Effect of the spin-orbit interaction at insulator/ferromagnet interfaces on spin-orbit torques

We theoretically investigate spin-orbit torques in insulator/ferromagnet/normal-metal structures with a focus on interfacial spin-orbit coupling effect at an insulator/ferromagnet interface. Based on the spin drift-diffusion formalism generalized to consider transverse spin currents in a ferromagnet and the boundary condition to consider transverse spin currents leaving from a ferromagnet, we find that interfacial spin-orbit coupling at the insulator/ferromagnet interface contributes to dampinglike spin-orbit torque, which is important for current-driven magnetization dynamics, even when the interfacial spin-orbit coupling generates the only fieldlike component. We also calculate spin-orbit torques in a single ferromagnet sandwiched by two dissimilar insulators, which provides additional information about interfacial spin-orbit interaction at insulator/ferromagnet interfaces.