Half-Metallic Superconducting Triplet Spin MultiValves

We study spin switching effects in finite-size superconducting multivalve structures. We examine $\rm F_1F_2SF_3$ and $\rm F_1F_2SF_3F_4$ hybrids where a singlet superconductor ($\rm S$) layer is sandwiched among ferromagnet ($\rm F$) layers with differing thicknesses and magnetization orientations. Our results reveal a considerable number of experimentally viable spin valve configurations that lead to on-off switching of the superconducting state. For $\rm S$ widths on the order of the superconducting coherence length $\xi_0$, non-collinear magnetization orientations in adjacent $\rm F$ layers with multiple spin-axes leads to a rich variety of triplet spin-valve effects. Motivated by recent experiments, we focus on samples where magnetizations in the $\rm F_1$ and $\rm F_4$ layers exist in a fully spin-polarized half metallic phase, and calculate the superconducting transition temperature, spatially and energy resolved density of states, and the spin-singlet and spin-triplet superconducting correlations. Our findings demonstrate that superconductivity in these devices can be completely switched on or off over a wide range of magnetization misalignment angles due to the generation of equal-spin and opposite-spin triplet pairings.