Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice

Abstract

Selection of the ground state of the kagomé-lattice $XXZ$ antiferromagnet by quantum fluctuations is investigated by combining non-linear spin-wave and real-space perturbation theories. The two methods unanimously favor $\mathbf{q}=0$ over $\sqrt{3}\times \sqrt{3}$ magnetic order in a wide range of the anisotropy parameter $0\le \Delta \le 0.72$. Both approaches are also in an accord on the magnitude of the quantum order-by-disorder effect generated by topologically non-trivial, loop-like spin-flip processes. A tentative $S-\Delta$ phase diagram of the model is proposed.

5 pages, 4 figures + 6.2 pages, 4 figures supplemental, minor changes, accepted version

References in corpus (12)

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• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
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• Pinwheel VBS state and triplet excitations in the two-dimensional deformed kagome lattice
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• Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice
• Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet
• XY checkerboard antiferromagnet in external field
• Structure factor of low-energy spin excitations in a S=1/2 kagome antiferromagnet

Cited by in corpus (12)

• Topological Thermal Hall Effect in Frustrated Kagomé Antiferromagnets
• Frustration and Dzyaloshinsky-Moriya anisotropy in the kagome francisites Cu${}_3$Bi(SeO${}_3{)}_2$O${}_2$X
• Functional-renormalization-group analysis of Dzyaloshinsky-Moriya and Heisenberg spin interactions on the kagome lattice
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Finite-temperature crossover phenomenon in the $S=1/2$ antiferromagnetic Heisenberg model on the kagome lattice
• Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice
• Real-space perturbation theory for frustrated magnets: application to magnetization plateaus
• Magnonic Analogue of Edelstein Effect in Antiferromagnetic Insulators
• Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures
• Magnetic excitations in quasi-one dimensional helimagnets: Magnon decays and in uence of the inter-chain interactions
• Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet
• Absence of long-range order in a general spin-$S$ kagome lattice Ising antiferromagnet