Current and spin torque in double tunnel barrier ferromagnet-superconductor-ferromagnet systems

We calculate the current and spin torque in small symmetric double tunnel barrier ferromagnet-superconductor-ferromagnet (F-S-F) systems. Spin accumulation in the superconductor governs the transport properties when the spin-flip relaxation time is longer than the transport dwell time. In the elastic transport regime, it is demonstrated that the relative change in the current (spin torque) for F-S-F systems equals the relative change in the current (spin torque) for F-N-F systems upon changing the relative magnetization direction of the two ferromagnets. This differs from the results in the inelastic transport regime where spin accumulation suppresses the superconducting gap and dramatically changes the magnetoresistance [S. Takahashi, H. Imamura, and S. Maekawa, Phys. Rev. Lett. 82, 3911 (1999)]. The experimental relevance of the elastic and inelastic transport regimes, respectively, as well as the reasons for the change in the transport properties are discussed.