Microscopic theory of magnon-drag electron flow in ferromagnetic metals

A temperature gradient applied to a ferromagnetic metal induces not only independent flows of electrons and magnons but also drag currents because of their mutual interaction. In this paper, we present a microscopic study of the electron flow induced by the drag due to magnons. The analysis is based on the s-d model, which describes conduction electrons and magnons coupled via the s-d exchange interaction. Magnetic impurities are introduced in the electron subsystem as a source of spin relaxation. The obtained magnon-drag electron current is proportional to the entropy of magnons and to alpha - beta (more precisely, to 1 - beta/alpha), where alpha is the Gilbert damping constant and beta is the dissipative spin-transfer torque parameter. This result almost coincides with the previous phenomenological result based on the magnonic spin-motive forces, and consists of spin-transfer and momentum-transfer contributions, but with a slight disagreement in the former. The result is interpreted in terms of the nonequilibrium spin chemical potential generated by nonequilibrium magnons.