Heisenberg antiferromagnet with anisotropic exchange on the Kagome lattice: Description of the magnetic properties of volborthite

Abstract

We study the properties of the Heisenberg antiferromagnet with spatially anisotropic nearest-neighbour exchange couplings on the kagome net, i.e. with coupling J in one lattice direction and couplings J' along the other two directions. For J/J' > 1, this model is believed to describe the magnetic properties of the mineral volborthite. In the classical limit, it exhibits two kinds of ground states: a ferrimagnetic state for J/J' < 1/2 and a large manifold of canted spin states for J/J' > 1/2. To include quantum effects self-consistently, we investigate the Sp(N) symmetric generalisation of the original SU(2) symmetric model in the large-N limit. In addition to the dependence on the anisotropy, the Sp(N) symmetric model depends on a parameter kappa that measures the importance of quantum effects. Our numerical calculations reveal that in the kappa-J/J' plane, the system shows a rich phase diagram containing a ferrimagnetic phase, an incommensurate phase, and a decoupled chain phase, the latter two with short- and long-range order. We corroborate these results by showing that the boundaries between the various phases and several other features of the Sp(N) phase diagram can be determined by analytical calculations. Finally, the application of a block-spin perturbation expansion to the trimerised version of the original spin-1/2 model leads us to suggest that in the limit of strong anisotropy, J/J' >> 1, the ground state of the original model is a collinearly ordered antiferromagnet, which is separated from the incommensurate state by a quantum phase transition.

21 pages, 22 figures. Final version, PRB in press

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Cited by in corpus (23)

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• A Field Guide to Spin Liquids
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• One-Third Magnetization Plateau with a Preceding Novel Phase in Volborthite
• Spatially Anisotropic Heisenberg Kagome Antiferromagnet
• Magnetic susceptibilities in a family of S=1/2 Kagome antiferromagnet
• Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet
• Local study of the insulating quantum kagome antiferromagnets YCu3(OH)6OxCl3-x (x=0,1/3)
• Spin-1/2 Heisenberg antiferromagnet on an anisotropic kagome lattice
• Pair Correlations, Short Range Order and Dispersive Excitations in the Quasi-Kagome Quantum Magnet Volborthite
• Spin-1/2 kagome compounds: volborthite vs herbertsmithite
• Magnetic order in a spin-1/2 interpolating kagome-square Heisenberg antiferromagnet
• The symmetry of the spin Hamiltonian in herbertsmithite, a spin-1/2 kagomé lattice
• Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets
• Partial ferromagnetic ordering and indirect exchange interaction in spatially anisotropic kagome antiferromagnet Cs_2Cu_3CeF_{12}
• Magnetic ordering of the distorted kagome antiferromagnet Y${}_3$Cu${}_9$(OH)${}_{18}$[Cl${}_8$(OH)] prepared via optimal synthesis
• Distorted Kagome Lattice Generated by a Unique Orbital Arrangement in the Copper Mineral KCu3As2O7(OH)3
• Spatially anisotropic kagome antiferromagnet with Dzyaloshinskii-Moriya interaction
• Quantum spin liquid and magnetic order in a two-dimensional non-symmorphic lattice: considering the distorted Kagome lattice of Volborthite
• Strain tuning of highly frustrated magnets: Order and disorder in the distorted kagome Heisenberg antiferromagnet
• Correlations in the Ising antiferromagnet on the anisotropic kagome lattice
• Ferromagnetism induced in anisotropic stacked kagome-lattice antiferromagnet Cs${}_2$Cu${}_3$CeF${}_{12}$
• Magnetic response and antiferromagnetic correlations in strained kagome ribbons