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 femtoseconds; this is considerably faster than the time to establish the longitudinal component of the spin current.

• Received 30 November 2004

DOI:https://doi.org/10.1103/PhysRevB.71.184417