Quantitative comparison of electrically induced spin and orbital polarizations in heavy-metal/3d-metal bilayers

Electrical control of magnetization is of crucial importance for integrated spintronics devices. Spin-orbit torques (SOT) in heavy-metal/ferromagnetic heterostructures have emerged as promising tool to achieve efficiently current-induced magnetization reversal. However, the microscopic origin of the SOT is being debated,with the spin Hall effect (SHE) due to nonlocal spin currents and the spin Rashba-Edelstein effect (SREE) due to local spin polarization at the interface being the primary candidates. We investigate the electrically induced out-of-equilibrium spin and orbital polarizations in pure Pt films and in Pt/3d-metal (Co, Ni, Cu) bilayer films using ab initio electronic structure methods and linear-response theory. We compute atom-resolved response quantities that allow us to identify the induced spin-polarization contributions that lead to fieldlike SOTs, mostly associated with the SREE, and dampinglike (DL) SOTs, mostly associated with the SHE, and compare their relative magnitude, dependence on the magnetization direction, as well as their Pt-layer thickness dependence. We find that both the FL and DL components contribute to the resulting SOT at the Pt/Co and Pt/Ni interfaces, with the former contributions being larger at the Pt interface layer and the latter larger in the Co or Ni layers. Our calculations show that the electrically-induced transverse orbital polarization is exceedingly larger than the induced spin polarization and present even without spin-orbit coupling, in contrast to the spin polarization.