Topological and Chiral Spin Hall Effects

Abstract

This paper presents a theoretical analysis of the spin Hall effect driven by an asymmetrical electron scattering on chiral spin textures. It is demonstrated that in the adiabatic regime the transverse spin current is proportional to the topological charge of the spin texture and does not depend on its size. With the scattering T‐matrix formalism, the reason is clarified for the spin Hall effect to vanish in the weak coupling regime while conserving the charge Hall effect. Adding a spin‐independent term to the scattering potential restores the spin Hall effect. It is shown that in the weak coupling regime the scattering asymmetry vanishes in a half metallic case due to the suppression of spin‐flip scattering. The existence of spin swapping effect for the exchange scattering on chiral spin textures is also demonstrated.