Flux flow spin Hall effect in type-II superconductors with spin-splitting field

We predict the very large spin Hall efect in type-II superconductors whose mechanism is drastically diferent from the previously known ones. We fnd that in the fux-fow regime the spin is transported by the spin-polarized Abrikosov vortices moving under the action of the Lorenz force in the direction perpendicular to the applied electric current. Due to the large vortex velocities the spin Hall angle can be of the order of unity in realistic systems based on the high-feld superconductors, superconductor/ ferromagnet hybrid structures or the recently developed superconductor/ferromagnetic insulator proximity structures. We propose the realization of high-frequency pure spin current generator based on the periodic structure of moving vortex lattices. We fnd the patterns of charge imbalance and spin accumulation generated by moving vortices, which can be used for the electrical detection of individual vortex motion. The new mechanism of inverse fux-fow spin Hall efect is found based on the driving force acting on the vortices in the presence of injected spin current which results in the generation of transverse voltage.