Microscopic derivation of magnon spin current in a topological insulator/ferromagnet heterostructure

We investigate a spin-electricity conversion effect in a topological insulator/ferromagnet heterostructure. In the spin-momentum-locked surface state, an electric current generates nonequilibrium spin accumulation, which causes a spin-orbit torque that acts on the ferromagnet. When spins in the ferromagnet are completely parallel to the accumulated spin, this spin-orbit torque is zero. In the presence of spin excitations, however, a coupling between magnons and electrons enables us to obtain a nonvanishing torque. In this paper, we consider a model of the heterostructure in which a three-dimensional magnon gas is coupled with a two-dimensional massless Dirac electron system at the interface. We calculate the torque induced by an electric field, which can be interpreted as a magnon spin current, up to the lowest order of the electron-magnon interaction. We derive the expressions for high and low temperatures and estimate the order of magnitude of the induced spin current for realistic materials at room temperature.