Spin Ice, Fractionalization and Topological Order

Abstract

The spin ice compounds {\dys} and {\holm} are highly unusual magnets which epitomize a set of concepts of great interest in modern condensed matter physics: their low-energy physics exhibits an emergent gauge field and their excitations are magnetic monopoles which arise from the fractionalization of the microscopic magnetic spin degrees of freedom. In this review, we provide an elementary introduction to these concepts and we survey the thermodynamics, statics and dynamics---in and out of equilibrium---of spin ice from these vantage points. Along the way, we touch on topics such as emergent Coulomb plasmas, observable "Dirac strings", and irrational charges. We close with the outlook for these unique materials.

(15 pages, 9 figures) see http://www.annualreviews.org/doi/abs/10.1146/annurev-conmatphys-020911-125058 for the published version

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• Power-law spin correlations in pyrochlore antiferromagnets
• Artificial square ice and related dipolar nanoarrays
• Low Temperature Spin Freezing in Dy2Ti2O7 Spin Ice
• Why spin ice obeys the ice rules
• Theoretical and Experimental Status of Magnetic Monopoles
• A new macroscopically degenerate ground state in the spin ice compound Dy2Ti2O7 under a magnetic field
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Cited by in corpus (255)

• Quantum Spin Liquids
• Quantum Spin Liquids
• A Field Guide to Spin Liquids
• Colloquium: Artificial spin ice: Designing and imaging magnetic frustration
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Quantum Many-Body Scars: A Quasiparticle Perspective
• Thermal Hall conductivity in the frustrated pyrochlore magnet Tb2Ti2O7
• Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore
• Quantum Spin Ice and dimer models with Rydberg atoms
• Theory of multiple--phase competition in pyrochlore magnets with anisotropic exchange, with application to Yb2Ti2O7, Er2Ti2O7 and Er2Sn2O7
• Living on the edge : ground-state selection in quantum spin-ice pyrochlores
• Quantum Slow Relaxation and Metastability due to Dynamical Constraints
• A quantum liquid of magnetic octupoles on the pyrochlore lattice
• Disorder in quantum many-body systems
• Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb${}_2$Ti${}_2$O${}_7$ in Magnetic Field
• Dipolar quantum solids emerging in a Hubbard quantum simulator
• Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores
• Experimental signatures of emergent quantum electrodynamics in Pr${}_2$Hf${}_2$O${}_7$
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Pinch Point Singularities of Tensor Spin Liquids
• Machine Learning Assisted Insight to Spin Ice Dy${}_2$Ti${}_2$O${}_7$
• Ice Rule and Emergent Frustration in Particle Ice and Beyond
• How quantum are classical spin ices?
• Quantum Magnetism in Minerals
• Probing hidden spin order with interpretable machine learning
• Lattice-site-specific spin-dynamics in double perovskite Sr2CoOsO6
• Cavity-induced quantum spin liquids
• Observation of long range magnetic ordering in pyrohafnate Nd2Hf2O7: A neutron diffraction study
• A spin liquid with pinch-line singularities on the pyrochlore lattice
• Magnetic Monopole Noise
• Candidate quantum spin ice in the pyrochlore Pr${}_2$Hf${}_2$O${}_7$
• Crystal field parameters of the rare earth pyrochlores $R_2$Ti${}_2$O${}_7$ ($R$ = Tb, Dy, Ho)
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
• Antiferromagnetic Spin Ice Correlations at (1/2,1/2,1/2) in the Ground State of the Pyrochlore Magnet Tb2Ti2O7
• Thermodynamic properties of the Yb2Ti2O7 pyrochlore as a function of temperature and magnetic field: validation of a quantum spin ice exchange Hamiltonian
• Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: A pseudo-fermion functional renormalization group perspective
• Direct Visualization of Memory Effects in Artificial Spin Ice
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Experimental signatures of quantum and topological states in frustrated magnetism
• How does a locally constrained quantum system localize?
• Single-ion properties of the $S_{eff}$ = 1/2 XY antiferromagnetic pyrochlores, Na$A^{\prime }$Co${}_2$F${}_7$ ($A^{\prime }=$ Ca${}^{2+}$, Sr${}^{2+}$)
• Spin-state ice in geometrically frustrated spin-crossover materials
• Physical properties of a candidate quantum spin-ice system Pr2Hf2O7
• Spectroscopic fingerprints of gapped quantum spin liquids, both conventional and fractonic
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• Chiral nature of magnetic monopoles in artificial spin ice
• Topological Sector Fluctuations and Curie Law Crossover in Spin Ice
• Realizing three-dimensional artificial spin ice by stacking planar nanoarrays
• Thickness dependence of electronic structure and optical properties of a correlated van der Waals antiferromagnet NiPS${}_3$ thin film
• Topological Route to New and Unusual Coulomb Spin Liquids
• Single-ion anisotropy and magnetic field response in spin ice materials Ho${}_2$Ti${}_2$O${}_7$ and Dy${}_2$Ti${}_2$O${}_7$
• Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model
• New physics in frustrated magnets: Spin ices, monopoles, etc
• Charge ordering in a pure spin model: dipolar spin-ice
• Ground-state selection and spin-liquid behaviour in the classical Heisenberg model on the breathing pyrochlore lattice
• A Supercooled Spin Liquid State in the Frustrated Pyrochlore Dy2Ti2O7
• Novel phases in a square-lattice frustrated ferromagnet : 1/3-magnetisation plateau, helicoidal spin-liquid and vortex crystal
• The Emergent Fine Structure Constant of Quantum Spin Ice Is Large
• Fragmentation in Frustrated Magnets -- A review
• Understanding Thermal Annealing of Artificial Spin Ice
• Of chain-based order and quantum spin liquids in dipolar spin ice
• Cluster-glass phase in pyrochlore XY antiferromagnets with quenched disorder
• Dynamical fractal and anomalous noise in a clean magnetic crystal
• Non-reciprocal frustration: time crystalline order-by-disorder phenomenon and a spin-glass-like state
• Instabilities of a U(1) quantum spin liquid in disordered non-Kramers pyrochlores
• Pyrochlore U(1) spin liquid of mixed symmetry enrichments in magnetic fields
• Logical gates embedding in Artificial Spin Ice
• Ice Rule Fragility via Topological Charge Transfer in Artificial Colloidal Ice
• Tunable non-equilibrium dynamics: field quenches in spin ice
• Coulomb phase diagnostics as function of temperature, interaction range and disorder
• Topological Nematic Spin Liquid on the Square-Kagome Lattice
• Classical and quantum theories of proton disorder in hexagonal water ice
• Temperature and Magnetic Field Dependence of Spin Ice Correlations in the Pyrochlore Magnet Tb2Ti2O7
• Why a noninteracting model works for shot noise in fractional charge experiments
• Order-by-disorder and quantum Coulomb phase in quantum square ice
• Magnetic field effects in an octupolar quantum spin liquid candidate
• Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered Systems
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Monopole density and antiferromagnetic domain control in spin-ice iridates
• AC Wien effect in spin ice, manifest in non-linear non-equilibrium susceptibility
• Anomalous magnetic noise in imperfect flat bands in the topological magnet Dy2Ti2O7
• Hastatic Order in URu2Si2 : Hybridization with a Twist
• Spin Hamiltonian, {Order Out of a Coulomb Phase} and Pseudo-Criticality in the Highly Frustrated Pyrochlore Heisenberg Antiferromagnet FeF${}_3$}
• Investigations of the effect of nonmagnetic Ca substitution for magnetic Dy on spin-freezing in Dy2Ti2O7
• Ergodicity breaking provably robust to arbitrary perturbations
• Order Induced by Dilution in Pyrochlore XY Antiferromagnets
• Electronic transport in the Coulomb phase of the pyrochlore spin ice
• Ultrasonic investigations of spin-ices Dy${}_2$Ti${}_2$O${}_7$ and Ho${}_2$Ti${}_2$O${}_7$ in and out of equilibrium
• A field trip through spin ice
• Symmetry fractionalization in the gauge mean-field theory of quantum spin ice
• Muon spin relaxation and inelastic neutron scattering investigations of all-in/all-out antiferromagnet Nd2Hf2O7
• Discovery of Emergent Photon and Monopoles in a Quantum Spin Liquid
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• Coexistence of long-range and algebraic correlations for short-range valence-bond wave functions in three dimensions
• Dipolar spin-misalignment correlations in inhomogeneous magnets: comparison between neutron scattering and micromagnetic approaches
• Spin-orbit coupling and strong electronic correlations in cyclic molecules
• Exploring the phases of 3D artificial spin ice: From Coulomb phase to magnetic monopole crystal
• Monopole holes in a partially ordered spin liquid
• Identification of hidden order and emergent constraints in frustrated magnets using tensorial kernel methods
• Hydrogenic states of monopoles in diluted quantum spin ice
• Spinon walk in quantum spin ice
• Spectrum of itinerant fractional excitations in quantum spin ice
• Evidence for a dynamical ground state in a frustrated pyrohafnate Tb2Hf2O7
• Topological order: from long-range entangled quantum matter to an unification of light and electrons
• Magnetic monopole polarons in spin ice with mixed coordination numbers
• Single crystal growth, structure and magnetic properties of Pr2Hf2O7 pyrochlore
• Emergent Coulombic criticality and Kibble-Zurek scaling in a topological magnet
• Spectroscopic signatures of fractionalization in octupolar quantum spin ice
• Frustrated magnetism in the Heisenberg pyrochlore antiferromagnets $A$Yb${}_2$$X$${}_4$ ($A$ = Cd, Mg, $X$ = S, Se)
• Spin ice thin films: Large-N theory and Monte Carlo simulations
• A Bionic Coulomb Phase on the Pyrochlore Lattice
• Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice
• Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores
• Real-space investigation of short-range magnetic correlations in fluoride pyrochlores NaCaCo${}_2$F${}_7$ and NaSrCo${}_2$F${}_7$ with magnetic pair distribution function analysis
• Artificial Spin Ice Phase-Change Memory Resistors
• Recent progress on magnetic-field studies on quantum-spin-liquid candidates
• Emergent particles and gauge fields in quantum matter
• Spectroscopy of spinons in Coulomb quantum spin liquids
• Free coherent spinons in quantum square ice
• Semi-classical Approach to Quantum Spin Ice
• Confinement of monopoles and scaling theory near unconventional critical points
• Rod motifs in neutron scattering in spin ice
• Electric field control of emergent electrodynamics in quantum spin ice
• Anomalous Magnetoresistance by Breaking Ice Rule in Bi2Ir2O7/Dy2Ti2O7 Heterostructure
• Maxwell electromagnetism as an emergent phenomenon in condensed matter
• Magnetism and spin dynamics of an S=3/2 frustrated trillium lattice antiferromagnet K2CrTi(PO4)3
• Probing Flat Band Physics in Spin Ice Systems via Polarized Neutron Scattering
• Ferromagnetic Coulomb phase in classical spin ice
• Emergent magnetic behaviour in the frustrated Yb${}_3$Ga${}_5$O${}_{12}$ garnet
• Quantum slush state in Rydberg atom arrays
• Charge and spin correlations in the Monopole Liquid
• Frustration on a centred pyrochlore lattice in metal-organic frameworks
• A New Spin on Material Properties: Local Magnetic Structure in Functional and Quantum Materials
• Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice
• A neutron scattering measurement of crystalline-electric fields in magnesium rare-earth selenide spinels
• A Classical Chiral Spin-Liquid from Chiral Interactions on the Pyrochlore Lattice
• The Colored Noise of Magnetic Monopoles: Subdiffusion in a Coevolving Vacuum and Spin Ice Exponents
• Persistence of the flat band in a kagome magnet with dipolar interactions
• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Giant Magnetoelastic-Coupling Driven Spin-Lattice Liquid State in Molybdate Pyrochlores
• Superconducting phase transition reveals an electromagnetic coupling to a scalar field potential that generates mechanical work
• Gauge field entanglement of Kitaev's honeycomb model
• Fragmented spin ice and multi-$k$ ordering in rare-earth antiperovskites
• Analytical theory for proton correlations in common water ice $I_h$
• Epitaxial stabilization of (111)-oriented frustrated quantum pyrochlore thin films
• Reweight-annealing method for evaluating the partition function via quantum Monte Carlo calculations
• Prethermal time-crystalline spin ice and monopole confinement in a driven magnet
• Emergence of cooperative dynamics in fully packed classical dimers
• Universal monopole scaling near transitions from the Coulomb phase
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Multiple Coulomb phases with temperature tunable ice rules in pyrochlore spin crossover materials
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Proton strings and rings in atypical nucleation of ferroelectricity in ice
• Structural magnetic glassiness in spin ice Dy${}_2$Ti${}_2$O${}_7$
• Optimization of single crystal growth of candidate quantum spin-ice Pr2Hf2O7 by optical floating-zone method
• Structural, magnetic and magnetocaloric properties of triangular-lattice transition-metal phosphates
• Magnetotransport of single crystal Sm${}_2$Ir${}_2$O${}_7$ across the pressure-induced quantum-critical phase boundary
• Quantum percolation of monopole paths and the response of quantum spin ice
• The fate of $p$-wave spin polarization in helimagnets with Rashba spin-orbit coupling
• Structural and magnetic properties of the new quantum magnet BaCuTe${}_2$O${}_6$
• Magnetic Monopoles and Dark Matter
• The Classical Heisenberg Model on the Centred Pyrochlore Lattice
• A pseudofermion functional renormalization group study of dipolar-octupolar pyrochlore magnets
• Amorphous ferromagnetism and re-entrant magnetic glassiness in Sm${}_2$Mo${}_2$O${}_7$: new insights into the electronic phase diagram of pyrochlore molybdates
• Four-coloring model and frustrated superfluidity in the diamond lattice
• Topological sectors, dimer correlations and monomers from the transfer-matrix solution of the dimer model
• Dynamical Axions in $U(1)$ Quantum Spin Liquids
• Spinless fermions in a ${\mathbb{Z}}_2$ gauge theory on the triangular ladder
• Investigation of the monopole magneto-chemical potential in spin ices using capacitive torque magnetometry
• The Concept of Spin Ice Graphs and a Field Theory for their Topological Monopoles and Charges
• Hybrid Dyons, inverted Lorentz force and magnetic Nernst effect in quantum spin ice
• Dynamically Generated Synthetic Electric Fields for Photons
• Dichotomous Dynamics of Magnetic Monopole Fluids
• Emergent Gauge Fields in Band Insulators
• Spiral Spin Liquid Noise
• Fragile spin liquid in three dimensions
• Fermionic spinon and holon statistics in the pyrochlore quantum spin liquid
• Finite Temperature Dynamics in 0-Flux and $\pi$-Flux Quantum Spin Ice: Self-Consistent Exclusive Boson Approach
• Orientation-dependent stabilization of MgCr${}_2$O${}_4$ spinel thin films
• Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets
• Magnetization process and ordering of the $S=1/2$ pyrochlore magnet in a field
• Irrational moments and signatures of higher-rank gauge theories in diluted classical spin liquids
• Spin ice in a general applied magnetic field: Kasteleyn transition, magnetic torque and rotational magnetocaloric effect
• [111]-strained spin ice: Localization of thermodynamically deconfined monopoles
• Composite symmetry protected topological order and effective models
• Trimer classical spin liquid from interacting fractional charges
• Synchronization transition in the double dimer model on the cubic lattice
• Thermodynamics and fractal dynamics of nematic spin ice, a doubly frustrated pyrochlore Ising magnet
• Deconstructing Magnetization Noise: Degeneracies, Phases, and Mobile Fractionalized Excitations in Tetris Artificial Spin Ice
• Revisiting spin ice physics in the ferromagnetic Ising pyrochlore Pr${}_2$Sn${}_2$O${}_7$
• Probing emergent QED in quantum spin ice via Raman scattering of phonons: shallow inelastic scattering and pair production
• Theory of collective excitations in the quadruple-$Q$ magnetic hedgehog lattices
• Spin-state smectics in spin crossover materials
• On the Degeneracy of Spin Ice Graphs, and its Estimate via the Bethe Permanent
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Lattice dynamics and spin-phonon coupling in the kagome spin ice HoAgGe
• Stabilization of high-pressure GeCu${}_2$O${}_4$ spinel cuprate with quasi-1D $S=1/2$ chains in the epitaxial thin-film form
• Interplay of uniform U(1) quantum spin liquid and magnetic phases in rare earth pyrochlore magnets : a fermionic parton approach
• Perfectly hidden order and Z2 confinement transition in a fully packed monopole liquid
• Single Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$: No Apparent Octupolar Correlations Above $T=0.05$ K
• Crystal-field magnetostriction of the spin ice under ultrahigh magnetic fields
• An efficient perturbation theory of density matrix renormalization group
• Partial magnetic order in kagome spin ice
• A model for the Mediated Artificial Square Ice phenomenology
• Epitaxial stabilization of thin films of the frustrated Ge-based spinels
• Dephasing with strings attached
• Symmetry, Superposition and Fragmentation in Classical Spin Liquids: A General Framework and Applications to Square Kagome Magnets
• Frustration and chirality in three-dimensional trillium lattices: Insights and Perspectives
• Metal-insulator transitions in pyrochlore oxides
• Time scales in the thermal dynamics of magnetic dipolar clusters
• Coexistence of anomalous spin dynamics and weak magnetic order in a chiral trillium lattice K2FeSn(PO4)3
• Phase diagram of the SU($N$) antiferromagnet of spin $S$ on a square lattice
• Anomalous out-of-equilibrium dynamics in the spin-ice material Dy${}_2$Ti${}_2$O${}_7$ under moderate magnetic fields
• Magnetically disordered ground state in the triangular-lattice antiferromagnets Rb${}_3$Yb(VO${}_4$)${}_2$ and Cs${}_3$Yb(VO${}_4$)${}_2$
• Analytical theory of pyrochlore cooperative paramagnets
• Magnetic Field Response of Dipolar-Octupolar Quantum Spin Ice
• Engineering Hierarchical Symmetries
• Some exactly solvable and tunable frustrated spin models
• Probing topological properties of 3D lattice dimer model with neural networks
• Topology by Design in Magnetic nano-Materials: Artificial Spin Ice
• Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model
• Crossover from string to cluster dynamics following a field quench in spin ice
• A solvable embedding mechanism for one-dimensional spinless and Majorana fermions in higher-dimensional spin-1/2 magnets
• The monopole movement
• The dipolar spin glass transition in three dimensions
• Quantum Spin Liquids in Pyrochlore Magnets With Non-Kramers Local Moments
• Universal dynamics of magnetic monopoles in two-dimensional kagomé ice
• Derivation of field theory for the classical dimer model using bosonization
• Thermal Conductivity of Square Ice
• One-Dimensional Quantum Magnetism in the S = 1/2 Mo(V) system, KMoOP2O7
• Influence of controlled disorder on the dipolar spin ice state of Ho-based pyrochlores
• Geometric fragmentation and anomalous thermalization in cubic dimer model
• Longitudinal magnons in large-$S$ easy-axis magnets
• Magnetic monopole relaxation effects in spin ice Dy${}_2$Ti${}_2$O${}_7$
• Mean-field theory for confinement transitions and magnetization plateaux in spin ice
• Random Transverse Field Effects on Magnetic Noise in Spin Systems
• Dynamic scaling theory for a field quench near the Kasteleyn transition in spin ice
• Classical ground states, spin-wave and PCUT analysis of ${\mathrm{H}}_2\mathrm{SQ}$ system
• Scaling study of diffusion in dynamic crowded spaces
• Long-range Coulomb interactions and nonhydrodynamic behavior in thermal quenches in spin ice
• Spin fractionalization and zero modes in the spin-$\frac{1}{2}$ XXZ chain with boundary fields
• Collinear Magnetic Structure in the Diamond Network Magnet EuTi${}_2$Al${}_{20}$
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Flux fractionalization transition in anisotropic $S=1$ antiferromagnets and dimer-loop models
• Dynamic scaling near the Kasteleyn transition in spin ice: critical relaxation of monopoles and strings following a field quench
• Ising spin ladders of orthopyroxene CoGeO${}_3$
• Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model
• Anisotropic Spin Ice on a Breathing Pyrochlore Lattice
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Towards a global phase diagram of Ce-based dipolar-octupolar pyrochlore magnets under magnetic fields
• Ice on curved surfaces: defect rings and differential local dynamics
• Quantum dynamics of a domain wall in the presence of dephasing
• Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K2Fe2(MoO4)(PO4)2
• Entropic magnetic interlayer coupling