First principles approach to phonon thermal Hall effect

We have recently developed first-principles based approach for treating generic spin-phonon interactions in materials with strong spin-orbit coupling (SOC). This allows for estimation of various terms relevant to the phonon thermal Hall effect, acoustic Faraday effect, ultrasound attenuation, and magnon-phonon hybridization. In the example material alpha-RuCl3, we find that SOC significantly enriches the form of these interactions, and imbues them with chirality that is conducive to generating finite phonon Berry curvatures through coupling of phonons and spins. 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. With these tools, we aim to address the thermal Hall effect in magnetic insulators in a material-specific way, identifying potentially key phononic contributions, and their microscopic origin.