The theory of nonlinear magnon spin current induced by the electric field

The magnon spin current is attracting much attention from the viewpoint of the spintronics. Unlike electrons, usually magnons do not couple with the electric field. Therefore, most of previous studies considered the magnon spin current induced by the thermal gradient or magnetic field. However, spin systems with a broken inversion symmetry supports magnetic excitations accompanying electric polarization, known as electro-magnons. Here, we consider the nonlinear magnon spin current induced by the electric field in broken inversion symmetry systems. Focusing on the dc spin current responses, we derive the formula for "the magnon spin shift current" induced by the linearly polarized light and "the spin injection current" induced by the circularly polarized light, in an analogous way to electronic nonlinear current responses. The magnon spin shift current does not depend on the relaxation time of the magnon, while the injection current is proportional to the relaxation time which we expect exhibits large responses for a long magnon lifetime. Furthermore, we clarify the relation between the magnon spin shift current and the topology of the magnon band. In addition, we demonstrate the magnon spin shift current and injection current numerically based on a few toy models and realistic models for multiferroics.