Quantitative Comparison of Electrically Induced Spin and Orbital Polarizations in Heavy-Metal/3d-metal Bilayers

Electrical control of magnetization is of crucial importance for integratedspintronics devices. Spin-orbit torques (SOT) in heavy-metal/ferromagneticheterostructures have emerged as promising tool to achieve efficientlycurrent-induced magnetization reversal. However, the microscopic origin of theSOT is being debated,with the spin Hall effect (SHE) due to nonlocal spincurrents and the spin Rashba-Edelstein effect (SREE) due to local spinpolarization at the interface being the primary candidates. We investigate theelectrically induced out-of-equilibrium spin and orbital polarizations in purePt films and in Pt/3d-metal (Co, Ni, Cu) bilayer films using ab initioelectronic structure methods and linear-response theory. We computeatom-resolved response quantities that allow us to identify the inducedspin-polarization contributions that lead to fieldlike SOTs, mostly associatedwith the SREE, and dampinglike (DL) SOTs, mostly associated with the SHE, andcompare their relative magnitude, dependence on the magnetization direction, aswell as their Pt-layer thickness dependence. We find that both the FL and DLcomponents 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 thelatter larger in the Co or Ni layers. Our calculations show that theelectrically-induced transverse orbital polarization is exceedingly larger thanthe induced spin polarization and present even without spin-orbit coupling, incontrast to the spin polarization.