Spin-lattice coupling in frustrated antiferromagnets

Abstract

We review the mechanism of spin-lattice coupling in relieving the geometrical frustration of pyrochlore antiferromagnets, in particular spinel oxides. The tetrahedral unit, which is the building block of the pyrochlore lattice, undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom are coupled to the antiferromagnetism. By restricting our considerations to distortions which preserve the translational symmetries of the lattice, we present a general theory of the collective spin-Jahn-Teller effect in the pyrochlore lattice. One of the predicted lattice distortions breaks the inversion symmetry and gives rise to a chiral pyrochlore lattice, in which frustrated bonds form helices with a definite handedness. The chirality is transferred to the spin system through spin-orbit coupling, resulting in a long-period spiral state, as observed in spinel CdCr2O4. We discuss explicit models of spin-lattice coupling using local phonon modes, and their applications in other frustrated magnets.

23 pages, 6 figures. Lecture notes for Trieste Summer School, August 2007. To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mila

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• Adiabatic state preparation of stripe phases with strongly magnetic atoms
• Synchronization transition in the double dimer model on the cubic lattice
• Noncollinear magnetic structure in U2Pd2In at high magnetic fields
• Thermodynamic properties of the macroscopically degenerate tetramer-dimer phase of the spin-1/2 Heisenberg model on the diamond-decorated square lattice
• Fractonic Berezinskii-Kosterlitz-Thouless transition from a renormalization group perspective
• Orbital order in a bosonic $p$-band triangular lattice
• Dynamical structure factors in the nematic phase of frustrated ferromagnetic spin chains
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Role of orbital degrees of freedom in investigating the magnetic properties of geometrically frustrated vanadium spinels
• Striped critical spin liquid in a spin-orbital entangled RVB state in a projected entangled-pair state representation
• Magnetization process in the exactly solved spin-1/2 Ising-Heisenberg model on decorated Bethe lattices
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Infinite Series of Ferrimagnetic Phases Emergent from the Gapless Spin Liquid Phase of Mixed Diamond Chains
• Computation of microcanonical entropy at fixed magnetization without direct counting
• Monte Carlo study on the detection of classical order by disorder in real antiferromagnetic Ising pyrochlores
• Quantum Fluctuations in the van der Walls material $\mathrm{NiP}{\mathrm{S}}_3$
• Machian fractons, Hamiltonian attractors and non-equilibrium steady states
• Interplay of disorder and geometrical frustration in doped Gadolinium Gallium Garnet
• Mean-field theory of interacting triplons in a two-dimensional valence-bond solid: stability and properties of many-triplon states
• Zero-energy excitation in the classical kagome antiferromagnet NaBa${}_2$Mn${}_3$F${}_{11}$
• Quantum dimer models emerging from large-spin ultracold atoms
• Spin-lattice Coupling in U(1) Quantum Spin Liquids
• Ferromagnetic spin-orbital liquid of dipolar fermions in zigzag lattices
• An efficient perturbation theory of density matrix renormalization group
• The quantum spin quadrumer
• Classical spin models of the windmill lattice and their relevance for PbCuTe${}_2$O${}_6$
• Ground state and finite temperature behavior of 1/4-filled band zigzag ladders
• Inducing critical phenomena in spin chains through sparse alternating fields
• Triplet excitations in the frustrated spin ladder Li${}_2$Cu${}_2$O(SO${}_4$)${}_2$
• Quantum state transfer using 1D Heisenberg Hamiltonian on quasi-1D lattices
• Experimental determination of the magnetic interactions of frustrated Cairo pentagon lattice materials
• Models of interacting bosons with exact ground states: a unified approach
• Exotic Spin Order due to Orbital Fluctuations
• The Interplay between Frustration and Entanglement in Many-Body Systems
• Diabatic quantum and classical annealing of the Sherrington-Kirkpatrick model
• Notes on Ground-State Properties of Mixed Spin-1 and Spin-1=2 Lieb-Lattice Heisenberg Antiferromagnets
• Emergent Quadrupolar Order in the Spin-$1/2$ Kitaev-Heisenberg Model
• Time scales in the thermal dynamics of magnetic dipolar clusters
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• Evidence of Low-Energy Singlet Excited States in the Spin-1/2 Polyhedral Clusters {Mo${}_{72}$V${}_{30}$} and {W${}_{72}$V${}_{30}$} with Strongly Frustrated Kagomé Networks
• Rigorous construction of coherent state path integrals through dualization
• $\mu$-Symmetry breaking: an algebraic approach to finding mean fields of quantum many-body systems
• Many body population trapping in ultracold dipolar gases
• Dynamics of quantum spin-nematics: Comparisons with canted antiferromagnets
• Real Space Imaging of Spin Polarons in Zn Doped SrCu2(BO3)2
• Square ice Coulomb phase as a percolated vertex lattice
• Fractional Dynamics and Modulational Instability in Long-Range Heisenberg Chains
• Anticollinear order and degeneracy lifting in square lattice antiferromagnet LaSrCrO4
• One-dimensional frustrated plaquette compass model: Nematic phase and spontaneous multimerization
• Quench of symmetry broken ground states
• Crossover between tricritical and Lifshitz points in pyrochlore FeF${}_3$
• Valence-Bond Solid phases in the spin-$1/2$ Kekule-Heisenberg model
• Qubits on programmable geometries with a trapped-ion quantum processor
• Ab initio determination of magnetic ground state of pyrochlore Y${}_2$Mn${}_2$O${}_7$
• Comparison of the Magnetic properties of Mn3Fe2Si3O12 as a crystalline garnet and as a glass
• Finding and classifying an infinite number of cases of the marginal phase transition in one-dimensional Ising models
• Quantum to classical transition in the ground state of a spin-$S$ quantum antiferromagnet
• Kinetic samplers for neural quantum states
• Magnetic-field-induced reorientation in the SDW and the spin-stripe phases of the frustrated spin-1/2 chain compound $\beta$-TeVO${}_4$
• Quantum disordered ground state for the frustrated square lattice
• Anisotropic propagative excitations and quadrupolar effects in Tb${}_2$Ti${}_2$O${}_7$
• Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions
• Metallic bonding in close packed structures: structural frustration from a hidden gauge symmetry
• The effect of Al doping on the structure and magnetism in cobaltite CaBaCo4O7
• Spontaneous chiral symmetry breaking on a fully polarized frustrated magnet at finite temperature
• Stability and magnetization curve of spin-nematic phase slightly below saturation field
• (1+1)-d U(1) Quantum link models from effective Hamiltonians of dipolar molecules
• Role of the compensating current in the weak Josphson coupling regime: An extended study on excitonic Josephson junctions
• Transient selection of competing order in frustrated spin Peierls systems after a quench
• Spin amplitude wave due to dipole-quadrupole hybridization in spin-1 pyrochlore magnets
• Spin dynamics in natural multiferroic pyroxene NaFeSi${}_2$O${}_6$
• Synthesis, structure and magnetism of the new $S=\frac{1}{2}$ kagome magnet NH${}_4$Cu${}_{2.5}$V${}_2$O${}_7$(OH)${}_2$.H${}_2$O
• Non-chiral spin frustration versus highly degenerate ferromagnetic state with local chiral degrees of freedom of an exactly solvable spin-electron planar model of inter-connected trigonal bipyramids
• Fluctuating local field method for the disordered Ising model
• Synthesis and magnetic properties of a quantum magnet PbCuTeO5
• Magnetic lattices for ultracold atoms
• Evidence for Emergent Kagome Spin Configuration with Concomitant Transverse and Longitudinal Spin-Glass Freezing in the Chemically Ordered M-type Hexaferrite BaFe12O19
• Exact solution of Ising model of an alternating delta spin chain