Layer by layer approach to transport in noncollinear magnetic structures

By now a common method to solve for transport phenomena in a multilayered structure is to solve the equations of motion in each layer and use boundary conditions to match the solutions across interfaces. This has worked quite well for magnetic multilayers as long as the magnetic layers are collinear, however, when they are noncollinear one has to introduce an artifice to account for correlations between states in different layers that are left out in the layer by layer approach. We have calculated the steady state transport properties, i.e., the charge and spin currents, spin torque, and resistance, as a function of the angle between two magnetic layers separated by a normal (nonmagnetic) spacer, by using the Boltzmann equations of motion for spin transport in the layers and by including current induced spin flip scattering at interfaces (the artifice). We compare our results to those found when one does not include the artifice at the interfaces, and find they agree only at times before which the current driven spin accumulation in the spacer layer has been able to couple the scattering at its interfaces with the magnetic layers.