Inverse Spin Hall Effect Driven by Spin Motive Force

The spin Hall effect is a phenomenon in which 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 Eₛ, 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 sigmaSHn x Eₛ, where n is the local spin direction and sigmaSH 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.