Supplemental Material to "A first-principles linear response description of the spin Nernst effect"

A first-principles description of the spin Nernst effect, denoting the occurrence of a transverse spin current due to a temperature gradient, is presented. The approach, based on an extension to the Kubo-Streda equation for spin transport, supplies in particular the formal basis for investigations of diluted as well as concentrated alloys. Results for corresponding applications to the alloy system Au-Cu give the intrinsic and extrinsic contributions to the relevant transport coefficients. Using scaling laws allows in addition to split the extrinsic contribution into its skew scattering and side-jump parts.