Spin-orbit physics of j=1/2 Mott insulators on the triangular lattice

Abstract

The Heisenberg-Kitaev (HK) model on the triangular lattice is conceptually interesting for its interplay of geometric and exchange frustration. HK models are also thought to capture the essential physics of the spin-orbital entanglement in effective $j=1/2$ Mott insulators studied in the context of various 5d transition metal oxides. Here we argue that the recently synthesized Ba${}_3$IrTi${}_2$O${}_9$ is a prime candidate for a microscopic realization of the triangular HK model. We establish that an infinitesimal Kitaev exchange destabilizes the 120${}^{\circ }$ order of the quantum Heisenberg model and results in the formation of an extended ${\mathbb{Z}}_2$-vortex crystal phase in the parameter regime most likely relevant to the real material. Using a combination of analytical and numerical techniques we map out the entire phase diagram of the model, which further includes various ordered phases as well as an extended nematic phase around the antiferromagnetic Kitaev point.

12 pages, 11 figures

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• Noncoplanar multiple-$Q$ spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy
• Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
• Global phase diagram, possible chiral spin liquid and topological superconductivity in the triangular Kitaev-Heisenberg model
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Semiclassical ground-state phase diagram and multi-Q phase of a spin-orbit coupled model on triangular lattice
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• Revisiting the Kitaev material candidacy of Ir4+ double perovskite iridates
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• Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices studied by improved finite-temperature Lanczos methods
• Quantum spin liquid ground states of the Heisenberg-Kitaev model on the triangular lattice
• Putative spin liquid in the triangle-based iridate Ba${}_3$IrTi${}_2$O${}_9$
• Unconventional magnetism in the 4d${}^4$ based ($S=1$) honeycomb system Ag${}_3$LiRu${}_2$O${}_6$
• Spin-orbit effects in pentavalent Iridates: Models and materials
• Stability of Skyrmion Crystal Phase in Centrosymmetric Distorted Triangular-Lattice Antiferromagnets
• Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling
• Coupled spin-1/2 antiferromagnetic chain Cs${}_2$LiRuCl${}_6$ with partially disordered crystal lattice
• Meron-antimeron crystals in noncentrosymmetric itinerant magnets on a triangular lattice