Spin Hall response at finite wave vector in ferromagnets

TL;DR

This paper theoretically investigates the spin Hall effect at finite wave vectors in ferromagnetic conductors, revealing a broad response region and confirming the local nature of spin-charge conversion effects.

Contribution

It provides a theoretical analysis of the spin Hall response at finite wave vectors considering different spin-orbit interactions in ferromagnets.

Findings

Spin Hall effect has a broad response for wave vector q less than approximately 2 times the Fermi wave vector.

The results confirm the local nature of spin-charge conversion effects.

The study considers both impurity-induced and localized Rashba spin-orbit interactions.

Abstract

Spin Hall effect at finite wave vector in a ferromagnetic conductor is theoretically studied by calculating the spin density as the linear response to an applied electric field. The cases of a spin-orbit interaction due to random impurities and a localized Rashba interaction are considered. It is shown that the spin Hall effect has a broad response for the wave vector $q\lesssim 2\kf$ where $\kf $ is the Fermi wave vector. This fact confirms the local nature of the spin-charge conversion effects.