  We study the topological property of the magnetoelastic excitation in
non-collinear antiferromagnets. As a toy model, we consider the magnon-phonon
coupling in a triangular antiferromagnet with a $120^\circ$ N\`eel order. We
find that in the presence of out-of-plane external magnetic field, the
magnon-polaron bands, which arise from hybridization of magnons and phonons,
can carry Chern number, even though the individual magnon and phonon bands are
topologically trivial. Large Berry curvature is induced from the anti-crossing
regions between the magnon and phonon bands, which renormalizes the thermal
Hall conductivity of phonon bands. To compute the Berry curvature and Chern
number of magnon-polarons, we give a simple algorithm to diagonalize
magnetoelastic Hamiltonian without diagonalizing the phonon Hamiltonian, by
mapping the problem to the diagonalization of bosonic Bogoliubov-de-Gennes
(BdG) Hamiltonian. This is necessary because the contribution to the Berry
curvature from phonon cannot be properly captured if we compute the Berry
curvature from magnetoelastic Hamiltonian whose phonon sector has been already
diagonalized.

Mesoscale and Nanoscale Physics