Spin injection and magnetoresistance in ferromagnet/superconductor/ferromagnet tunnel junctions

We theoretically study the spin-dependent transport in a ferromagnet/superconductor/ferro-magnet double barrier tunnel junction. The spin-polarized tunneling currents give rise to spin imbalance in the superconductor. The resulting nonequilibrium spin density suppresses the superconductivity with increase of the tunneling currents. We focus on the effect of asymmetry in the double tunnel junction, where the barrier height of the tunnel junction and the spin-polarization of the ferromagnets are different, on spin injection, and discuss how the superconductivity is suppressed in the asymmetric junction. Our results explain recent experimental results on the critical current suppression in high-$T_c$ SCs by spin injection.