Spin Transport at Interfaces with Spin-Orbit Coupling: Phenomenology
Mark D. Stiles, Vivek P. Amin
Spin transport remains poorly understood in multilayer systems with interfacial spin-orbit coupling. While the important consequences of interfacial spin-orbit scattering can be captured by a spin-dependent Boltzmann nist-equation, currently they cannot be captured by drift- diffusion models, which are the primary tools used for analyzing experiments. Here we present boundary conditions suitable for drift-diffusion models that capture the phenomenology of spin- orbit coupling at interfaces. We compare solutions of the drift-diffusion nist-equations using these boundary conditions to solutions of the spin-dependent Boltzmann nist-equation for a heavy metal/ferromagnet bilayer. We find that these drift-diffusion nist-equations predict spin torques in quantitative agreement with the Boltzmann nist-equation and allow for much simpler interpretation of the results. A key finding is that in-plane electric fields can create spin accumulations and spin currents at interfaces that are polarized in all directions; this finding is a generalization of the Rashba-Edelstein and spin Hall effects. In heavy metal/ferromagnet bilayers, these spin accumulations and spin currents provide mechanisms for the creation of damping-like and field-like torques; they also lead to possible reinterpretations of experiments in which interfacial torques are thought to be suppressed. We reproduce magnetoelectronic circuit theory in the appropriate limit, and discuss the interpretation of experiments involving spin orbit torque, spin pumping and memory loss, the Rashba-Edelstein effect, and the spin Hall magnetoresistance.