Ground-state phase diagram of the Kitaev-Heisenberg model on a kagome lattice

Abstract

The Kitaev-Heisenberg model on the honeycomb lattice has been studied for the purpose of finding exotic states such as quantum spin liquid and topological orders. On the kagome lattice, in spite of a spin-liquid ground state in the Heisenberg model, the stability of the spin-liquid state has hardly been studied in the presence of the Kitaev interaction. Therefore, we investigate the ground state of the classical and quantum spin systems of the kagome Kitaev-Heisenberg model. In the classical system, we obtain an exact phase diagram that has an eight-fold degenerated canted ferromagnetic phase and a subextensive degenerated Kitaev antiferromagnetic phase. In the quantum system, using the Lanczos-type exact diagnalization and cluster mean-field methods, we obtain two quantum spin-liquid phases, an eight-fold degenerated canted ferromagnetic phase similar to the classical spin system, and an eight-fold degenerated $\mathbf{q}=0$ $120^{\circ }$ ordered phase induced by quantum fluctuation. These results may provide a crucial clue to recently observed magnetic structures of the rare-earth-based kagome lattice compounds $A_2$RE${}_3$Sb${}_3$O${}_{14}$ ($A$ = Mg, Zn; RE = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb).

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• A Néel-type antiferromagnetic order in the spin 1/2 rare-earth honeycomb YbCl${}_3$
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Microscopic nature of the charge-density wave in kagome superconductor RbV${}_3$Sb${}_5$
• Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods
• Rare-earth chalcohalides: A family of van der Waals layered Kitaev spin liquid candidates
• Magnetization plateau and supersolid phases in the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice
• Ordered ground states of kagome magnets with generic exchange anisotropy
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• Degenerate magnetic ground state and metastable state on trihexagonal Co-sublattices in Co3Sn2(S,Se)2 single crystals
• Field-induced multipolar character in the dipolar ground state of the honeycomb rare-earth chalcohalide NdOF
• Sizable Ligand-Mediated Bond-Dependent Interactions in a Spin-1 Triangular Antiferromagnet NiI${}_2$
• Multiple topological phases of magnons induced by Dzyaloshinskii-Moriya and pseudodipolar anisotropic exchange interactions in Kagome ferromagnets
• Negligible Kitaev interaction in the van der Waals antiferromagnet NiBr${}_2$ revealed by neutron spectroscopy