Anatomy of spin Hall effect in ferromagnetic metals

Abstract: The spin Hall effect in nonmagnetic materials has been intensively studied and became one of the most crucial spin-charge conversion mechanism in spintronics. However, the spin Hall effect in ferromagnetic metals has been less investigated and remains unclear. In this work, we investigate the spin Hall effect in representative ferromagnetic alloy by using first-principles calculations. We first clarify the spin Hall effect into three different types including conventional (CSHE), spin anomalous (SAHE) and magnetic spin Hall effect (MSHE) and then calculate the corresponding spin Hall conductivity and spin Hall angle for (Fe, Co, Ni)Pt, NiFe and CoFe alloy. We find the above three spin Hall mechanisms do coexist in ferromagnetic metals. Particularly, for Pt-based ferromagnetic alloy, a sizable conventional and magnetic spin Hall angles comparable to that of Pt have been predicted. The remarkable unconventional spin Hall effect in ferromagnetic metal may enrich the spin-charge conversion phenomena. For instance, the spin current generated by remarkable MSHE with out-of-plane spin-polarization should be helpful for field-free switching of perpendicular magnetization through spin-orbit torque effect. This work may stimulate future studies on the spin Hall effect in ferromagnetic metals and pave their promising applications for spin-charge conversion devices in spintronics.