Conditions for the generation of spin and charge currents in bulk spin Hall devices

We investigate the out-of-equilibrium stationary states of spin Hall devices on the basis of the least dissipation principle in the two-spin-channel model. The variational technique allows the values of the free parameters of the Hall device to be derived. The free parameters are the chemical potentials, the transverse Hall currents and the charge accumulations in the two spin channels. We show that, for a bulk paramagnet with spin-orbit interaction, in the case of the Hall bar geometry the principle of minimum dissipated power prevents the generation of transverse spin and charge currents, while in the case of the Corbino disk geometry, transverse currents, can be produced. More generally, we show that electric charge accumulation prevents the stationary spin to charge current conversion from occurring inside the device.