Spin Ice (Springer Series in Solid-State Sciences, 197)

✍ Scribed by Masafumi Udagawa (editor), Ludovic Jaubert (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 492
• Category: Library

✦ Synopsis

This book deals with a new class of magnetic materials, spin ice. Spin ice has become the canonical example of modern frustrated magnetism where competing interactions between spins set the rules for an emergent magnetostatic gauge field theory. Excitations take the form of magnetic monopoles or can condense via a Higgs mechanism. Beyond classical spin ice, the book describes the new physics emerging when quantum coherence (spin liquids, photon-like excitations) and itinerant electrons (anomalous Hall effect) are included in artificial systems. This first book dedicated to spin ice is a review of the current understanding of the field, both on the theoretical and experimental levels, written by leading experts. The book is written in a linear way with very few prerequisites. It also contains textbook-like descriptions of theoretical methods to help advanced students and researchers to enter the field.

✦ Table of Contents

Preface
Contents
Contributors
1 Spin Ice: Microscopic Physics
1.1 Introduction
1.2 Rare-Earth Magnetism
1.3 Single-Ion Physics
1.4 Microscopic Interactions in Insulating Rare Earth Magnets with Application to the Spin Ices
References
2 Crystal Growth of Pyrochlore Compounds
2.1 Introduction
2.2 Experimental
2.2.1 Material Synthesis
2.2.2 Flux Growth Technique
2.2.3 Optical Floating-Zone Technique
2.2.4 Czochralski Technique
2.2.5 Characterisation
2.2.6 Defects in the Crystal
2.3 Conclusions
References
3 Spin Ice As a Coulomb Liquid: From Emergent Gauge Fields to Magnetic Monopoles
3.1 Order and Disorder in Magnetism
3.1.1 Symmetry Breaking
3.1.2 Emergence of New Degrees of Freedom
3.1.3 Landau–Ginzburg–Wilson Theory
3.2 Magnetism Beyond the Landau–Ginzburg–Wilson Paradigm
3.3 The Minimal Model for the Coulomb Liquid: Nearest-Neighbour Spin Ice
3.3.1 Coarse-Graining and Emergent Gauge Field
3.3.2 Fractionalisation with Strings Attached
3.4 Dipolar Spin Ice and Projective Equivalence
3.5 Magnetic Monopoles
3.5.1 Self-Screening and Residual Ordering Tendency
3.5.2 Irrational Charge and Emergent Versus Intrinsic Gauge Charges
3.5.3 `Dirac Strings'
3.5.4 Magnetolyte Physics and Magnetricity
3.5.5 Electric Properties of Magnetic Monopoles
3.6 The Coulomb Phase in a Magnetic Field
3.6.1 Kasteleyn Transition
3.6.2 Kagome Ice
3.7 Disorder in a Coulomb Phase—Diluted Spin Ice
3.7.1 Thermodynamics of Diluted Spin Ice
3.7.2 Ghost Spins
3.7.3 Topological Spin Glass
3.7.4 Ghost Monopoles, Hydrogenic and Continuum States
3.8 What About Water Ice?
3.9 Summary and Outlook
References
4 Dynamics
4.1 Spin Dynamics of Spin Ice Compounds to Spin Ice State
4.2 Spin Dynamics of Typical Spin Ice Compound Dy2Ti2O7 at Low Temperature
4.3 Topics on Slow Dynamics of Dy2Ti2O7 at Very Low Temperature
References
5 Magnetic Field as an External Probe of Spin Ice Anisotropy
5.1 A System Composed of Isolated Tetrahedra
5.1.1 Zeeman Effect and Magnetization
5.1.2 Spin-Flip Crossover in H Near the [111] Direction
5.2 Spin Ice in Magnetic Fields
5.2.1 Magnetization Anisotropy: Overview
5.2.2 Response to a Magnetic Field: H parallel [100]
5.2.3 Response to a Magnetic Field: Hparallel [110]
5.2.4 Response to a Magnetic Field: Hparallel [111]
5.2.5 Effect of Tilting H from [111]
References
6 Topology of the Vacuum
6.1 The Vacuum is Not Empty
6.1.1 A 6-Vertex Model
6.1.2 Stochastic Worm Dynamics
6.1.3 Topological Sectors Made of Fluctuating Strings
6.1.4 Topological Charges Out of the Vacuum
6.2 Loop Statistics of the Coulomb Phase
6.2.1 Loops in Two Dimensions
6.2.2 Loops in Three Dimensions
6.3 Topological Phase Transitions
6.3.1 Repulsion Between Strings: The Kasteleyn Transition
6.3.2 Non-Repulsive Strings : KDP and 1st Order Transitions
6.4 Conclusion
References
7 Modelling of Classical Spin Ice: Coulomb Gas Description of Thermodynamic and Dynamic Properties
7.1 Introduction
7.2 Emergent Electrolyte Physics in Spin Ice
7.2.1 The Magnetolyte as a Model for Spin Ice
7.2.2 Debye-Hückel Theory
7.3 Monopoles and Dynamics
7.3.1 Hydrodynamic Description
7.3.2 Wien Effect
7.3.3 Behaviour Far From Equilibrium
7.3.4 Thermal Quenches
7.3.5 Field Quenches
References
8 Experimental Observation of Magnetic Monopoles in Spin Ice
8.1 Introduction
8.1.1 What Are Magnetic Monopoles in Spin Ice?
8.1.2 Magnetic Monopoles as Quasiparticles
8.1.3 Confirmation or Falsification of Monopole Theory
8.1.4 Spin Ice as a Magnetic Electrolyte
8.1.5 Direct Observation of Magnetic Monopoles
8.2 Quantities Available to Experiment
8.2.1 Equilibrium Thermodynamics
8.2.2 Linear Response and Non-equilibrium Thermodynamics
8.3 Experiments in Weak Applied Fields
8.3.1 Magnetisation Correlations Measured by Neutron Scattering
8.3.2 Specific Heat
8.3.3 dc-Susceptibility
8.3.4 ac-Susceptibility
8.3.5 Summary: Success and Failures of the Monopole Theory in the Weak Field Regime
8.4 Strong Field Response
8.4.1 Monopole Condensation with Applied Field Along [111]
8.4.2 Strong Field Correlations
8.4.3 Strong Field Sweeps and Quenches
8.5 Monopole Derived Properties
8.5.1 Thermal Conductivity
8.5.2 Field Distribution at Point Probes
8.5.3 Dielectric Response
8.6 Future Directions for Monopole Observation
8.6.1 Plasmas
8.6.2 Phonons
8.6.3 New Materials
8.6.4 Quantum Spin Ice
8.7 Conclusion
8.7.1 Different Viewpoints
8.7.2 Definitions and Disagreements
8.7.3 Final Word
References
9 Quantum Coherence: Quantum Spin Ice and Lattice Gauge Theory
9.1 What Is Quantum Spin Ice?
9.1.1 Hamiltonian
9.1.2 Near the Spin Ice Point
9.1.3 Mean Field Limit
9.2 Perturbative Gauge Theory
9.2.1 Derivation and Formulation
9.2.2 Relation to Compact QED
9.2.3 Phases of Compact QED
9.2.4 Electric Charges and Duality
9.2.5 Application to Quantum Spin Ice
9.3 A Global View
9.3.1 Slave Spinon Formulation
9.3.2 Gauge Mean Field Theory
9.3.3 Phases of gMFT and Their Interpretation
9.3.4 Wavefunction
9.4 Comparison of Classical and Quantum Spin Ice
9.5 Observing Quantum Spin Ice
9.6 Frontier Topics
9.6.1 Antiferromagnetic XY Coupling
9.6.2 Quantum Phase Transitions
9.6.3 Numerics
9.6.4 Disorder
References
10 Quantum Monte Carlo Simulations of Quantum Spin Ice
10.1 Introduction
10.1.1 Preamble—Why Try to Simulate a Quantum Spin Ice?
10.1.2 So What Is a Quantum Spin Ice, Anyway ?
10.1.3 A Short Tour of Models, and the Maths Used to Describe Them
10.1.4 How Can Simulations Help ?
10.2 Simulation of Quantum Spin Ice at Zero Temperature
10.2.1 Overview of Section
10.2.2 Topology, Quantum Numbers and Simulation
10.2.3 Evidence for a Spin–Liquid from Finite–Size Scaling of Energy Spectra
10.2.4 Evidence for a QSL Ground State from Correlation Functions
10.3 Simulation of Quantum Spin Ice at Finite Temperature
10.3.1 Overview of Section
10.3.2 Evidence for a QSL from Correlations at Finite Temperature
10.3.3 Thermodynamics of Quantum Spin Ice
10.4 An Honourable Mention—Work on Related Models
10.4.1 The Quantum Dimer Model on a Diamond Lattice
10.4.2 Quantum Square Ice, Also Known as the Quantum Six–Vertex Model
10.5 Where Next ?
10.6 Conclusions
References
11 Analytical Approaches to Quantum Spin Ice
11.1 Emergent Photons in Quantum Spin Ice
11.1.1 Constructing the Photon
11.1.2 Correlation Functions of the Electromagnetic Fields
11.2 Point Group Symmetries of the Pyrochlore Lattice and Anisotropic Exchange Interactions
11.2.1 Classical Vector Spins on the Corners of a Tetrahedron
11.2.2 Rewriting the Hamiltonian in Terms of Local Order Parameter Fields
11.2.3 Irreducible Representations of Td
11.2.4 Local Order Parameter Fields
References
12 Experimental Search for Quantum Spin Ice
12.1 Introduction
12.1.1 Experimental Signatures of Classical Spin Ice
12.1.2 Experimental Signatures of Quantum Spin Ice
12.2 Quantum Spin Ice Materials
12.2.1 Yb3+-Based Pyrochlores
12.2.2 Tb3+-Based Pyrochlores
12.2.3 Pr3+-Based Pyrochlores
12.2.4 Summary and Outlook
References
13 Novel Electronic Phases of Matter: Coupling to Itinerant Electrons
13.1 Spin Ice Meets Mobile Carriers
13.2 Classical Kondo Lattice Model
13.3 Basic Properties of Classical Kondo Lattice Model
13.3.1 Ground State
13.3.2 Finite-Temperature Properties
13.3.3 Rigorous Results
13.3.4 Basic Analytical/Numerical Techniques
13.3.5 Dual Property of Classical Kondo Lattice Model
13.4 Itinerant Spin Ice
13.4.1 Brief Summary of Experiments
13.4.2 Theoretical Formulation with Classical Kondo Lattice Model
13.4.3 Comparison with Experiments
13.5 Other Frustrated Itinerant Systems
13.5.1 Charge Ice
13.5.2 Heavy Fermion Behavior
13.5.3 Magnetic Chern Insulator and Dynamics
13.5.4 Tight-Binding Model on Line Graphs
13.6 Summary
References
14 Anomalous Transport Properties of Pyrochlore Iridates
14.1 Pyrochlore Rare-Earth Iridates
14.2 Metal-Insulator Transition of Pyrochlore Iridate
14.3 Pressure-Induced Magnetic Ordering in Nd2Ir2O7
14.4 Unconventional Anomalous Hall Effect in the Spin Ice Metal Pr2Ir2O7
14.4.1 Material Properties of Pr2Ir2O7
14.4.2 Four Characteristic Temperature Regions
14.4.3 Hall Response in Spin-Ice and Spin-Liquid Regions
References
15 Artificial Spin Ice: Beyond Pyrochlores and Magnetism
15.1 Artificial Spin Ice: Basic Energetics and Dynamics
15.2 Thermodynamic Behaviors
15.3 Disorder and Nonequilibrium Dynamics
15.4 Elementary Excitations: Monopoles
15.5 Elementary Excitations: Magnons
15.6 Emergent Frustration by Design
15.7 Other Artificial Ices
15.8 Conclusion and Outlook
References
16 Experimental Studies of Artificial Spin Ice
16.1 Introduction
16.2 The First Artificial Spin Ices
16.3 Experimental Methods
16.3.1 Fabrication Methods
16.3.2 Measurement and Imaging Methods
16.4 Monopoles and Magnetricity
16.5 Array Topology and Geometry
16.6 From Effective to Real Thermodynamics
16.7 Outlook
References
Index