Theory of the bipolar spin switch

We extend the Valet-Pert model of the perpendicular magnetoresistance in magnetic multilayers to describe the spin accumulation and relaxation effects in the spin switch structure introduced by Johnson and calculate the output voltage of the device. In contrast to the usual treatment by Johnson, we take into account the spin relaxation in the ferromagnetic layers, and also the influence of interface resistances and interface spin flips. We show that, for thin nonmagnetic layers, the output voltage is limited by the spin relaxation in the ferromagnetic layers. We find that the interpretation of the experimental data requires surprisingly long spin diffusion lengths in both the magnetic and nonmagnetic layers, much longer than those derived from perpendicular magnetoresistance in multilayers of similar materials.