Inverse Spin Hall Effect Driven by Spin Motive Force

TL;DR

This paper investigates the inverse spin Hall effect driven by spin motive force in ferromagnetic conductors, revealing how spin-dependent electric fields induce charge currents and how this effect is enhanced by spin polarization.

Contribution

It introduces a theoretical framework for the inverse spin Hall effect driven by spin motive force, including detailed calculations of Hall current density considering spin-orbit interactions.

Findings

Hall current density is proportional to the cross product of local spin direction and spin motive force.

The Hall angle is enhanced by a factor of P^2 compared to the anomalous Hall effect.

Estimated Hall voltage for domain wall oscillation in a ferromagnetic nanowire.

Abstract

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 ${\bm E}_{\rm s}$, 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 ${\bm n}$ is the local spin direction and $\sigma_{\rm SH}$ 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.