Electrical probing of the spin conductance of mesoscopic cavities

We investigate spin-dependent transport in multiterminal mesoscopic cavities with spin-orbit coupling. Focusing on a three-terminal set-up we show how injecting a pure spin current or a polarized current from one terminal generates additional charge current and/or voltage across the two output terminals. When the injected current is a pure spin current, a single measurement allows us to extract the spin conductance of the cavity. The situation is more complicated for a polarized injected current, and we show in this case how two purely electrical measurements on the output currents give the amount of current that is solely due to spin-orbit interaction. This allows us to extract the spin conductance of the device in this case as well. We use random matrix theory to show that the spin conductance of chaotic ballistic cavities fluctuates universally about zero mesoscopic average and describe experimental implementations of mesoscopic spin to charge current converters.