Effects of spin accumulation in magnetic multilayers

The diffusion equation for the spin accumulation in magnetic multilayers is extended to capture the time-dependent buildup of spin accumulation as well as the influence of an external field and arbitrary magnetization orientations on the spin accumulation. One obtains a consistent formulation for spin accumulation that can explain such important effects as spin injection, spin filtering, and spin transfer on an equal footing. Spin transfer is determined by the amount of spin accumulation at the interfaces whereas spin filtering by the departure from collinear magnetization orientations. The noncollinear magnetization orientations lead to a spatial decay of the spin accumulation in the transverse direction of the multilayer plane. Spin filtering can thus be associated with a new length scale in the transverse direction. Moreover, spin filtering is in correspondence with a biquadratic coupling between layers and changes in the angular dependence of the giant magnetoresistance. What is interesting is that spin filtering is not a prerequisite to spin transfer. Different scenarios for current-induced magnetization reversal are discussed in which, depending largely on the geometry of the magnetic. multilayer, either spin injection or spin transfer will be dominant.