Theory of the spin Hall effect, and its inverse, in a ferromagnetic metal near the Curie temperature

Gu, B.; Ziman, T.*; Maekawa, Sadamichi

We give a theory of the spin Hall effect (SHE) and its inverse in ferromagnetic metals based on skew-scattering via collective spin fluctuations. This extends Kondo's theory of the anomalous Hall effect (AHE) to include short range spin-spin correlations. We find a novel relation between the SHE and the four-spin correlations near the Curie temperature Tc. Such four-spin correlations were defined 50 years ago in Kondo's theory, but do not contribute to the AHE, which relates to the three-spin correlations. Thus our theory shows an essential difference between the AHE and SHE. Our theory can be compared to recent experimental results by Wei et al for the SHE in ferromagnetic alloys.