Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet

Abstract

We study the low-temperature behaviour of the classical Heisenberg antiferromagnet with nearest neighbour interactions on the pyrochlore lattice. Because of geometrical frustration, the ground state of this model has an extensive number of degrees of freedom. We show, by analysing the effects of small fluctuations around the ground-state manifold, and from the results of Monte Carlo and molecular dynamics simulations, that the system is disordered at all temperatures, T, and has a finite relaxation time, which varies as 1/T for small T.

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Cited by in corpus (306)

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• Classical dipoles on the kagome lattice
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• Ground state selection under pressure in the quantum pyrochlore magnet Yb2Ti2O7
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• Geometrical frustration induced (semi-)metal to insulator transition
• The planar pyrochlore antiferromagnet: A large-N analysis
• Pseudo-Goldstone magnons in the frustrated S=3/2 Heisenberg helimagnet ZnCr2Se4 with a pyrochlore magnetic sublattice
• Cluster Frustration in the Breathing Pyrochlore Magnet LiGaCr4S8
• Semi-classical simulation of spin-1 magnets
• Quantum dimer models and effective Hamiltonians on the pyrochlore lattice
• Vacancy-induced spin textures and their interactions in a classical spin liquid
• The Spin Liquid State of the Tb2Ti2O7 Pyrochlore Antiferromagnet: A Puzzling State of Affairs
• Magnetic properties of geometrically frustrated SrGd2O4
• Competing phases and topological excitations of spin-one pyrochlore antiferromagnets
• Aging and memory properties of topologically frustrated magnets
• Frustrated Heisenberg $J_1-J_2$ model within the stretched diamond lattice of LiYbO2
• Theory of Ca${}_{10}$Cr${}_7$O${}_{28}$ as a bilayer breathing-kagome magnet: Classical thermodynamics and semi-classical dynamics
• Valence-Bond Crystal, and Lattice Distortions in a Pyrochlore Antiferromagnet with Orbital Degeneracy
• How many spin liquids are there in Ca${}_{10}$Cr${}_7$O${}_{28}$?
• Combined approach to analyze and classify families of classical spin liquids
• Quantum Disordered Ground States in Frustrated Antiferromagnets with Multiple Ring Exchange Interactions
• Field-Driven Transitions in the Dipolar Pyrochlore Antiferromagnet Gd${}_2$Ti${}_2$O${}_7$
• Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet
• Dynamics of K${}_2$Ni${}_2$(SO${}_4$)${}_3$ governed by proximity to a 3D spin liquid model
• Jammed spin liquid in the bond-disordered kagome Heisenberg antiferromagnet
• Competing $U(1)$ and ${\mathbb{Z}}_2$ dipolar-octupolar quantum spin liquids on the pyrochlore lattice: application to Ce${}_2$Zr${}_2$O${}_7$
• Uncovering footprints of dipolar-octupolar quantum spin ice from neutron scattering signatures
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• Order and Disorder in AKLT Antiferromagnets in Three Dimensions
• Effect of magnetoelastic coupling on spin-glass behavior in Heisenberg pyrochlore antiferromagnets with bond disorder
• Field-induced pseudo-skyrmion phase in the antiferromagnetic kagome lattice
• Manifolds of magnetic ordered states and excitations in the almost Heisenberg pyrochlore antiferromagnet MgCr2O4
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• Field induced multiple order-by-disorder state selection in antiferromagnetic honeycomb bilayer lattice
• Spin ordering induced by lattice distortions in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice
• A classification of magnetic frustration and metamaterials from topology
• Plaquette order in classical spin liquid stabilized by strong off-diagonal exchange
• Relief of Frustration in the Heisenberg Pyrochlore Antiferromagnet Gd${}_2$Pt${}_2$O${}_7$
• Partially disordered state and spin-lattice coupling in an S=3/2 triangular lattice antiferromagnet Ag2CrO2
• Dzyaloshinsky-Moriya-Induced Order in the Spin-Liquid Phase of the S=1/2 Pyrochlore Antiferromagnet
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• Identification of hidden order and emergent constraints in frustrated magnets using tensorial kernel methods
• Projective symmetry group classification of chiral ${\mathbb{Z}}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model
• Novel ordering of the pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbor interaction
• Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems
• Classical heisenberg antiferromagnet away from the pyrochlore lattice limit: entropic versus energetic selection
• Low temperature spin fluctuations in geometrically frustrated Yb3Ga5O12
• Spin-lattice-coupled order in Heisenberg antiferromagnets on the pyrochlore lattice
• Field-dependent low-field enhancement in effective paramagnetic moment with nano-scaled Co3O4
• Spin-liquid dynamics of pyrochlore magnets Gd2Ti2O7 and Gd2Sn2O7
• Spin freezing in the disordered pyrochlore magnet NaCaCo${}_2$F${}_7$: NMR studies and Monte-Carlo simulations
• From Cooperative Paramagnet to Néel Order in Y_2Ru_2O_7
• Identifying, and constructing, complex magnon band topology
• Spin-orbital glass transition in a model of a frustrated pyrochlore magnet without quenched disorder
• Gd pyrochlore under a staggered molecular field in Gd${}_2$Ir${}_2$O${}_7$
• Neel to Spin-Glass-like Phase Transition versus Dilution in Geometrically Frustrated ZnCr_{2-2x}Ga_{2x}O_4
• Degeneracy and Strong Fluctuation-Induced First-Order Phase Transition in the Dipolar Pyrochlore Antiferromagnet
• Frustrated magnetism in the Heisenberg pyrochlore antiferromagnets $A$Yb${}_2$$X$${}_4$ ($A$ = Cd, Mg, $X$ = S, Se)
• Semiclassical degeneracies and ordering for highly frustrated magnets in a field
• Spin ice thin films: Large-N theory and Monte Carlo simulations
• Antiferromagnetism and crystalline-electric field excitations in tetragonal NaCeO2
• A Bionic Coulomb Phase on the Pyrochlore Lattice
• Quantum generalized constant coupling model for geometrically frustrated antiferromagnets
• Spiral-spin-liquid behaviors and persistent reciprocal kagomé structure in frustrated van der Waals magnets and beyond
• Degenerate and chiral states in the extended Heisenberg model in the kagome lattice
• Classical and quantum order in hyperkagome antiferromagnets
• A magnetocaloric study on the series of 3d-metal chromites ACr${}_2$O${}_4$ where A = Mn, Fe, Co, Ni, Cu and Zn
• Topology and geometry of spin origami
• Freezing and large time scales induced by geometrical frustration
• Supersymmetry "protected" topological phases of isostatic lattices and kagome antiferromagnets
• Evolution of magnetic properties in the normal spinel solid solution Mg(1-x)Cu(x)Cr2O4
• Critical phenomena in a highly constrained classical spin system: Neel ordering from the Coulomb phase
• Enhanced symmetry-breaking tendencies in the $S=1$ pyrochlore antiferromagnet
• Low-energy properties of two-dimensional quantum triangular antiferromagnets: Non-perturbative renormalization group approach
• Competing Gauge Fields and Entropically-Driven Spin Liquid to Spin Liquid Transition in non-Kramers Pyrochlores
• Free coherent spinons in quantum square ice
• Symmetry considerations on the magnetization process of the Heisenberg model on the pyrochlore lattice
• Maxwell electromagnetism as an emergent phenomenon in condensed matter
• Structural phase transitions in geometrically frustrated antiferromagnets
• Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice
• Semiclassical theory for liquid-like behaviour of the frustrated magnet ${\mathrm{Ca}}_{10}{\mathrm{Cr}}_7{\mathrm{O}}_{28}$
• Order by disorder in classical kagome antiferromagnets with chiral interactions
• Novel magnetic phases in a Gd2Ti2O7 pyrochlore for a field applied along the [100] axis
• Classical generalized constant coupling model for geometrically frustrated antiferromagnets
• Effects of spin-lattice coupling and a magnetic field in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice
• Affine lattice construction of spiral surfaces in classical Heisenberg models
• Magnetic-field dependence of low-energy magnons, anisotropic heat conduction, and spontaneous relaxation of magnetic domains in the cubic helimagnet ZnCr2Se4
• A Classical Chiral Spin-Liquid from Chiral Interactions on the Pyrochlore Lattice
• Persistence of the flat band in a kagome magnet with dipolar interactions
• Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions
• Spin Correlations in the Dipolar Pyrochlore Antiferromagnet Gd2Sn2O7
• Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice
• Field Induced Quantum Phase Transitions in $S=1/2$ $J_1$-$J_2$ Heisenberg Model on the Square Lattice
• Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets
• Ordering of the Antiferromagnetic Heisenberg Model on a Pyrochlore Slab
• Quantum half-orphans in kagome antiferromagnets
• Possible realization of three-dimensional quantum spin liquid behavior in HoVO4
• The classical Generalized Constant Coupling method for Geometrically Frustrated Magnets revisited: Microscopic formulation and effect of perturbations beyond nearest neighbor interactions
• Coexisting Magnetic Order and Cooperative Paramagnetism in the Stuffed Pyrochlore Tb_{2+x}Ti_{2-2x}Nb_xO_7
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Spin-liquid phase and order-by-disorder of classical Heisenberg spins on the swedenborgite lattice
• Loop algorithm for classical Heisenberg models with spin-ice type degeneracy
• Anisotropic re-entrant spin-glass features in a metallic kagome lattice, Tb3Ru4Al12
• Chiral magnetism and helimagnons in a pyrochlore antiferromagnet
• Metal-Insulator Transition and Magnetic Order in the Pyrochlore Oxide Hg2Ru2O7
• The $3d$-Electron Heisenberg Pyrochlore Mn${}_2$Sb${}_2$O${}_7$
• Effective theories for quantum spin clusters: Geometric phases and state selection by singularity
• Incommensurate, helical spin ground states on the Hollandite lattice
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet
• Dynamics and energy landscape of the jammed spin-liquid
• Spin dynamics of the antiferromagnetic Heisenberg model on a kagome bilayer
• Projective symmetry group classification of Abrikosov fermion mean-field ansätze on the square-octagon lattice
• Classification of Classical Spin Liquids: Topological Quantum Chemistry and Crystalline Symmetry
• The Classical Heisenberg Model on the Centred Pyrochlore Lattice
• Spin-orbital correlations from complex orbital order in MgV${}_2$O${}_4$
• Deconfined quantum criticality driven by Dirac fermions in SU(2) antiferromagnets
• Fragile spin liquid in three dimensions
• Goldstone modes in the emergent gauge fields of a frustrated magnet
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• Adiabatic spin cooling using high-spin Fermi gases
• Thermodynamic Study of Excitations in a 3D Spin Liquid
• Sublattice Pairing in Pyrochlore Heisenberg Antiferromagnets
• Higher-Rank Spin Liquids and Spin Nematics from Competing Orders in Pyrochlore Magnets
• Classical Heisenberg and planar spin models on the windmill lattice
• Emergent gauge dynamics of highly frustrated magnets
• 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
• Degenerate ground state in the classical pyrochlore antiferromagnet Na${}_3$Mn(CO${}_3$)${}_2$Cl
• Large and exact quantum degeneracy in a Skyrmion magnet
• Role of orbital degrees of freedom in investigating the magnetic properties of geometrically frustrated vanadium spinels
• The ground state phases of orbitally degenerate spinel oxides
• Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln${}_2$InSbO${}_7$ family
• Probing emergent QED in quantum spin ice via Raman scattering of phonons: shallow inelastic scattering and pair production
• Inelastic Neutron Scattering Study of the Spin Dynamics in the Breathing Pyrochlore System LiGa0.95In0.05Cr4O8
• Magnetic properties of the spiral spin liquid and surrounding phases in the square lattice XY model
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Classical spin models of the windmill lattice and their relevance for PbCuTe${}_2$O${}_6$
• Classical and quantum spin liquids
• Loop algorithm for classical antiferromagnetic Heisenberg models with biquadratic interactions
• Pulling order back from the brink of disorder: Observation of a nodal line spin liquid and fluctuation stabilized order in K${}_2$IrCl${}_6$
• Absence of magnetic long range order in Y${}_2$CrSbO${}_7$: bond-disorder induced magnetic frustration in a ferromagnetic pyrochlore
• The quantum spin quadrumer
• A frustrated antipolar phase analogous to classical spin liquids
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Machian fractons, Hamiltonian attractors and non-equilibrium steady states
• Replica theory for disorder-free spin-lattice glass transition on a tree-like simplex network
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice
• On the complexity of spinels: Magnetic, electronic, and polar ground states
• Order, Disorder and Monopole Confinement in the Spin-$1/2$ XXZ Model on a Pyrochlore Tube
• Intermediate-scale theory for electrons coupled to frustrated local-moments
• $T-$linear resistivity from magneto-elastic scattering: application to PdCrO${}_2$
• Frustrated Kondo chains and glassy magnetic phases on the pyrochlore lattice
• Symmetry, Superposition and Fragmentation in Classical Spin Liquids: A General Framework and Applications to Square Kagome Magnets
• Three-dimensional checkerboard spin structure on a breathing pyrochlore lattice
• Helimagnons in a chiral ground state of the pyrochlore antiferromagnets
• Theory of transverse magnetization in spin-orbit coupled antiferromagnets
• Spin-nematic order in the frustrated pyrochlore-lattice quantum rotor model
• Tricritical transition in the classical XY model on Kagomé lattice under local anisotropy
• Pinch-point spectral singularity from the interference of topological loop states
• An electric-field representation of the harmonic XY model
• Quantum Systems Exactly
• Classical fracton spin liquid and Hilbert space fragmentation in a 2D spin-$1/2$ model
• Simulating the Palmer-Chalker state in an orbital superfluid
• Critical slowing down in the geometrically frustrated pyrochlore antiferromagnet Gd_2Ti_2O_7
• Evidence for spin liquid behavior in the frustrated three-dimensional $S=1/2$ Heisenberg garnet NaCa${}_2$Cu${}_2$(VO${}_4$)${}_3$
• Quantitative functional renormalization for three-dimensional quantum Heisenberg models
• Nematic correlations and nematic Berezinskii-Kosterlitz-Thouless transition in spin-1 kagome lattice antiferromagnets
• Spinor ice correlation in flat-band electronic states on kagome and pyrochlore lattices with spin-orbit coupling
• Low frequency spin dynamics in XY quantum spin ice Yb${}_2$Pt${}_2$O${}_7$
• Incoherent transport in a classical spin liquid
• Honeycomb-lattice Gamma model in a magnetic field: hidden Néel order and spin-flop transition
• Spin liquid state in a three-dimensional pyrochlore-like frustrated magnet
• Spin wave interactions in the pyrochlore Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions
• Field-induced Multi-$\vec{\mathbf{Q}}$ States in a Pyrochlore Heisenberg Magnet
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• Emergence of topological defects and spin liquid in a two-orbital spin-fermion model on the honeycomb lattice
• Unconventional Spin Dynamics and Supersolid Excitations in the Triangular-Lattice XXZ Model
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• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• A Green's function method for the two-dimensional frustrated spin-1/2 Heisenberg magnetic lattice
• Phase-space networks and connectivity of the kagome antiferromagnet
• Dynamics of magnetic collective modes in the square and triangular lattice Mott insulators at finite temperature