Time-dependent spin diffusion in noncollinear magnetic multilayers

We solve the time-dependent spin diffusion equation for spin transport across two noncollinear magnetic layers, While the spin current is discontinuous at the interface at t=0, it is continuous in the steady state. The characteristic time scale to establish the component of the spin current transverse to the magnetization is on the order of femoseconds; this is considerably faster than the time to establish the longitudinal component of the spin current.