Wannier interpolation of spin accumulation coefficient

Abstract: The spin Hall (SH) effect is widely understood as a phenomoenon in which spin current flows perpendicular to an electric field. In the presence of a spin-orbit coupling, however, spin current is ambiguous, and the SH conductivity depends on the definition of spin current. In this article, we develop an \textit{ab initio} computational scheme for the spin accumulation coefficient, which characterizes the spin accumulation and would be an alternative indicator of the SH effect. The proposed method has been implemented into an open-source software Wannier90 and serves high-precision \textit{ab initio} research on the SH effect.