Inverse Spin Hall Effect Driven by Spin Motive Force

The spin Hall effect is a phenomenon that an electric field induces a spin Hall current. In this Letter, we examine the inverse effect that, in a ferromagnetic conductor, a charge Hall current is induced by a spin motive force, or a spin-dependent effective ` electric’ field ${\mathit{E}}_{\mathrm{s}}$, arising from the time variation of magnetization texture. By considering skew-scattering and side-jump processes due to spin-orbit interaction at impurities, we obtain the Hall current density as $\sigma_{\rm SH} {\bm n}\times{\bm E}{\rm s}$,where${\bm n}$isthelocalspindirectionand$\sigma{\rm SH}$ is the spin Hall conductivity. The Hall angle due to the spin motive force is enhanced by a factor of $P^2$ compared to the conventional anomalous Hall effect due to the ordinary electric field, where $P$ is the spin polarization of the current. The Hall voltage is estimated for a field-driven domain wall oscillation in a ferromagnetic nanowire.