Conversion efficiency of spin power to charge power in a normal metal with spin-orbit coupling

We theoretically investigate the conversion efficiency of spin power to charge power in a normal metal with spin-orbit coupling based on the Green's function method. The normal metal is connected with three leads. A spin current injected in one lead can induce a charge current between another two leads. We find that the conversion efficiency of spin power to charge power is roughly proportional to tSO4 when the spin-orbit coupling tSO is weak, suggesting that the efficiency is limited. Moreover, an increase of temperature may reduce the efficiency. The results may be useful in determining the overall efficiency of a thermoelectric setup based on the longitudinal spin Seebeck effect.