SPIN ICE

Geometric frustration usually arises in systems that comprise magnetic moments (spins) which reside on the sites of a lattice made up of elementary triangular or tetrahedral units and which interact via antiferromagnetic nearest-neighbor exchange. Albeit much less common, geometric frustration can also arise in systems with strong non-collinear single-ion easy-axis (Ising-like) anisotropy and ferromagnetically coupled spins. This is what happens in some pyrochlore oxide materials where Ising-like magnetic rare earth moments (Ho, Dy) sit on a lattice of corner-shared tetrahedra and are coupled via effectively ferromagnetic (dipolar) interactions. These systems possess a macroscopic number of quasi-degenerate classical ground states and display an extensive low-temperature entropy closely related to the extensive proton disorder entropy in common water ice. For this reason, these magnetic systems are called spin ice. This chapter reviews the essential ingredients of spin ice phenomenology in magnetic pyrochlore oxides.

• Publication year

  2009

• Venue

  Frustrated Spin Systems

• Publication date

  2009-03-16

• Fields of study

  Materials Science, Physics

• Identifiers
  DOI 10.1142/9789814440745_0007arXiv 0903.2772
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Frustrated Spin Systems

  2020cited by this paper
• Classical Electrodynamics

  2020cited by this paper
• Electron Paramagnetic Resonance Of Transition Ions

  2016cited by this paper
• Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order

  2010cited by this paper
• The ``Coulomb Phase'' in Frustrated Systems

  2009cited by this paper
• Monopole and Dirac string Dynamics in Spin Ice

  2009cited by this paper
• Magnetic Pyrochlore Oxides

  2009cited by this paper
• Direct observation of a nuclear spin excitation in Ho2Ti2O7.

  2009cited by this paper
• Measurement of the charge and current of magnetic monopoles in spin ice

  2009cited by this paper
• Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7

  2009cited by this paper
• Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7

  2009cited by this paper
• Revisiting static and dynamic spin-ice correlations in Ho 2 Ti 2 O 7 with neutron scattering

  2008cited by this paper
• Static magnetic order in Tb2Sn2O7 revealed by muon spin relaxation with exterior muon implantation.

  2008cited by this paper
• Ordering of the Pyrochlore Ising Model with the Long-Range RKKY Interaction(Condensed matter: electronic structure and electrical, magnetic, and optical properties)

  2008cited by this paper
• Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet

  2008cited by this paper
• Dynamic spin ice: Pr2Sn2O7.

  2008cited by this paper
• Spin-ice behavior in Dy 2 Sn 2 − x Sb x O 7 + x ∕ 2 and Dy 2 Nb Sc O 7

  2007cited by this paper
• Magnetic monopoles in spin ice

  2007cited by this paper
• Magnetic excitations in Tb 2 Sn 2 O 7 and Tb 2 Ti 2 O 7 as measured by inelastic neutron scattering

  2007cited by this paper
• Three-dimensional Kasteleyn transition: spin ice in a [100] field.

  2007cited by this paper
• Relaxation in the spin ice Dy 2 Ti 2 O 7 studied using nuclear forward scattering

  2007cited by this paper
• μSR investigation of spin dynamics in the spin-ice material Dy2Ti2O7

  2007cited by this paper
• Ground state lost but degeneracy found: the effective thermodynamics of artificial spin ice.

  2007cited by this paper
• Dy2Ti2O7 spin ice: a test case for emergent clusters in a frustrated magnet.

  2007cited by this paper
• Structural distortion and the spin liquid state in Tb 2 Ti 2 O 7

  2007cited by this paper
• Nonmonotonic zero-point entropy in diluted spin ice.

  2007cited by this paper
• Unconventional anomalous Hall effect enhanced by a noncoplanar spin texture in the frustrated Kondo lattice Pr2Ir2O7.

  2007cited by this paper
• Pinch points and Kasteleyn transitions in kagome ice

  2007cited by this paper
• Structural disorder and properties of the stuffed pyrochlore Ho2TiO5

  2007cited by this paper
• Direct evidence for a dynamical ground state in the highly frustrated Tb(2)Sn(2)O(7) pyrochlore.

  2006cited by this paper
• Zero-point entropy in stuffed spin-ice

  2006cited by this paper
• The dynamics of diluted Ho Spin Ice Ho2−xYxTi2O7 studied by neutron spin echo spectroscopy

  2006cited by this paper
• Kagomé ice state in the dipolar spin ice Dy2Ti2O7.

  2006cited by this paper
• Realizing colloidal artificial ice on arrays of optical traps.

  2006cited by this paper
• Metallic spin-liquid behavior of the geometrically frustrated Kondo lattice.

  2006cited by this paper
• Spin dynamics and magnetic order in magnetically frustrated Tb2Sn2O7.

  2006cited by this paper
• Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands

  2006cited by this paper
• Four triazole-bridging coordination polymers containing (m-phenol)-1,2,4-triazole: Syntheses, structures and properties of fluorescence and magnetism

  2006cited by this paper
• Dynamically induced frustration as a route to a quantum spin ice state in Tb2Ti2O7 via virtual crystal field excitations and quantum many-body effects.

  2006cited by this paper
• Field-induced transition on a triangular plane in the spin-ice compound Dy2Ti2O7.

  2005cited by this paper
• Finite-temperature transitions in dipolar spin ice in a large magnetic field.

  2005cited by this paper
• Why spin ice obeys the ice rules.

  2005cited by this paper
• Neutron scattering investigation of the spin ice state in Dy2Ti2O7

  2004cited by this paper
• Dipolar spin correlations in classical pyrochlore magnets.

  2004cited by this paper
• Superconductivity in frustrated systems

  2004cited by this paper
• TOPICAL REVIEW: Monte Carlo studies of the dipolar spin ice model

  2004cited by this paper
• Ordered Phase of Dipolar Spin Ice under [110] Magnetic Field

  2004cited by this paper
• Magnetocaloric Effect Study on the Pyrochlore Spin Ice Compound Dy2Ti2O7 in a [111] Magnetic Field

  2004cited by this paper
• The generalization of the extended Stevens operators to higher ranks and spins, and a systematic review of the tables of the tensor operators and their matrix elements

  2004cited by this paper
• Low-temperature spin freezing in the Dy 2 Ti 2 O 7 spin ice

  2003cited by this paper
• Ferromagnetic Ising Spin Chains Emerging from the Spin Ice under Magnetic Field

  2003cited by this paper
• Quantum-classical reentrant relaxation crossover in Dy2Ti2O7 spin ice.

  2003cited by this paper
• Observation of a liquid-gas-type transition in the pyrochlore spin ice compound Dy2Ti2O7 in a magnetic field.

  2003cited by this paper
• Theory of paramagnetic scattering in highly frustrated magnets with long-range dipole-dipole interactions: The case of the Tb 2 Ti 2 O 7 pyrochlore antiferromagnet

  2003cited by this paper
• Theory of the [111] magnetization plateau in spin ice

  2003cited by this paper
• Methods of statistical physics

  2002cited by this paper
• Spin Correlations in Ho2Ti2O7

  2001cited by this paper
• Spin correlations in Ho2Ti2O7: a dipolar spin ice system.

  2001cited by this paper
• Geometrically frustrated magnetic materials

  2001cited by this paper
• Magnetic anisotropy of the spin-ice compound Dy2Ti2O7

  2001cited by this paper
• Spin Ice State in Frustrated Magnetic Pyrochlore Materials

  2001cited by this paper
• Neutron scattering study of dipolar spin ice Ho2Sn2O7: Frustrated pyrochlore magnet

  2001cited by this paper
• Short-range Magnetic interactions in the Spin-Ice compound Ho$_{2}$Ti$_{2}$O$_{7}$

  2001cited by this paper
• Spin Chirality, Berry Phase, and Anomalous Hall Effect in a Frustrated Ferromagnet

  2001cited by this paper
• Long-range order at low temperatures in dipolar spin ice.

  2000cited by this paper
• Dipolar interactions and origin of spin ice in ising pyrochlore magnets

  2000cited by this paper
• Crystal-field interaction in the pyrochlore magnet Ho2Ti2O7

  2000cited by this paper
• Thermodynamic and single-ion properties of Tb3+ within the collective paramagnetic-spin liquid state of the frustrated pyrochlore antiferromagnet Tb2Ti2O7

  2000cited by this paper
• Origin of spin-ice behavior in Ising pyrochlore magnets with long-range dipole interactions: an insight from mean-field theory

  2000cited by this paper
• Zero-point entropy in ‘spin ice’

  1999cited by this paper
• On the generation of operator equivalents and the calculation of their matrix elements.

  1999cited by this paper
• Cooperative Paramagnetism in the Geometrically Frustrated Pyrochlore Antiferromagnet Tb 2 Ti 2 O 7

  1999cited by this paper
• Ising Pyrochlore Magnets: Low-Temperature Properties, "Ice Rules," and Beyond

  1999cited by this paper
• Monte Carlo Methods in Statistical Physics

  1999cited by this paper
• Liquid-Gas Critical Behavior in a Frustrated Pyrochlore Ferromagnet

  1998cited by this paper
• LOW-TEMPERATURE PROPERTIES OF CLASSICAL GEOMETRICALLY FRUSTRATED ANTIFERROMAGNETS

  1998cited by this paper
• LETTER TO THE EDITOR: Frustration in Ising-type spin models on the pyrochlore lattice

  1998cited by this paper
• Magnetic structures of highly frustrated pyrochlores

  1998cited by this paper
• Monte Carlo simulation of ice models

  1997cited by this paper
• GEOMETRICAL FRUSTRATION IN THE FERROMAGNETIC PYROCHLORE HO2TI2O7

  1997cited by this paper
• Absence of long-range order in a three-dimensional geometrically frustrated antiferromagnet.

  1992cited by this paper
• Spin freezing in the geometrically frustrated pyrochlore antiferromagnet Tb2Mo2O7.

  1992cited by this paper
• Mean-field approach to magnetic ordering in highly frustrated pyrochlores.

  1991cited by this paper
• Spin-glass-like behavior in Y2Mo2O7, a concentrated, crystalline system with negligible apparent disorder

  1986cited by this paper
• Spin glasses: Experimental facts, theoretical concepts, and open questions

  1986cited by this paper
• Exactly solved models in statistical mechanics

  1982cited by this paper
• Models of Disorder: The Theoretical Physics of Homogeneously Disordered Systems

  1979cited by this paper
• Insulating spin glasses

  1979cited by this paper
• Introduction to Solid State Physics

  1967cited by this paper
• Lattice Statistics of Hydrogen Bonded Crystals. I. The Residual Entropy of Ice

  1966cited by this paper
• Monte Carlo Methods

  1964cited by this paper
• Ordering and Antiferromagnetism in Ferrites

  1956cited by this paper
• Dynamical Theory of Crystal Lattices

  1954cited by this paper
• Antiferromagnetism. The Triangular Ising Net

  1950cited by this paper
• Introduction to statistical mechanics

  1949cited by this paper
• The Entropy of Water and the Third Law of Thermodynamics. The Heat Capacity of Ice from 15 to 273°K.

  1936cited by this paper
• The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement

  1935cited by this paper
• Molecular Rotation in Ice at 10°K. Free Energy of Formation and Entropy of Water

  1933cited by this paper
• A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions

  1933cited by this paper
• Quantised Singularities in the Electromagnetic Field

  1931cited by this paper

• Phase-space networks and connectivity of the kagome antiferromagnet

  2026cites this paper
• Hyperuniformity of weighted particle systems

  2026cites this paper
• Transport in close-packed solids with stacking defects

  2026cites this paper
• Electron-phonon coupled Langevin dynamics for Mott insulators

  2025cites this paper
• Geometrically Frustrated Quadrupoles on the Pyrochlore Lattice and Generalized Spin Liquids

  2025cites this paper
• Quantum spin liquids in pyrochlore magnets with non-Kramers local moments

  2025cites this paper
• Monopoles, Dirac strings, and magnetic noise in model spin ice

  2025cites this paper
• Coupling quantum spin ice to matter on the centered pyrochlore lattice

  2025cites this paper
• Generation-recombination magnetic monopole noise in 2D artificial spin ices

  2025cites this paper
• Low-temperature state of the spin-ice material <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Dy</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Ti</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal

  2025cites this paper
• Fragmented Spin Liquid and Shadow Pinch Points in Dipole-Octupole Pyrochlore Spin Systems

  2025cites this paper
• Resonant valence bond Coulomb phase: From spins to phonons

  2025cites this paper
• Active-Hydraulic Flows Solve the Six-Vertex Model (and Vice Versa).

  2025cites this paper
• From hierarchical triangular spin liquid to multi-$q$ spin texture in spinel GeFe$_2$O$_4$

  2025cites this paper
• Metal-insulator transitions in pyrochlore oxides

  2025influential citation
• Investigation into the low temperature state of the spin-ice material Dy_2 Ti_2 O_7

  2025cites this paper
• Symmetrizing the constraints: Density matrix renormalization group for constrained lattice models

  2025cites this paper
• Spinor ice correlation in flat-band electronic states on kagome and pyrochlore lattices with spin-orbit coupling

  2025cites this paper
• Theta electromagnetism in quantum spin ice: Microscopic analysis of improper symmetries

  2025cites this paper
• Random transverse field effects on magnetic noise in spin systems

  2025cites this paper
• Towards a global phase diagram of Ce-based dipolar-octupolar pyrochlore magnets under magnetic fields

  2025cites this paper
• Magnetic AC Susceptibility and Relaxation Processes in Y- And Bi-Doped Rare Earth Holmium Titanates

  2025cites this paper
• Magnetic Properties and Specific Heat of Quasi-Two-Dimensional Triangular Lattice Antiferromagnet Ba3CoNb2O9 Single Crystals

  2025cites this paper
• Electronic anisotropy and rotational symmetry breaking at a Weyl semimetal/spin ice interface

  2025cites this paper
• Hearing the light: stray-field noise from the emergent photon in quantum spin ice

  2025cites this paper
• Hardware Acceleration of Frustrated Lattice Systems using Convolutional Restricted Boltzmann Machine

  2025cites this paper
• Charge glass from supercooling topological-ordered liquid

  2025cites this paper
• Quantum Spin Liquids Stabilized by Disorder in Non‐Kramers Pyrochlores

  2025cites this paper
• Quantum Fisher Information as a Thermal and Dynamical Probe in Frustrated Magnets: Insights from Quantum Spin Ice

  2025cites this paper
• Spinon band flattening by its emergent gauge field in quantum kagome ice

  2025cites this paper
• Emergence of topological defects and spin liquid in a two-orbital spin-fermion model on the honeycomb lattice

  2024cites this paper
• Quantum entanglement entropy and Tomonaga-Luttinger liquid to liquid transition in biquadratic spin-1 XY chain with rhombic single-ion anisotropy

  2024cites this paper
• Dipolar effects on the behavior of magnetically diluted spin ice

  2024cites this paper
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice

  2024cites this paper
• An Atlas of Classical Pyrochlore Spin Liquids

  2024cites this paper
• Exploring possible magnetic monopoles-induced magneto-electricity in spin ices

  2024cites this paper
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice

  2024cites this paper
• Synthetic magnetoelectric response of lattice bosonic insulators

  2024cites this paper
• Dichotomous dynamics of magnetic monopole fluids

  2024cites this paper
• Epitaxial Stabilization of a Pyrochlore Interface between Weyl Semimetal and Spin Ice.

  2024cites this paper
• Reweight-annealing method for evaluating the partition function via quantum Monte Carlo calculations

  2024cites this paper
• Active-hydraulic flows solve the 6-vertex model (and vice versa)

  2024cites this paper
• Satisfaction and Violation of the Fluctuation-Dissipation Relation in Spin Ice Materials.

  2024cites this paper
• Wigner-Yanase skew information, quantum entanglement and spin nematic quantum phase transitions in biquadratic spin-1 and spin-2 XY chains with single-ion anisotropies

  2024influential citation
• Hidden order and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mstyle mathvariant="double-struck"><mml:mi>ℤ</mml:mi></mml:mstyle><mml:mn>2</mml:mn></mml:msub></mml:math> confinement transition in a fully packed monopole liquid

  2024cites this paper
• Square ice Coulomb phase as a percolated vertex lattice

  2024cites this paper
• Classical <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> spin liquid on the generalized four-color Kitaev model

  2024cites this paper
• Magnetic Properties of Rare Earth Titanates Ho2Ti2O7 and Yb2Ti2O7 Doped with Y and Bi

  2024cites this paper
• Ice on curved surfaces: Defect rings and differential local dynamics

  2024cites this paper
• Magnetic field response of dipolar-octupolar quantum spin ice

  2024cites this paper
• [111]-strained spin ice: Localization of thermodynamically deconfined monopoles

  2024cites this paper
• Finite-temperature dynamics in 0-flux and π -flux quantum spin ice: Self-consistent exclusive boson approach

  2024cites this paper
• Uncommon Magnetic Ordering in the Quantum Magnet Yb_{3}Ga_{5}O_{12}.

  2024cites this paper
• Pinch-point spectral singularity from the interference of topological loop states

  2024cites this paper
• The challenges of measuring spin Seebeck noise

  2023cites this paper
• Thermodynamics and fractal dynamics of a nematic spin ice: A doubly frustrated pyrochlore Ising magnet

  2023cites this paper
• Partial magnetic order in kagome spin ice

  2023cites this paper
• Emergent classical spin liquid phases in an Ising lattice via size effects

  2023cites this paper
• Revisiting spin ice physics in the ferromagnetic Ising pyrochlore <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Pr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Sn</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:msub><mml:mi mathvariant="normal">

  2023influential citation
• Numerical simulations of the magnetodielectric response in Ising pyrochlores

  2023cites this paper
• 2-form U(1) spin liquids: A classical model and quantum aspects

  2023cites this paper
• Ground state of the $S$=1/2 pyrochlore Heisenberg antiferromagnet: A quantum spin liquid emergent from dimensional reduction

  2023cites this paper
• Experimentally tunable QED in dipolar-octupolar quantum spin ice

  2023cites this paper
• Quantum Spin Ice in Three-Dimensional Rydberg Atom Arrays

  2023cites this paper
• Spectroscopic Signatures of Fractionalization in Octupolar Quantum Spin Ice.

  2023cites this paper
• Replica theory for disorder-free spin-lattice glass transition on a treelike simplex network

  2023cites this paper
• Derivation of field theory for the classical dimer model using bosonization.

  2023cites this paper
• Pseudo-Goldstone Modes and Dynamical Gap Generation from Order by Thermal Disorder.

  2023cites this paper
• Hybrid dyons, inverted Lorentz force, and magnetic Nernst effect in quantum spin ice

  2023cites this paper
• Phonon thermal Hall effect in a non-Kramers paramagnet

  2023cites this paper
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet

  2023cites this paper
• The classical Heisenberg model on the centred pyrochlore lattice

  2023cites this paper
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models

  2023cites this paper
• Phase diagram of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>SU</mml:mi><mml:mtext>(</mml:mtext><mml:mi>N</mml:mi><mml:mtext>)</mml:mtext></mml:math> antiferromagnet of spin <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>S</mml:mi></mml:math> on a squar

  2023cites this paper
• Curie-law crossover in spin liquids

  2023cites this paper
• Active hydraulics laws from frustration principles

  2023cites this paper
• Flux Fractionalization Transition in Anisotropic S=1 Antiferromagnets and Dimer-Loop Models

  2023cites this paper
• Geometrical control of topological charge transfer in Shakti-Cairo colloidal ice

  2023cites this paper
• Dynamics of the antiferromagnetic spin ice phase in pyrochlore spinels

  2023cites this paper
• Classification of classical spin liquids: Detailed formalism and suite of examples

  2023cites this paper
• Nonequilibrium generation of charge defects in kagome spin ice under slow cooling.

  2023cites this paper
• Structural magnetic glassiness in spin ice Dy_2Ti_2O_7

  2023cites this paper
• Emergent tricriticality in magnetic metamaterials

  2022cites this paper
• Probing emergent QED in quantum spin ice via Raman scattering of phonons: Shallow inelastic scattering and pair production

  2022cites this paper
• Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice

  2022cites this paper
• Phonon thermal Hall effect in a metallic spin ice

  2022cites this paper
• Frustration on a centered pyrochlore lattice in metal-organic frameworks

  2022cites this paper
• Flux roughening in spin ice with mixed $\pm J$ interactions

  2022cites this paper
• Tensor electromagnetism and emergent elasticity in jammed solids.

  2022cites this paper
• Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice

  2022cites this paper
• Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice

  2022cites this paper
• Flux roughening in spin ice with mixed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>±</mml:mo><mml:mi>J</mml:mi></mml:mrow></mml:math> interactions

  2022cites this paper
• Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a Z2 gauge theory in three dimensions

  2022cites this paper
• Ergodicity Breaking Provably Robust to Arbitrary Perturbations.

  2022cites this paper
• Symmetry fractionalization in the gauge mean-field theory of quantum spin ice

  2022cites this paper
• Chemical tuning of a honeycomb magnet through a critical point

  2022cites this paper
• Dynamical fractal and anomalous noise in a clean magnetic crystal

  2022cites this paper
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions

  2022cites this paper
• An ultra-low field SQUID magnetometer for measuring antiferromagnetic and weakly remanent magnetic materials at low temperatures.

  2022cites this paper
• Spin nematics meet spin liquids: Exotic quantum phases in the spin-1 bilinear-biquadratic model with Kitaev interactions

  2022cites this paper