Frequency doubling and memory effects in the spin Hall effect

We predict that when an alternating voltage is applied to a semiconducting system with inhomogeneous electron density in the direction perpendicular to main current flow, the spin Hall effect results in a transverse voltage containing a double-frequency component. We also demonstrate that there is a phase shift between applied and transverse-voltage oscillations, related to the general memristive behavior of semiconductor spintronic systems. A different method to achieve frequency doubling based on the inverse spin Hall effect is also discussed.