Spin transport at interfaces with spin-orbit coupling: Phenomenology

This paper presents the boundary conditions needed for drift-diffusion models to treat interfaces with spin-orbit coupling. Using these boundary conditions for heavy-metal/ferromagnet bilayers, solutions of the drift-diffusion equations agree with solutions of the spin-dependent Boltzmann equation and allow for a much simpler interpretation of the results. A key feature of these boundary conditions is their ability to capture the role that in-plane electric fields have in the generation of spin currents that flow perpendicularly to the interface. The generation of these spin currents is a direct consequence of the effect of interfacial spin-orbit coupling on interfacial scattering. In heavy-metal/ferromagnet bilayers, these spin currents provide an important mechanism for the creation of dampinglike and fieldlike torques; they also lead to possible reinterpretations of experiments in which interfacial contributions to spin torques are thought to be suppressed.