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

We theoretically study the intrinsic thermal Hall and spin Nernst effect in collinear ferrimagnets on a honeycomb lattice with broken inversion symmetry. The broken inversion symmetry allows in-plane Dzyaloshinskii-Moriya interaction between the nearest neighbors, which does not affect the magnon spectrum in the linear spin wave theory. However, the Dzyaloshinskii-Moriya interaction can induce large Berry curvature in the magnetoelastic excitation spectrum through the magnon-phonon interaction to produce thermal Hall current. Furthermore, we find that the magnetoelastic excitations transport spin, which is inherited from the magnon bands. Therefore, the thermal Hall current is accompanied by spin Nernst current. Because the magnon-phonon interaction does not conserve the spin, we also study the spin density induced by thermal gradient in the presence of magnon-phonon interaction. We find that the intrinsic part of the spin density shows no asymmetric spin accumulation near the boundary of the system having a stripe geometry. However, because of the magnon-phonon interaction, we find nonzero total spin density in the system having armchair edges. The extrinsic part of the spin density, on the other hand, shows asymmetric spin accumulation near the boundary for both armchair and zigzag edges because of the magnon-phonon interaction. In addition, we find nonzero total spin density in the system having zigzag edge.