Equations-of-motion approach of spin-motive force

Yamane, Yuta; Ieda, Junichi   ; Oe, Junichiro; Barnes, S. E.*; Maekawa, Sadamichi

Here, we formulate a quantitative theory of the spin-motive force by studying an equation of motion of an electron, which enables us to gain better understanding of its origin. In ferromagnetic metals, the electron spin prefers to be parallel with local magnetization because of the exchange coupling. We show, however, when the magnetization dynamics depends both on time and space, there arises a misalignment between them. We find that the misalignment causes a spin dependent force, which accelerates the electrons in a direction in which the exchange energy is lower. We obtain the general formula of the spin-motive force, and show the results of numerical simulations in a variety of ferromagnetic nanostructures.