Octupolar ordering of classical kagome antiferromagnets in two and three dimensions

Abstract

Classical Heisenberg antiferromagnets on two-dimensional kagome and three-dimensional hyperkagome lattices are investigated by Monte Carlo simulations. For both models the symmetry-breaking states at low temperatures are described by non-zero octupole moments or third-rank spin tensor order parameters. In the case of the two-dimensional kagome antiferromagnet, a sharp crossover into a coplanar state takes place at T_k ~ 0.004J, which we attribute to proliferation of fractional vortices. The three-dimensional model exhibits a first-order transition at T_c ~ 0.002J into a phase with critical spin correlations, which possesses a long-range order of octupole moments.

12+ pages, 14 figures, accepted version

References in corpus (30)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Dipolar spin correlations in classical pyrochlore magnets
• Enhanced magnetocaloric effect in frustrated magnets
• Spin-1/2 Kagome Like Lattice in Volborthite Cu3V2O7(OH)2-H2O
• Coulomb and Liquid Dimer Models in Three Dimensions
• Power-law spin correlations in pyrochlore antiferromagnets
• Theory of Banana Liquid Crystal Phases and Phase Transitions
• Spin waves in the Frustrated Kagome Lattice Antiferromagnet KFe3(OH)6(SO4)2
• Theory of the [111] magnetization plateau in spin ice
• Field induced transitions in a kagome antiferromagnet
• Classical Spin Liquid: Exact Solution for the Infinite-Component Antiferromagnetic Model on the Kagomé Lattice
• Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8
• Approaching the ground state of the kagome antiferromagnet
• Less than 50% sublattice polarization in an insulating S=3/2 kagome' antiferromagnet at low T
• Classical antiferromagnet on a hyperkagome lattice
• Octupolar order in the multiple spin exchange model on a triangular lattice
• Vortex-induced topological transition of the bilinear-biquadratic Heisenberg antiferromagnet on the triangular lattice
• Fluctuation-Driven 1st-Order Isotropic-to-Tetrahedratic Phase Transition
• Chirality and $Z_2$ vortices in an Heisenberg spin model on the kagomé lattice
• Phase transitions in the antiferromagnetic XY model with a kagome lattice
• Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations
• Spin Hamiltonian, Competing Small Energy Scales and Incommensurate Long Range Order in the Highly Frustrated Gd3Ga5O12 Garnet Antiferromagnet
• Classical Heisenberg antiferromagnet on a garnet lattice: a Monte Carlo simulation
• Spin-stiffness and topological defects in two-dimensional frustrated spin systems
• The Heisenberg antiferromagnet on a triangular lattice: topological excitations
• Evidence for a topological transition in nematic-to-isotropic phase transition in two dimensions

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