Exchange striction induced thermal Hall effect in van der Waals antiferromagnet MnPS$_3$

The thermal Hall effect has emerged as an ideal probe for investigating topological phenomena of charge-neutral excitation. Notably, it reveals crucial aspects of spin-lattice couplings that have been difficult to access for decades. However, the exchange striction mechanism from a lattice-induced change in exchange interaction has often been ignored in thermal Hall experiments. MnPS3 can offer a platform to study exchange striction on the thermal Hall effect due to its significant spin-lattice coupling and field-induced non-collinear spin configuration. Our thermal transport data show distinct temperature and field dependence of longitudinal thermal conductivity ($\kappa_{xx}$) and thermal Hall effect ($\kappa_{xy}$). By using detailed theoretical calculation, we found that the inclusion of the exchange striction is essential for a better description of both $\kappa_{xx}$ and $\kappa_{xy}$. Our result demonstrates the importance of the exchange striction mechanism for a complete understanding of the magnon-phonon-driven thermal Hall effect.