Spin-Transfer Torque and Magnetoresistance in Superconducting Spin-Valves

We study the spin-transfer torque and magnetoresistance of a ferromagnet$\mid$superconductor$\mid$ferromagnet spin-valve, allowing for an arbitrary magnetization misorientation and treating both s-wave and d-wave symmetries of the superconductor. We take fully into account Andreev reflection and also the spin-triplet correlations that are generated when the magnetizations are non-collinear. It is found that the torque and magnetoresistance are both strongly enhanced when topological zero-energy states are present at the interfaces, which is the case for d-wave superconductors with a crystallographic orientation of [110] relative to the interface ($d_{xy}$-wave symmetry). Moreover, we find that the magnetoresistance displays a strong oscillatory and non-monotonous behavior as a function of $d_S/ξ$ where $d_S$ and $ξ$ are the interlayer width of the superconducting region and the superconducting coherence length, respectively. This feature is also attributed to the crossover from layers of size $d_S\sim 2ξ$ to layers of size $d_S\gg 2ξ$, where the contribution to transport from zero-energy states gradually vanishes.

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