Calculation of magnon drag force induced by an electric current in ferromagnetic metals

Magnon drag effect induced by an applied electric field in ferromagnetic metals is theoretically studied by a microscopic calculation of the force on magnons arising from magnon emission/absorption and scattering due to driven electrons. It is shown that magnon scattering contribution dominates over the emission/absorption one in a wide temperature regime in good metals with long elastic lifetime $\text{taue}$, as the latter has a relative suppression factor of $(\text{Deltasd}\text{taue}{)}^{-2}$ due to the electron spin flip by the magnon, where $\text{Deltasd}$ is the $sd$ exchange interaction energy. Spin-transfer efficiency is discussed including the magnon drag effect.