Thermal Hall Effect in the Kitaev-Heisenberg System with Spin-Phonon Coupling

Abstract

We investigate the thermal Hall effect in a Kitaev-Heisenberg system, a model for Kitaev candidate $\alpha$-RuCl${}_3$, in the presence of the coupling between spin and phonon arising from chlorine atoms' vibration. We observe that the coupling modifies the relative stability between different magnetic states under a magnetic field, especially stabilizing a canted zigzag antiferromagnetic state. Remarkably, the spin-phonon interaction has distinct effects on the thermal Hall conductivity in different magnetically ordered states. For the canted zigzag state, which is relevant to $\alpha {\text{-RuCl}}_3$, the spin-phonon interaction enhances the energy gap that is induced by a magnetic field and suppresses the thermal Hall conductivity at low temperatures. Importantly, we find that the spin-phonon interaction destabilizes the quantized thermal Hall effect in the spin-liquid state. Our results demonstrate a crucial role of phonon degrees of freedom to the thermal Hall effect in Kitaev materials.

arXiv comment6 pages, 4 figures

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