Thermal Hall effect, spin Nernst effect, and spin density induced by thermal gradient in collinear ferrimagnets from magnon-phonon interaction

We study the thermal Hall and spin Nernst effect in collinear ferrimagnets on a honeycomb lattice with broken inversion symmetry between the nearest neighbors. The broken inversion symmetry allows nearest-neighbor inplane Dzyaloshinskii-Moriya interaction, which has no effect in the linear spin wave theory. However, it induces large Berry curvature in the magnetoelastic excitation spectrum through the magnon-phonon interaction (MPI) to produce spin-polarized thermal Hall current, so that both spin Nernst and thermal Hall currents are produced. Because the MPI does not conserve the spin, we also compute the boundary spin accumulation. Surprisingly, we do not find any asymmetric boundary spin accumulation, which we attribute to spin nonconservation. However, the MPI induces non-vanishing total spin expectation value in the system with armchair edges.