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

We give a theory of the inverse spin Hall effect (ISHE) 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 relation between the ISHE and the four-spin correlations near the Curie temperature T-C. Such four-spin correlations do not contribute to the AHE, which relates to the three-spin correlations. Thus our theory shows an essential difference between the AHE and ISHE, providing an essential complement to Kondo's classic theory of the AHE in metals. We note the relation to skew-scattering mechanisms based on impurity scattering. Our theory can be compared to recent experimental results by Wei et al. [Nat. Commun. 3, 1058 (2012)] for the ISHE in ferromagnetic alloys. DOI: 10.1103/PhysRevB.86.241303