Inverse spin-Hall effect and spin-swapping in spin-split superconductors

Abstract

When a spin-splitting field is introduced to a thin film superconductor, the spin currents polarized along the field couples to energy currents that can only decay via inelastic scattering. We study spin and energy injection into such a superconductor where spin-orbit impurity scattering yields inverse spin-Hall and spin-swapping currents. We show that the combined presence of a spin-splitting field, superconductivity, and inelastic scattering gives rise to a renormalization of the spin-Hall and spin-swap angles. In addition to an enhancement of the ordinary inverse spin-Hall effect, spin-splitting gives rise to unique inverse spin-Hall and spin-swapping signals five orders of magnitude stronger than the ordinary inverse spin-Hall signal. These can be completely controlled by the orientation of the spin-splitting field, resulting in a long-range charge and spin accumulations detectable much further from the injector than in the normal-state. Our results demonstrate that superconductors provide tunable inverse spin-Hall and spin-swapping signals with high detection sensitivity.Comment: 6 + 9 pages, 3 figure