Rare-Earth Borides

Rare-earth borides have attracted continuous interest for more than half a century both from the point of view of fundamental condensed matter physics and for practical applications in various fields of engineering. They demonstrate a wealth of unusual electronic and magnetic properties that have been closely investigated in recent decades using advanced spectroscopies and state-of-the-art physical characterization methods. Authored by leading experts in the field, this book features a comprehensive collection of reviews offering a cutting-edge summary of the research on rare-earth borides from various viewpoints. It includes chapters on the growth and characterization of single-crystal and thin-film samples, detailed description of their lattice structure and dynamics, electronic and magnetic properties in the bulk and at the surface, low-temperature ordering phenomena, and theoretical and experimental description of the unusual spectroscopic properties from the perspective of modern x-ray and neutron scattering, Raman spectroscopy, and electron spin resonance. The book will appeal to anyone interested in the physics and chemistry of solids and low-temperature physics, especially to researchers and postgraduate students who study magnetic and electronic properties of rare-earth compounds. Cover Half Title Title Page Copyright Page Table of Contents Preface Chapter 1: Crystal Chemistry and Crystal Growth of Rare-Earth Borides 1.1: Introduction 1.2: Principles of the Main Crystal-Growth Techniques 1.2.1: The Czochralski Method 1.2.2: The Flux Method 1.2.3: Floating-Zone Melting Technique 1.2.4: Other Techniques 1.3: Metal-Rich Borides 1.3.1: Rare-Earth Diborides (RB2) 1.3.2: R2B5 1.4: Rare-Earth Tetraborides (RB4) 1.4.1: General Overview 1.4.2: Yttrium Tetraboride (YB4) 1.4.3: Cerium Tetraboride (CeB4) 1.4.4: RB4 (R = Y, Nd, Gd–Tm, Lu) 1.5: Rare-Earth Hexaborides (RB6) 1.5.1: General Overview 1.5.2: Synopsis of RB6 Crystal Growth 1.5.3: Samarium Hexaboride (SmB6) 1.5.4: Ytterbium Hexaboride (YbB6) 1.5.5: Yttrium Hexaboride (YB6) 1.5.6: Boron Isotope Effects 1.6: Higher Borides 1.6.1: Rare-Earth Dodecaborides (RB12) 1.6.2: Rare-Earth Hectoborides (RB66) 1.7: Concluding Remarks Chapter 2: Thin Films of Rare-Earth Hexaborides 2.1: Overview of Rare-Earth Hexaborides 2.2: Lanthanum Hexaboride (LaB6) 2.3: Cerium Hexaboride (CeB6) 2.4: Gadolinium Hexaboride (GdB6) 2.5: Ytterbium Tetra- and Hexaborides (YbB4 and YbB6) 2.6: Neodymium Hexaboride (NdB6) 2.7: Other Hexaborides 2.8: Samarium Hexaboride (SmB6) 2.8.1: Fabrication of SmB6 Thin Films 2.8.2: Proximity Effect in Nb/SmB6 Bilayers 2.9: Superconductivity in Yttrium Hexaboride (YB6) 2.10: SmB6/YB6 Thin-Film Bilayer Heterostructures 2.10.1: Point-Contact Spectroscopy Measurements 2.10.2: Dirac-BTK Theory 2.11: Summary and Perspective Chapter 3: Crystal Structures of Dodecaborides: Complexity in Simplicity 3.1: Introduction 3.2: Cooperative Jahn–Teller Effect as a Driving Force behind Structural Instability in Dodecaborides 3.3: Modeling the Dynamics of the Dodecaboride Lattice Using X-Ray Diffraction Data 3.4: Crystal Structure: Problems and Results 3.4.1: The Jahn–Teller Distortions of Structural Parameters 3.4.2: Structural Peculiarities of Dodecaborides Different in Isotopic Boron Composition 3.4.3: Formation of Charge Stripes in Voids of the Crystal Lattice 3.5: Conclusions Chaper 4: Magnetism, Quantum Criticality, and Metal–Insulator Transitions in RB12 4.1: Introduction 4.2: Electronic Band Structure of Dodecaborides 4.2.1: Rough Estimations 4.2.2: Metallic RB12 4.2.3: Strongly Correlated Semiconductor YbB12 4.3: Nonmagnetic Reference Compound LuB12 4.3.1: Charge Transport 4.3.2: Thermal Properties 4.3.3: Optical Properties 4.3.4: Magnetoresistance Anisotropy and Dynamic Charge Stripes 4.3.5: The Origin of Electron and Lattice Instability and the Energy Scales in LuB12 4.4: Magnetic Dodecaborides RB12 (R=Tb, Dy, Ho, Er, Tm) and the Solid Solutions RxLu1−xB12 4.4.1: Magnetic Properties 4.4.2: Electron Paramagnetic Resonance 4.4.3: Charge Transport 4.4.4: Thermal Conductivity 4.4.5: Thermal Expansion and Heat Capacity 4.4.6: Magnetic Structure 4.4.7: Magnetic H–T–φ Phase Diagrams 4.4.8: The Root of the Complexity of Magnetic Phase Diagrams of RB12 4.4.9: Quantum Critical Behavior in HoB12 4.5: Metal–Insulator Transition in YbB12 and Solid Solutions YbxR1−xB12 (R = Lu, Tm) 4.5.1: Metal–Insulator Transition in YbB12 4.5.2: Pressure-Induced Insulator-to-Metal Transition in YbB12 4.5.3: Field-Induced Insulator-to-Metal Transition in YbB12 4.5.4: Insulator-to-metal transition in YbxR1−xB12 (R = Y, Lu, Sc, Ca, and Zr) 4.5.5: Metal–Insulator Transition in Tm1−xYbxB12 4.6: Conclusions Chapter 5: Raman Spectroscopy of Metal Borides: Lattice and Electron Dynamics 5.1: Introduction 5.2: Raman Scattering by Phonons 5.2.1: Raman-Active Phonons in Hexaborides 5.2.2: Extra Phonon Features in Raman Spectra of Hexaborides 5.2.3: Anharmonicity vs. Electron–Phonon Interaction 5.2.4: Phononic Raman Spectra in Dodecaborides 5.2.5: Raman Spectroscopy of Phonons in Tetraborides 5.2.6: Raman Spectra of Other Rare-Earth Borides 5.3: Raman Scattering by Electronic Excitations 5.3.1: Crystal Electric Field Transitions 5.3.2: Electron–Hole Excitations: Collision-Limited Regime 5.3.3: Electron–Hole Excitations: Crossover from Clean to Dirty Regimes 5.3.4: Electron–Induced Phonon Renormalization 5.4: Conclusions Chapter 6: Neutron Spectroscopy on Rare-Earth Borides 6.1: Specifics of the Neutron-Scattering Technique in Condensed Matter Spectroscopy 6.1.1: Neutron Scattering Function in Relation to the Atomic Vibrations and Dynamic Magnetic Susceptibility 6.1.2: Characteristic Features of Inelastic Neutron Scattering with Respect to Heavy-Fermion and Mixed-Valence Phenomena 6.2: Magnetic Excitations in Hexa- and Dodecaborides 6.2.1: Crystal Electric Field Effects 6.2.2: Hybridization Effects: Intermediate-Valence and Kondo Insulator Systems 6.2.3: Excitation Spectra of the Intermediate-Valence Kondo Insulator SmB6 6.2.3.1: Intermultiplet transitions and the resonant mode in the magnetic neutron-scattering spectra of SmB6 6.2.3.2: The model of the exciton of an intermediate radius 6.2.3.3: The magnetic form factor study 6.2.3.4: Resonant exciton modes at the R and X points 6.2.3.5: Gd-impurity effect on SmB6 6.2.4: Magnetic Excitations in the Kondo Insulator YbB12 6.2.4.1: Resonant mode and temperature effects 6.2.4.2: Resonant mode and impurity effects in YbB12 6.3: Lattice Dynamics in RB6 and RB12 6.3.1: General Characterization of the Atomic Vibrational Spectra of RB6 and RB12 6.3.2: Electron–Phonon Interaction in RBn (n = 6, 12) 6.3.2.1: Intermediate-valence features of SmB6 in electron–phonon interaction 6.3.2.2: The magnetovibration interaction in YbB12 6.4: Conclusions Chapter 7: Competing Order Parameters in Rare-Earth Hexa- and Tetraborides 7.1: Introduction 7.2: Resonant and Nonresonant X-Ray Diffraction 7.2.1: Nonresonant X-Ray Diffraction 7.2.2: Resonant X-Ray Diffraction 7.3: Multipolar Order in CexLa1−xB6 7.3.1: The Parent Compound CeB6 7.3.2: Solid Solutions CexLa1−xB6 7.4: Rare-Earth Tetraborides (RB4) 7.4.1: An Overview 7.4.2: Magnetic Order in RB4 7.4.3: Fractional Magnetization Plateaus 7.4.4: Quadrupolar Fluctuation in DyB4 7.5: Conclusions Chapter 8: Multipolar Order and Excitations in Rare-Earth Boride Kondo Systems 8.1: Introduction 8.1.1: Conduction Bands and Fermi Surface 8.1.2: Localized 4f Shells, Their CEF States, Multipoles, and RKKY Interactions 8.2: Overview of RE Boride Compounds 8.3: Multipolar Hidden Order in CeB6 in the Localized 4f Scenario 8.3.1: Pseudospin Representation of 8-Quartet Multipoles 8.3.2: Multipole Interaction Model and Symmetry Breakings 8.3.3: Experimental Identification of Multipolar Order Parameters 8.4: Octupolar HO Phase IV in Diluted Ce1−xLaxB6 8.4.1: Phase Diagram and Evidence for Primary Octupolar Order 8.5: Collective Excitations in the AFQ Hidden-Order Phase II of CeB6 8.5.1: Generalized Multipolar RPA Method 8.5.2: Dependence of Mode Energies on Field Strength and Field Angular Rotation 8.6: Resonant Magnetic Excitations in the Itinerant CeB6 Kondo Lattice 8.6.1: Heavy Quasiparticle Band Properties in the PAM 8.6.2: Collective Spin Exciton Modes 8.7: Dispersive Doublet Spin Exciton Mode in the Kondo Semiconductor YbB12 8.8: Magnetic Excitations: Topological State in the Mixed-Valent Semiconductor SmB6 8.8.1: CEF and Collective Magnetic Excitations 8.8.2: SmB6 as a Strongly Correlated Topological Insulator 8.9: Conclusions and Outlook Chapter 9: Neutron-Scattering Studies of Spin Dynamics in Pure and Doped CeB6 9.1: Introduction 9.2: Electronic Properties and Ordering Phenomena 9.2.1: Magnetic Structure in the Antiferromagnetic Phases 9.2.2: Magnetically Hidden Order in Phase II 9.2.3: Mean-Field Description of the Ordering Phenomena in CeB6 9.3: Spin Excitations in the Absence of Magnetic Field 9.3.1: Collective Excitations in the Antiferromagnetic Phase 9.3.2: Quasielastic Magnetic Scattering 9.4: Magnetic-Field Dependence of the Collective Excitations 9.4.1: General Remarks 9.4.2: Zone-Center Excitations 9.4.3: Dispersion of the Field-Induced Collective Modes 9.4.4: Anisotropy with Respect to the Field Direction 9.5: Spin Dynamics in Ce1−xLaxB6 and Ce1−xNdxB6 9.5.1: The Influence of La and Nd Substitution on the Electronic Structure 9.5.2: Momentum-Space Structure of the Diffuse Spin Fluctuations 9.5.3: Temperature Dependence of the Quasielastic Magnetic Scattering 9.5.4: Field-Induced Collective Excitations in Ce1−xLaxB6 Chapter 10: Theory of Electron Spin Resonance in Strongly Correlated CeB6 10.1: Introduction 10.2: Kondo Impurity Model 10.3: Kondo Lattice Model 10.3.1: Paramagnetic Kondo Lattice 10.3.2: Antiferromagnetic Kondo Lattice 10.3.3: Kondo Lattice with Ferromagnetic Order 10.3.4: Summary 10.3.5: Other Theoretical Approaches and Experiments 10.4: Antiferroquadrupolar Ordered CeB6 10.4.1: ESR in a 8 Quartet 10.4.2: ESR for Ce3+ Ions with 8 Ground State 10.4.3: g-Factor for ESR in Phase II of CeB6 10.4.4: Ferromagnetic Correlations in Phase II of CeB6 10.4.5: Line Width of ESR in Phase II of CeB6 10.4.6: Second Resonance at High Fields in Phase II of CeB6 10.4.7: Inelastic Neutron Scattering in CeB6 10.4.8: Summary 10.5: Longitudinal Dynamical Susceptibility 10.6: Conclusions Chapter 11: Bulk and Surface Properties of SmB6 11.1: Introduction 11.2: Crystal Growth and Structural Properties 11.3: Theoretical Remarks 11.4: Surface Properties 11.4.1: dc Electrical Conductivity 11.4.2: Tunneling Spectroscopy and Thermopower 11.4.3: Quantum Oscillations 11.4.4: Angle-Resolved Photoelectron Spectroscopy 11.4.5: Thin Films and Nanowires 11.5: Bulk Properties 11.5.1: ac Electrical Conductivity 11.5.2: Quantum Oscillations 11.5.3: Thermal Conductivity 11.5.4: Specific Heat 11.5.5: Raman Spectroscopy 11.5.6: X-Ray, Neutron, and Mössbauer Spectroscopies 11.5.7: Nuclear, Electron, and Muon Spin Resonance 11.6: Concluding Remarks Index