Transport in ferromagnet/superconductor spin valves

We consider charge transport properties in realistic, fabricable, ferromagnet/superconductor spin valves having a layered structure ${F}₁/N/{F}₂/S$, where ${F}₁$ and ${F}₂$ denote the ferromagnets, $S$ the superconductor, and $N$ the normal-metal spacer usually inserted in actual devices. Our calculation is fully self-consistent, as required to ensure that conservation laws are satisfied. We include the effects of scattering at all the interfaces. We obtain results for the device conductance $G$, as a function of bias voltage, for all values of the angle $\ensuremath{\phi}$ between the magnetizations of the ${F}₁$ and ${F}₂$ layers and a range of realistic values for the material and geometrical parameters in the sample. We discuss, in the context of our results for $G$, the relative influence of all parameters on the spin valve properties. We also study the spin current and the corresponding spin-transfer torque in ${F}₁/{F}₂/S$ structures.