Spin Hall frequency doubling and spin memristive effects

It is shown that when a time dependent voltage is applied to a 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 demonstrate that there is a phase shift between applied and transverse voltage oscillations, related to memristive behavior of semiconductor spintronics systems. It is interesting that spin memristive effects in this system are manifested directly in the voltage response. A different method to achieve the second harmonic generation, based on the inverse spin Hall effect, is also discussed.