Nonperturbative approach to interfacial spin-orbit torques induced by the Rashba effect

Abstract

Current-induced spin-orbit torque (SOT) in normal metal/ferromagnet (NM/FM) bilayers bears great promise for technological applications, but the microscopic origin of purely interfacial SOTs in ultra-thin systems is not yet fully understood. Here, we show that a linear response theory with a nonperturbative treatment of spin-dependent interactions and impurity scattering potential predicts damping-like SOTs that are strictly absent in perturbative approaches. The technique is applied to a two-dimensional Rashba-coupled ferromagnet (the paradigmatic model of a NM/FM interface), where higher-order scattering processes encoding skew scattering from nonmagnetic impurities allow for current-induced spin polarization with nonzero components along all spatial directions. This is in stark contrast to previous results of perturbative methods (neglecting skew scattering), which predict a coplanar spin-polarization locked perpendicular to the charge current as a result of conventional Rashba-Edelstein effect. Furthermore, the angular dependence of ensuing SOTs and their dependence upon the scattering potential strength is analysed numerically. Simple analytic expressions for the spin-density--charge-current response function, and related SOT efficiencies, are obtained in the weak scattering limit. We find that the extrinsic damping-like torques driven by impurity scattering reaches efficiencies of up to 7% of the field-like (Rashba-Edelstein) torque. Our microscopic theory shows that bulk phenomena, such as the spin Hall effect, are not a necessity in the generation of the damping-like SOTs of the type observed in experiments on ultra-thin systems.