Theory of Intrinsic Phonon Thermal Hall Effect in $\alpha$-RuCl$_3$

TL;DR

This paper investigates how spin-phonon interactions, enhanced by spin-orbit coupling, can produce a phonon thermal Hall effect in $ ext{α-RuCl}_3$, aligning with experimental observations without invoking a spin liquid state.

Contribution

It introduces a first-principles approach to analyze spin-phonon couplings in $ ext{α-RuCl}_3$ and demonstrates how spin-orbit coupling induces chirality leading to a phonon thermal Hall effect.

Findings

Spin-orbit coupling enriches spin-phonon interactions with chirality.

Chiral spin-phonon interactions generate finite phonon Berry curvatures.

The model reproduces the field dependence of $rac{xy}$ observed experimentally.

Abstract

We apply a recently developed first-principles based approach for treating generic spin-phonon couplings in materials with strong spin-orbit coupling to study $\alpha$-RuCl$_3$. Of particular focus is the potential for this material to exhibit a phonon thermal Hall effect induced by spin-phonon interactions. We find that spin-orbit coupling significantly enriches the form of these interactions, and imbues them with chirality that is conducive to generating finite phonon Berry curvatures. We show that this leads to a phonon thermal Hall effect that qualitatively reproduces the measured field dependence of $\kappa_{xy}$ without requiring a field-induced spin liquid.