First Principles Approach to Phonon Thermal Hall Effect in α-RuCl₃

We apply a recently developed first-principles based approach for treating generic spin-phonon couplings in materials with strong spin-orbit coupling to study α-RuCl₃. 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 κ_xy without requiring a field-induced spin liquid.