Spin transport in half-metallic ferromagnets

We theoretically investigate spin transport in half-metallic ferromagnets at finite temperatures. The side-jump and skew-scattering contributions to spin Hall conductivity are derived using the Kubo formula. The electron-magnon interaction causes a finite density of states in the energy gap of the minority-spin band and induces spin Hall conductivity. We show that spin Hall conductivity is proportional to $T^{3/2}$, with $T$ being temperature and is sensitive to $T$. We propose that spin Hall conductivity may be a tool to study the minority-spin state.