Spin-Hall effects: from the two-channel model to the Dyakonov-Perel equations

摘要

The transport equations including spin-Hall effect and inverted spin-Hall effect are re-derived in the framework the Mesoscopic Non-Equilibrium Thermodynamic theory (MNET), on the basis of the Onsager reciprocity relations. It is shown that the two channel model is able to describe the spin-accumulation in all generality, including spin-dependent anisotropic magnetoresistance and spin-dependent Hall effect. In the case of non-ferromagnetic samples (zero conductivity asymmetry and zero anisotropic conductivity), the Dyakonov - Perel equations are recovered providing that only the density of electric charges is spin-dependent. Furthermore, it is shown that, according to the minimum entropy production theorem, the spin-dependent Hall voltage measured should correspond to zero pure spin-current for stationary states.