Theoretical Study of Extrinsic Spin-current Generation in Ferromagnets Induced by Anisotropic Spin-flip Scattering

TL;DR

This paper presents a theoretical analysis of an extrinsic spin-current generation mechanism in ferromagnets, arising from anisotropic spin-flip scattering influenced by spin-orbit interaction and orbital hybridization.

Contribution

It introduces a new extrinsic mechanism for spin-current generation in ferromagnets based on anisotropic spin-flip scattering, expanding understanding of spin Hall effects.

Findings

Identified a novel extrinsic mechanism involving anisotropic spin-flip scattering.

Demonstrated the mechanism's validity under cubic or tetragonal crystal symmetry.

Linked the mechanism to orbital-dependent hybridization and spin-orbit interaction.

Abstract

The spin Hall effect (SHE) and the magnetic spin Hall effect (MSHE) are responsible for electrical spin current generation, which is a key concept of modern spintronics. We theoretically investigated the spin conductivity induced by spin-dependent s-d scattering in a ferromagnetic 3d alloy model by employing microscopic transport theory based on the Kubo formula. We derived a novel extrinsic mechanism that contributes to both the SHE and MSHE. This mechanism can be understood as the contribution from anisotropic (spatial-dependent) spin-flip scattering due to the combination of the orbital-dependent anisotropic shape of s-d hybridization and spin flipping, with the orbital shift caused by spin-orbit interaction with the d-orbitals. We also show that this mechanism is valid under crystal-field splitting among the d-orbitals in either the cubic or tetragonal symmetry.