Spin-Transfer Torque and Magnetoresistance in Superconducting Spin-Valves

TL;DR

This paper investigates how spin-transfer torque and magnetoresistance in ferromagnet-superconductor-ferromagnet spin-valves are affected by superconducting symmetry, interface states, and layer dimensions, revealing enhanced effects with topological zero-energy states.

Contribution

It introduces a comprehensive analysis of spin-transfer torque and magnetoresistance considering arbitrary magnetization angles, superconducting symmetries, and interface states, highlighting the role of zero-energy states in transport properties.

Findings

Torque and magnetoresistance are enhanced by topological zero-energy states.

Magnetoresistance exhibits oscillatory behavior as a function of layer thickness.

Zero-energy state contributions diminish as layer thickness increases.

Abstract

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 $d_S/\xi$ where $d_S$ and $\xi$ 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 $d_S\sim 2\xi$ to layers of size $d_S\gg 2\xi$, where the contribution to transport from zero-energy states gradually vanishes.