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

TL;DR

This paper studies how spin-phonon coupling influences the thermal Hall effect in a Kitaev-Heisenberg system, revealing its impact on magnetic state stability and thermal Hall conductivity, especially in the context of $ ext{ extalpha}$-RuCl$_3$.

Contribution

It provides new insights into the role of phonons in modifying the thermal Hall response and magnetic stability in Kitaev materials.

Findings

Spin-phonon coupling stabilizes canted zigzag antiferromagnetic state.

It enhances the magnetic field-induced energy gap and suppresses thermal Hall conductivity.

The interaction destabilizes the quantized thermal Hall effect in the spin-liquid state.

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.