Spin Hall effect in 3d ferromagnetic metals for field-free switching of perpendicular magnetization: A first-principles investigation

Ferromagnetic metals, with the potential to generate spin current with unconventional spin polarization via the spin Hall effect, offer promising opportunities for field-free switching of perpendicular magnetization and for the spin-orbit torque devices. In this study, we investigate two distinct spin Hall mechanisms in 3d ferromagnetic metals including spin-orbit coupling driven spin Hall effect in Fe, Co, Ni and their alloys, and non-relativistic spin Hall effect arising from anisotropic spin-polarized transport by taking L10-MnAl as an example. By employing first-principles calculations, we examine the temperature and alloy composition dependence of spin Hall conductivity in Fe, Co, Ni and their alloys. Our results reveal that the spin Hall conductivities with out-of-plane spin polarization in 3d ferromagnetic metals are at the order of 1000 \frac{\hbar}{2e} \left( \Omega \, \text{cm} \right)^{-1} at 300 K, but with a relatively low spin Hall angles around 0.01~0.02 due to the large longitudinal conductivity. For L10-MnAl(101), the non-relativistic spin Hall conductivity can reach up to 10000\frac{\hbar}{2e} \left( \Omega \, \text{cm} \right)^{-1}, with a giant spin Hall angle around 0.25 at room temperature. By analyzing the magnetization switching process, we demonstrate deterministic switching of perpendicular magnetization without an external magnetic field by using 3d ferromagnetic metals as spin current sources. Our work may provide an unambiguous understanding on spin Hall effect in ferromagnetic metals and pave the way for their potential applications in related spintronic devices.