Magnons, Phonons, and Thermal Hall Effect in Candidate Kitaev Magnet $\alpha$-RuCl$_3$

TL;DR

This study investigates the thermal Hall effect in $ ext{RuCl}_3$, showing that magnon and phonon Berry curvatures contribute but are insufficient alone, and that extrinsic phonon mechanisms are necessary to match experimental observations.

Contribution

The paper demonstrates that a minimal spin model explains the thermal Hall effect qualitatively, and introduces a phenomenological ratio to account for extrinsic phonon contributions, aligning theory with experiments.

Findings

Magnons' Berry curvature contributes to thermal Hall effect.

Phonons coupled to spins acquire chirality, influencing the effect.

Extrinsic phonon mechanisms are essential to match experimental magnitude.

Abstract

We study the nature of the debated thermal Hall effect in the candidate Kitaev material $\alpha$-RuCl$_3$. Without assuming the existence of a gapped spin liquid, we show that a realistic minimal spin model in the canted zigzag phase suffices, at the level of linear spin-wave theory, to qualitatively explain the observed temperature and magnetic field dependence of the non-quantized thermal Hall conductivity $\kappa_{xy}$, with its origin lying in the Berry curvature of the magnon bands. The magnitude of the effect is however too small compared to the measurement by Czajka et al. [Nat. Mater. 22, 36-41 (2023)], even after scanning a broad range of model parameters so as to maximize $\kappa_{xy}/T$. Recent experiments suggest that phonons play an important role, which we show couple to the spins, endowing phonons with chirality. The resulting intrinsic contribution, from both magnons and phonons, is however still insufficient to explain the observed magnitude of the Hall signal. After careful analysis of the extrinsic phonon mechanisms, we use the recent experimental data on thermal transport in $\alpha$-RuCl$_3$ by Lefran\c{c}ois et al. [Phys. Rev. X 12, 021025 (2022)] to determine the phenomenological ratio of the extrinsic and intrinsic contributions $\eta\equiv \kappa_{xy}^{E}/\kappa_{xy}^{I}$. We find $\eta=1.2\pm 0.5$, which when combined with our computed intrinsic value, explains quantitavely both the magnitude and detailed temperature dependence of the experimental thermal Hall effect in $\alpha$-RuCl$_3$.