Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets

Abstract

The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Remarkably, the spin ices provide one of very few experimentally realised examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, the spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the classical spin ice state characterised by emergent photon-like excitations. Whereas in classical spin ices the excitations are akin to electrostatic charges, in the quantum spin liquid these charges interact through a dynamic and emergent electromagnetic field. In this review, we describe the latest developments in the study of such a quantum spin ice, focussing on the spin liquid phenomenology and the kinds of materials where such a phase might be found.

Review article; 29 pages, 8 figures, 1 table, 189 references, 12 footnotes

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• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
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• Quantum spin liquid at finite temperature: proximate dynamics and persistent typicality
• Refrustration and competing orders in the prototypical Dy2Ti2O7 spin ice material
• Sleuthing out exotic quantum spin liquidity in the pyrochlore magnet Ce${}_2$Zr${}_2$O${}_7$
• Structural and Magnetic Investigations of Single-Crystals of the Neodymium Zirconate Pyrochlore, Nd2Zr2O7
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• Signatures of a gearwheel quantum spin liquid in a spin-$\frac{1}{2}$ pyrochlore molybdate Heisenberg antiferromagnet
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• Frozen State and Spin Liquid Physics in Na4Ir3O8: an NMR study
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• Reentrant Phase Diagram of $\mathrm{Y}{\mathrm{b}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$ in $⟨111⟩$ Magnetic Field
• Chirality-driven Hall Transport Phenomena of Spins
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• Order by virtual crystal field fluctuations in pyrochlore XY antiferromagnets
• Novel Strongly Spin-Orbit Coupled Quantum Dimer Magnet: Yb${}_2$Si${}_2$O${}_7$
• The Spectral Periodicity of Spinon Continuum in Quantum Spin Ice
• Dirac's "magnetic monopole" in pyrochlore ice U(1) spin liquids: Spectrum and classification
• A Supercooled Spin Liquid State in the Frustrated Pyrochlore Dy2Ti2O7
• The Emergent Fine Structure Constant of Quantum Spin Ice Is Large
• Exact emergent higher-form symmetries in bosonic lattice models
• Quantum Kagome Ice
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• Universal Dynamic Magnetism in Yb-Pyrochlores with Disparate Ground States
• Effect of Chemical Pressure on the Crystal Electric Field States of Erbium Pyrochlore Magnets
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• Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet
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• Mesoscopic correlations in Tb2Ti2O7 spin liquid
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• Fingerprints of quantum spin ice in Raman scattering
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• Effective point-charge analysis of crystal electric fields -- application to rare-earth pyrochlores and tripod kagome magnets R3Mg2Sb3O14
• Electric field control of emergent electrodynamics in quantum spin ice
• Semi-classical Approach to Quantum Spin Ice
• Anomalous Magnetoresistance by Breaking Ice Rule in Bi2Ir2O7/Dy2Ti2O7 Heterostructure
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• Upper branch magnetism in quantum magnets: Collapses of excited levels and emergent selection rules
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• Fractional Spin fluctuations and quantum liquid signature in Gd2ZnIrO6
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• Deviation from the dipole-ice model in the new spinel spin-ice candidate, MgEr${}_2$Se${}_4$
• A Classical Chiral Spin-Liquid from Chiral Interactions on the Pyrochlore Lattice
• Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice
• Continuum excitation and pseudospin wave in quantum spin-liquid and quadrupole ordered states of Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
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• Modification of Spin Ice Physics in Ho${}_2$Ti${}_2$O${}_7$ Thin Films
• Crystal field excitations from $\mathrm{Y}{\mathrm{b}}^{3+}$ ions at defective sites in highly stuffed $\mathrm{Y}{\mathrm{b}}_2\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$
• Magnetic structure of a new quantum magnet SrCuTe${}_2$O${}_6$
• Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
• CSPEC: The cold chopper spectrometer of the European Spallation Source, a detailed overview prior to commissioning
• $\mu$SR Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$
• Constraining the Parameter Space of a Quantum Spin Liquid Candidate in Applied Field with Iterative Optimization
• On two phases inside the Bose condensation dome of Yb${}_2$Si${}_2$O${}_7$
• Optimization of single crystal growth of candidate quantum spin-ice Pr2Hf2O7 by optical floating-zone method
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• Quadrupole order in the frustrated pyrochlore magnet Tb${}_2$Ti${}_2$O${}_7$
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• Solving the quantum dimer and six vertex models one electric field line at a time
• Orientation Dependence of the Magnetic Phase Diagram of Yb${}_2$Ti${}_2$O${}_7$
• A Large-$S$ Study of Quantum Kagome Ice
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• Tunneling-induced restoration of classical degeneracy in quantum kagome ice
• Ultrasound detection of emergent photons in generic quantum spin ice
• Deriving quantum spin model for a zigzag-chain ytterbium magnet with anisotropic exchange interactions
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• Screening and the Pinch Point Paradox in Spin Ice
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• Dynamical Axions in $U(1)$ Quantum Spin Liquids
• Discovery of new magnetic orders on pyrochlore spinels
• Classification of symmetry-enriched topological quantum spin liquids
• Emergent Gauge Fields in Band Insulators
• Dipolar-octupolar correlations and hierarchy of exchange interactions in Ce${}_2$Hf${}_2$O${}_7$
• Frustration relief and reorientation transition in the kagome-like dolerophanite Cu${}_2$OSO${}_4$
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• Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln${}_2$InSbO${}_7$ family
• Tunable critical correlations in kagome ice
• Hidden phases born of a quantum spin liquid: Application to pyrochlore spin ice
• Dimensional change of quadrupole orders in pseudospin-$\frac{1}{2}$ pyrochlore magnets under [111] field
• Exact Continuum Representation of Long-range Interacting Systems and Emerging Exotic Phases in Unconventional Superconductors
• Long-wavelength correlations in ferromagnetic titanate pyrochlores as revealed by small angle neutron scattering
• Probing emergent QED in quantum spin ice via Raman scattering of phonons: shallow inelastic scattering and pair production
• Collective magnetic Higgs excitation in a pyrochlore ruthenate
• Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a ${\mathbb{Z}}_2$ gauge theory in three dimensions
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Revisiting spin ice physics in the ferromagnetic Ising pyrochlore Pr${}_2$Sn${}_2$O${}_7$
• Thermodynamics of the dipole-octupole pyrochlore magnet Ce${}_2$Hf${}_2$O${}_7$ in applied magnetic fields
• Magnetic properties of the spiral spin liquid and surrounding phases in the square lattice XY model
• Signatures of spinon dynamics and phase structure of dipolar-octupolar quantum spin ices in two-dimensional coherent spectroscopy
• Two-Peak Heat Capacity Accounts for $R\ln (2)$ Entropy and Ground State Access in the Dipole-Octupole Pyrochlore Ce${}_2$Hf${}_2$O${}_7$
• Topological physics in quantum critical systems
• Magnetoelastic coupling and Grüneisen scaling in NdB${}_4$
• Vison crystal in quantum spin ice on the breathing pyrochlore lattice
• Field-temperature phase diagram of the enigmatic Nd${}_2$(Zr${}_{1-x}$Ti${}_x$)${}_2$O${}_7$ pyrochlore magnets
• Neutron scattering from fragmented frustrated magnets
• Exploring magneto-electric coupling through lattice distortions: insights from a pantograph model
• Spin-lattice Coupling in U(1) Quantum Spin Liquids
• Relationship between the ground-state wave function of a magnet and its static structure factor
• Order, Disorder and Monopole Confinement in the Spin-$1/2$ XXZ Model on a Pyrochlore Tube
• 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
• Interplay of uniform U(1) quantum spin liquid and magnetic phases in rare earth pyrochlore magnets : a fermionic parton approach
• Classical and quantum spin liquids
• Frustration and chirality in three-dimensional trillium lattices: Insights and Perspectives
• Probing topological properties of 3D lattice dimer model with neural networks
• Hopfions in lattice dimer model
• Elastic study of electric quadrupolar correlation in the paramagnetic state of a frustrated quantum magnet $\mathrm{T}{\mathrm{b}}_{2+\delta }\mathrm{T}{\mathrm{i}}_{2-\delta }{\mathrm{O}}_7$
• Persistent dynamic magnetic state in artificial honeycomb spin ice
• Impact of disorder in Nd-based pyrochlore magnets
• Metal-insulator transitions in pyrochlore oxides
• Magnetically disordered ground state in the triangular-lattice antiferromagnets Rb${}_3$Yb(VO${}_4$)${}_2$ and Cs${}_3$Yb(VO${}_4$)${}_2$
• Electric Field Response In Breathing Pyrochlores
• Analytical theory of pyrochlore cooperative paramagnets
• Magnetic Field Response of Dipolar-Octupolar Quantum Spin Ice
• Magnetic field tuning of crystal field levels and vibronic states in Spin-ice Ho${}_2$Ti${}_2$O${}_7$ observed in far-infrared reflectometry
• Tuning interactions in the spin-ice materials Dy${}_2$Ge${}_{2-x}$Si${}_x$O${}_7$ by silicon substitution
• Theory of transverse magnetization in spin-orbit coupled antiferromagnets
• Two-stage evolution of magnetic correlations in spiral spin liquid material, Ca${}_{10}$Cr${}_7$O${}_{28}$
• Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics
• Low-temperature specific heat and heat transport of Tb${}_2$Ti${}_{2-x}$Zr${}_x$O${}_7$ single crystals
• Thermal Conductivity of Square Ice
• XY ring exchange model with frustrated Ising coupling on the triangular lattice
• Engineering a multi-level bath for transmons with three-wave mixing and parametric drives
• Quantum loops in the 1T transition metal dichalcogenides
• Communicating through a geometrically frustrated channel
• Crossover from string to cluster dynamics following a field quench in spin ice
• Coulombic antiferromagnet in spin-1/2 pyrochlores with dipole-octupole doublets
• Spin and quadrupole correlations by three-spin interaction in the frustrated pyrochlore magnet Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Quantum triangular ice in the easy-axis ferromagnetic phase
• Ground state properties of quantum triangular ice
• Quantum Spin Liquids in Pyrochlore Magnets With Non-Kramers Local Moments
• Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model
• Strong coupling of lattice and orbital excitations in quantum magnet Ca${}_{10}$Cr${}_7$O${}_{28}$: Anomalous temperature dependence of Raman phonons
• Crystalline phases and devil's staircase in qubit spin ice
• Low frequency spin dynamics in XY quantum spin ice Yb${}_2$Pt${}_2$O${}_7$
• Density-Matrix Mean-Field Theory
• Classical triangular lattice antiferromagnetic Ising model as a free-fermion/superconductor system
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
• Quantum entanglement of XY-type spin dimers in Shastry-Sutherland lattice
• Theta electromagnetism in quantum spin ice: Microscopic analysis of improper symmetries
• Coupling quantum spin ice to matter on the centered pyrochlore lattice
• Geometric fragmentation and anomalous thermalization in cubic dimer model
• Investigating structure and physical properties of quaternary layered transition metal oxide Na2Cu2TeO6
• Influence of controlled disorder on the dipolar spin ice state of Ho-based pyrochlores
• Rotational Grüneisen ratio: a probe for quantum criticality in anisotropic systems
• Low-temperature high-frequency dynamic magnetic susceptibility of classical spin-ice Dy${}_2$Ti${}_2$O${}_7$
• Dynamic scaling near the Kasteleyn transition in spin ice: critical relaxation of monopoles and strings following a field quench
• Unveiling the Fifth State of Matter: Insights into Ultra-Hot Plasma and its Applications
• Hearing the light: stray-field noise from the emergent photon in quantum spin ice
• Possibility of a Topological Phase Transition in Two-dimensional $R{P}^3$ Model
• Excitation spectrum and low-temperature magnetism in disordered defect-fluorite Ho2Zr2O7
• 5d-mediated indirect exchange and effective spin Hamiltonians in Ce triangular-lattice delafossites
• Finite-Size Spectral Signatures of Order by Quantum Disorder: A Perspective from Anderson's Tower of States
• Disorder-induced proximate quantum spin ice phase in Pr2Sn2O7
• Internal and External Field Effects upon Crystal Field Excitations in REFeO${}_3$ (RE = Nd${}^{3+}$, Er${}^{3+}$, Yb${}^{3+}$, Pr${}^{3+}$, and Ho${}^{3+}$)
• Enhanced-Entropy Phases in Geometrically Frustrated Pyrochlore Magnets
• Towards a global phase diagram of Ce-based dipolar-octupolar pyrochlore magnets under magnetic fields
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Strongly frustrated 2D magnetism in a 3D hexagonal perovskite