Magnets with strong geometric frustration

Abstract

A non-technical introduction to the theory of magnets with strong geometric frustration is given, concentrating on magnets on corner-sharing (kagome, pyrochlore, SCGO and GGG) lattices. Their rich behaviour is traced back to a large ground-state degeneracy in model systems, which renders them highly unstable towards perturbations. A systematic classification according to properties of their ground states is discussed. Other topics addressed in this overview article include a general theoretical framework for thermal order by disorder; the dynamics of how the vast regions of phase space accessible at low temperature are explored; the origin of the featureless magnetic susceptibility fingerprint of geometric frustration; the role of perturbations; and spin ice. The rich field of quantum frustrated magnets is also touched on.

Key-note theory talk of Conference on Highly Frustrated Magnetism (HFM-2000) in Waterloo, Canada, June 2000; 8 pages

References in corpus (11)

• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Local spin resonance and spin-Peierls-like phase transition in a geometrically frustrated antiferromagnet
• Ising pyrochlore magnets: Low temperature properties, ice rules and beyond
• Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice
• Two-dimensional periodic frustrated Ising models in a transverse field
• Order induced by dipolar interactions in a geometrically frustrated antiferromagnet
• The Kagome Antiferromagnet with Defects: Satisfaction, Frustration, and Spin Folding in a Random Spin System
• Quantum tetrahedral mean field theory of the magnetic susceptibility for the pyrochlore lattice
• Ground state properties of a fully frustrated quantum spin system
• Frustrated Order by Disorder: the Pyrochlore Antiferromagnet with Bond Disorder

Cited by in corpus (63)

• Magnetic Pyrochlore Oxides
• Dynamically-Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects
• Bose condensation in flat bands
• Structural, orbital, and magnetic order in vanadium spinels
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Spin-orbit effects in Na${}_4$Ir${}_3$O${}_8$, a hyper-kagomé lattice antiferromagnet
• Incompressible Quantum Liquids and New Conservation Laws
• Ground state lost but degeneracy found: the effective thermodynamics of artificial spin ice
• Effective Temperature in an Interacting, Externally Driven, Vertex System: Theory and Experiment on Artificial Spin Ice
• Generalized Elitzur's Theorem and Dimensional Reduction
• Phonon and crystal field excitations in geometrically frustrated rare earth titanates
• Discrete Sliding Symmetries, Dualities, and Self-dualities of Quantum Orbital Compass Models and (p+ip) Superconducting Arrays
• Energy as an Entanglement Witness for Quantum Many-Body Systems
• Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Modified kagome physics in the natural spin-1/2 kagome lattice systems - kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2
• Mechanisms of degeneracy breaking in pyrochlore antiferromagnets
• Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
• Coupled Cluster Treatment of the Shastry-Sutherland Antiferromagnet
• Mass enhancement, correlations, and strong coupling superconductivity in the beta-pyrochlore KOs2O6
• Spin nematics and magnetization plateau transition in anisotropic Kagome magnets
• Classical antiferromagnet on a hyperkagome lattice
• Absent pinch points and emergent clusters: further neighbour interactions in the pyrochlore Heisenberg antiferromagnet
• Quantum kagome antiferromagnet in a magnetic field: Low-lying non-magnetic excitations versus valence-bond crystal order
• Comparing artificial frustrated magnets: tuning symmetry in nanomagnet arrays
• High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets
• Dzyaloshinskii-Moriya anisotropy and non-magnetic impurities in the $s=1/2$ kagome system ZnCu_3(OH)_6Cl_2
• Magnetism and d-wave superconductivity on the half-filled square lattice with frustration
• Magnetic phase diagram of the antiferromagnetic pyrochlore Gd2Ti2O7
• Energy and multipartite entanglement in multidimensional and frustrated spin models
• Unusual superexchange pathways in a Ni triangular lattice of NiGa${}_2$S${}_4$ with negative charge-transfer energy
• Monopole Flux State on the Pyrochlore Lattice
• Quantum order by disorder in frustrated diamond lattice antiferromagnets
• Slow spin relaxation in a highly polarized cooperative paramagnet
• Magnetothermodynamics of the Ising Antiferromagnet Dy2Ge2O7
• Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field
• Low temperature specific heat and possible gap to magnetic excitations in the Heisenberg pyrochlore antiferromagnet Gd2Sn207
• Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice
• Ferromagnetically coupled Shastry-Sutherland quantum spin singlets in (CuCl)LaNb${}_2$O${}_7$
• The planar pyrochlore antiferromagnet: A large-N analysis
• Magnetization Process of the Classical Heisenberg Model on the Shastry-Sutherland Lattice
• Spin ice behavior in Dy2Sn2-xSbxO7+x/2 and Dy2NbScO7
• Dimer phases in quantum antiferromagnets with orbital degeneracy
• Magnetism in Geometrically Frustrated YMnO3 Under Hydrostatic Pressure Studied with Implanted Muons
• Heisenberg antiferromagnet with anisotropic exchange on the Kagome lattice: Description of the magnetic properties of volborthite
• The kagome staircase compounds Ni${}_3$V${}_2$O${}_8$ and Co${}_3$V${}_2$O${}_8$ studied with implanted muons
• Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy
• Magnetic phases and transitions of the two-species Bose-Hubbard model
• The magnetic properties of the Garnet and glass forms of Mn3Al2Si3O12
• Magnetization plateaus and sublattice ordering in easy axis Kagome lattice antiferromagnets
• Semiclassical degeneracies and ordering for highly frustrated magnets in a field
• Semiclassical spin liquid state of easy axis Kagome antiferromagnets
• Magnetothermal study of Dy Stuffed Spin Ice: Dy2(DyxTi2-x)O7-x/2
• Structural instability of two- and three-dimensional pyrochlore spin lattices in high magnetic fields
• Randomness-Induced Redistribution of Vibrational Frequencies in Amorphous Solids
• Two-dimensional Ising model with competing interactions and its application to clusters and arrays of $\pi$-rings and adiabatic quantum computing
• Coexisting Magnetic Order and Cooperative Paramagnetism in the Stuffed Pyrochlore Tb_{2+x}Ti_{2-2x}Nb_xO_7
• Magnetism in the S=1 frustrated antiferromagnet GeNi2O4 studied using implanted muons
• Energy-level ordering and ground-state quantum numbers for frustrated two-leg spin-1/2 ladder model
• Unconventional magnets in external magnetic fields
• Tricritical transition in the classical XY model on Kagomé lattice under local anisotropy
• Spin-nematic order in the frustrated pyrochlore-lattice quantum rotor model
• Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets