Theory of the spin Hall effect in ferromagnetic metals; Nonlinear behaviors around the Curie temperature

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

We give a theory of the spin Hall effect in ferromagnetic metals near the Curie temperature. We do this by extending Kondo's theory of the anomalous Hall effect in ferromagnetic metals to include the short range spin-spin correlations. We find a novel relation between the spin Hall effect and a second order nonlinear spin fluctuation in ferromagnetic metals near Curie temperature Tc. In 1962 Kondo gave a relation between the anomalous Hall effect and the first order nonlinear spin fluctuation in pure ferromagnetic metals near Tc. Thus our results show an essential difference between the anomalous and spin Hall effects in terms of the nonlinear spin correlations that are probed. Our theory can be compared to experiments in ferromagnetic alloys near Tc by Y. Otani et al.