Spin Transport at Interfaces with Spin-Orbit Coupling: Phenomenology

V. P. Amin, M. D. Stiles

Published 2016-04-21Version 1

Spin transport remains poorly understood in multilayer systems with interfacial spin-orbit coupling. While the important consequences of interfacial spin-orbit coupling can be captured by a spin-dependent Boltzmann 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 torques at interfaces. We compare solutions of the drift-diffusion equations using these boundary conditions to solutions of the spin-dependent Boltzmann equation for a heavy metal/ferromagnet bilayer. We find that the drift-diffusion equations predict spin torques in quantitative agreement with the 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 scattering that carriers experience while flowing along an interface. In the presence of interfacial spin-orbit coupling, this scattering generates spin currents that flow away from the interface. In heavy metal/ferromagnet bilayers, these spin currents provide an important mechanism for the creation of damping-like and field-like torques; they also lead to possible reinterpretations of experiments in which interfacial contributions to spin torques are thought to be suppressed.