  We propose a new mechanism for the thermal Hall effect in exchange spin-wave
systems, which is induced by the magnon-phonon interaction. Using symmetry
arguments, we first show that this effect is quite general, and exists whenever
the mirror symmetry in the direction of the magnetization is broken. We then
demonstrate our result in a collinear ferromagnet on a square lattice, with
perpendicular easy-axis anisotropy and Dzyaloshinskii-Moriya interaction from
mirror symmetry breaking. We show that the thermal Hall conductivity is
controlled by the resonant contribution from the anti-crossing points between
the magnon and phonon branches, and estimate its size to be comparable to that
of the magnon mediated thermal Hall effect.
