Time dependence of spin accumulation and magnetoresistance in magnetic multilayers

We derive and solve the equations that determine the time dependence of the spin accumulation attendant to driving a current across a magnetic multilayer, The time scales with the spin-flip relaxation time for the multilayer, which is of the order of picoseconds. As this is much shorter than the time it takes for current-induced switching of magnetic layers, the lack of spin accumulation does not seem to be a factor for the long switching times recently observed.