Phonon thermal Hall effect in Mott insulators via skew-scattering by the scalar spin chirality

Thermal transport is a crucial probe for studying excitations in insulators. In Mott insulators, the primary candidates for heat carriers are spins and phonons, and which dominates the thermal conductivity is a persistent issue. Typically, phonons dominate the longitudinal thermal conductivity while the thermal Hall effect (THE) is primarily associated with spins, which requires time-reversal symmetry breaking. The coupling between phonons and spins usually depends on spin-orbit interaction and is relatively weak. Here, we propose a new mechanism for this coupling and the associated THE: the skew scattering of phonons via spin fluctuations by the scalar spin chirality. This coupling does not require spin-orbit interaction and is ubiquitous in Mott insulators, leading to a thermal Hall angle on the order of $10^{-3}$ to $10^{-2}$. Based on this mechanism, we investigate the THE in YMnO$_3$ with a trimerized triangular lattice where the THE beyond spins was recognized, and predict the THE in the Kagome and square lattices.