VOLGENS BESLUIT VAN HET COLLEGE VAN DEKANEN TE VERDEDIGEN OP WOENSDAG 29 SEPTEMBER 1982 TE KLOKKE 15.15 UUR door FRANCISCUS JOHANNES ANTONIUS MARIA GREIDANUS geboren te Den Haag in 1953. NKB OFFSET BV - BLEISWIJK/LEIDEN Promotor: Prof. Dr. W.J. Huiskamp Co-promotor: Dr. L.J. de Jongh Referent: Prof. Dr. H.W. Capel This investigation is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (Foundation for Fundamental Research on Hatter) and was made possible by financial support from the Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek (Netherlands Organization for the Advancement of Pure Research). The neutron scattering experiments described in this thesis have been performed at the "Institut fUr Reaktortechnik der Eidg. Technische Hochschule Zurich, WUrenlingen» Switzerland". Sequuntur Metal la, quae sunt corpora mineralia ex particulis crassioribus et solidioribus subterraneis. Johannes Greydanus, Institutiones Physicae, 1664. Ter herinnering aan mijn vader \" f 1 '<•» •• .••'-•!• CONTENTS CHAPTER 1 GENERAL INTRODUCTION AND SURVEY 11 References 15 CHAPTER 2 EXPERIMENTAL TECHNIQUES 2.1. Introduction 16 2.2. Measurements with thermal neutrons 16 2.2.1. Inelastic neutron scattering 16 2.2.2. Neutron diffraction 18 2.3. Specific-heat measurements between 40 mK and 2 K 18 2.3.1. The experimental set-up 18 2.3.2. Therinometry 20 2.3.3. The resistance and mutual inductance bridge 21 2.3.4. Experimental procedure 23 2.3.5. Error analysis 24 2.4. Ac and dc susceptibilities between 25 mK and 1.4 K, measured with a SQUID 25 2.4.1. The He- He dilution refrigerator and the experimental set-up 25 2.4.2. Thermometry 27 2.4.3. A mutual inductance bridge utilizing a SQUID as a nulling device 31 2.4.4. Operation of the mutual inductance bridge 34 2.4.5. Accuracy of the bridge 35 References 36 CHAPTER 3 THEORY OF INTERACTING Pr3+I0NS Abstract 39 3.1. Introduction 39 3.2. Crystal-field theory 40 3.3. Molecular-field theory 42 3.4. First and second-order phase transitions 46 'i 3.5. Quadrupolar interactions 49 ,j 3.6. Hyperfine interactions 51 Mi Appendix I 53 .1 Appendix II 54 References 55 CHAPTER 4 CRYSTAL-FIELD SPLITTINGS OF PrX2 COMPOUNDS (X = Pt, Rhs Ir, Ru, Ni) STUDIED BY INELASTIC NEUTRON SCATTERING Abstract 57 4.1. Introduction 57 4.2. Sample preparation and experimental procedure 59 4.3. Crystal-field theory and neutron inelastic scattering 61 4.4. Experimental results 66 4.4.1. LaPt2; phonon contributions 66 4.4.2. PrPt2 in the paramagnetic state 67 4.4.3. PrPt2 in the ordered state 70 4.4.4. PrRu2 in the paramagnetic state 74 4.4.5. PrRuo in the ordered state 75 4.4.6. PrRh2 in the paramagnetic state 76 4.4.7. PrRh2 in the ordered state 78 4.4.8. PrNi2 in the paramagnetic state 79 4.4.9. Prlr2 in the ordered state 81 4.4.10. Prlr2 in the paramagnetic state 82 4.4.11. Summary of the experimental results and error analysis 83 4.5. Discussion and concluding remarks 84 References 88 CHAPTER 5 MAGNETIC PROPERTIES OF PrX? COMPOUNDS (X = Pt, Rh, Ru, Ir) STUDIED BY HYPERFINE SPECIFIC-HEAT, MAGNETIZATION AND NEUTRON-DIFFRACTION MEASUREMENTS Abstract 91 5.1. Introduction 91 5.2. Molecular-field theory for the magnetization 92 5.3. Sample preparation 95 5.4. High-field magnetization 95 5.5. Low-field magnetization 97 . 5.6. Hyperfine specific heat 98 5.7. Neutron diffraction 103 5.8. Discussion 106 5.9. Conclusion 109 References 109 f CHAPTER 6 SPECIFIC HEAT, RESISTIVITY AND AC SUSCEPTIBILITY OF THE CUBIC PrX2 COMPOUNDS (X = Pt, Ru, Ir, Rh) Abstract 111 6.1. Introduction 111 6.2. Molecular-field theory, the specific heat 112 6.3. Ac-susceptibility measurements 114 6.4. Specific-heat measurements 115 6.4.1. Experimental techniques 115 6.4.2. The non-magnetic LaX2 compounds (X = Ir, Ru, Rh) 116 6.4.3. The PrX2 compounds (X = Pt, Ir, Rh and Ru) 118 6.5. Quadrupolar interactions 127 6.6. Resistivity measurements 131 6.7. Summary 134 References 134 CHAPTER 7 SPECIFIC HEAT AND FREQUENCY-DEPENDENT AC SUSCEPTIBILITY OF PrNi2 BELOW 1 K Abstract 137 7.1. Introduction 137 7.2. Experimental techniques 139 7.3. Results of the measurements 140 7.4. Discussion and conclusion 143 References 146 CHAPTER 8 SPECIFIC-HEAT AND DIFFERENTIAL-SUSCEPTIBILITY MEASUREMENTS ON Pr3+ INTERMETALLIC COMPOUND? WITH A SINGLET OR NON-MAGNETIC DOUBLET GROUND STATE Abstract 148 8.1. General introduction 148 i f 8.2. Specific heat and differential susceptibility of PrZn2 149 8.2.1. Introduction 149 8.2.2. Experimental techniques 150 8.2.3. Experimental data 150 8.2.4. Discussion 152 8.3. The specific heat and differential susceptibility of PrX.Alg compounds (X = Cu, Cr, Mn) below 1.4 K 154 *,";•""• 8.3.1. Introduction 154 8.3.2. Experimental techniques 155 8.3.3. Results and discussion 155 8.4. The specific heat of PrMg3 below 1.3 K 158 8.4.1. Introduction 158 8.4.2. Experimental techniques 159 8.4.3. Results and discussion 160 8.5. The specific heat of Pr La, vPb, (x = 0.8, 0.9, 1.0) below 1.4 K 162 8.5.1. Introduction 162 8.5.2. Experimental techniques 163 8.5.3. Results and discussion 163 References 166 SAMENVATTING 168 CURRICULUM VITAE 171 NAWOORD 172 V V CHAPTER 1 GENERAL INTRODUCTION AND SURVEY In the past decade rare-earth intermetallic compounds have become the sub- ject of many investigations. From a physical point of view an interesting property of rare-earth compounds is the presence of a well localized 4f shell at the rare-earth sites. While the 4f electrons play only a minor role in the valency forces which determine the chemical properties of the rare-earth compounds, they play a major role in several of the physical properties. Fcr most lanthanide ions the orbital angular momentum (L) and spin angular momentum (S) do not cancel, but produce strongly paramagnetic ions. The spin-orbit interaction for the 4f electrons, which couples the angular momenta L and S to give a total angular momentum J, is relatively strong as compared to inter- ionic interactions. As a result J is a good quantum number and the lowest manifolds can be characterized by a single value of J. Usually the energy separation between the ground manifold and the next excited manifold is 2000 cm" or more. In the solid state the lowest J mainfold is split due to the crystal field created by the surrounding electrical charges. The number of new levels arising, as well as the degeneracy of the ground level is determined by the local symmetry at the rare-earth site. By expanding the crystalline electric field potential in spherical harmonics and by applying the operator- -equivalent method of Stevens [ 1,2] it is possible to calculate the eigenstates as well as the energy separation between the sublevels for an arbitrary crystal- -field potential. Lea, Leask and Wolf [3] calculated both the eigenstates and eigenvalues for various J values in cubic symmetry as a function of the ratio of fourth and sixth-order term in the crystal-field potential. An interesting situation arises for rare-earth ions with an integral value of the angular momentum, which is the case for Pr3+(I=4), Pm3+(I=4), Tb3+(I=6), Ho3+(I=8) and Tm +(I=6). Here the ground state may be a singlet (group theoretical designation Tj.IV) or a non-magnetic doublet (To). In this thesis we shall pay particular attention to such ground-state systems. The r3 doublet has to be distinguished 11 from Kramers doublets arising in rare-earth ions vrth non-integral angular momentum values. Because both the singlet and the doublet level are non-magnet- ic, i.e. independent of an applied magnetic field, a magnetic moment can only arise by the admixture of excited states. Phase transitions to a state of long- -range order in systems containing such non-magnetic ground-state ions can only occur if the exchange interaction exceeds a critical value. This gives rise to a special kind of magnetism: induced magnetism, contrary to the magnet- ism in systems where permanent magnetic moments exist in the paramagnetic regime. Excellent reviews on this topic have been written by Cooper [4] and Birgeneau [5]. The absence of an electronic magnetic moment, combined with the possibility of admixing higher states into the ground state, can be used advantageously in obtaining ultralow temperatures. The nuclear moment can be enhanced by a factor 10-100, which makes it possible to perform nuclear demagnetizations in moderate external fields. In this respect praseodymium intermetallic compounds appear to be suitable, partially because of their large hyperfine constant. At present it is possible to obtain temperatures as low as 0.19 mK, by enhanced nuclear cooling of PrNig [6] . In intermetallic compounds various mechanisms contribute to the interactions between the localized 4f moments. Generally the conduction electrons play an important role. A well known mechanism is the Ruderman-Kittel-Kasuya-Yoshida interaction (RKKY-interaction), based on the exchange interaction between the localized 4f electrons and the itinerant conduction electrons.
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