In-plane magnetization effect on current-induced spin-orbit torque in a ferromagnet/topological insulator bilayer with hexagonal warping

Abstract

Current-induced spin polarization and the resulting spin-orbit torque (SOT) in a ferromagnet/topological insulator (FM/TI) bilayer have been investigated by taking into account the hexagonal warping spectrum of topological surface states. We find that the usually ignored in-plane FM magnetization plays an important role to the spin polarization. The resulting spin polarization and spin torque significantly depend on azimuthal angle of the magnetization, which has not been reported theoretically before in the linear dispersion TI model. These interesting results arise from the combination effect of in-plane magnetization and warping effect by modifying the Berry curvature and impurity scattering. Based on Matsubara-Green function approach, we derive the formula of SOT and analyze the results analytically and numerically, including the contribution from intrabands and interbands, and intrinsic and extrinsic contribution. More importantly, it is found that the hexagonal warping can prominently enhance the antidamping SOT if there exists the in-plane FM magnetization, which provides a new perspective to understand the recent giant SOT effect.