Topological magnetoelastic excitations in noncollinear antiferromagnets

We study the topological property of the magnetoelastic excitation in noncollinear antiferromagnets. As a toy model, we consider the magnon-phonon coupling in a triangular antiferromagnet with a 120 degrees Neel 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 anticrossing 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.