Spin Hall effect of alloys: Extrinsic and intrinsic contribution

TL;DR

This paper presents a relativistic theoretical framework for understanding the spin Hall effect in alloys, decomposing it into intrinsic and extrinsic parts, and validates the approach with detailed calculations.

Contribution

It introduces a Kubo-Streda-like formalism for spin Hall conductivity and combines it with KKR-CPA methods to analyze alloy systems, including extrinsic and intrinsic contributions.

Findings

Decomposition of spin Hall conductivity into intrinsic and extrinsic parts.

Validation of the formalism through skew-scattering calculations.

Agreement between Boltzmann and Kubo approaches in dilute alloys.

Abstract

A fully relativistic description of the spin-orbit induced spin Hall effect is presented that is based on Kubo's linear response formalism. Using an appropriate operator for the spin current density a Kubo-St\v{r}eda-like equation for the spin Hall conductivity (SHC) is obtained. An implementation using the Korringa-Kohn-Rostoker (KKR) band structure method in combination with the Coherent Potential Approximation (CPA) allow detailed investigations on various alloy systems. A decomposition of the SHC into intrinsic and extrinsic contributions is suggested. Accompanying calculations for the skew-scattering contribution of the SHC using the Boltzmann equation demonstrate the equivalence to the Kubo formalism in the dilute alloy regime and support the suggested decomposition scheme.