Temperature dependence of the side-jump spin Hall conductivity

In the conventional paradigm of the spin Hall effect, the side-jump conductivity due to electron-phonon scattering is regarded to be temperature independent. In contrast, we draw the distinction that, while this side-jump conductivity is temperature independent in the classical equipartition regime where the longitudinal resistivity is linear in temperature, it can be temperature dependent below the equipartition regime. The mechanism resulting in this temperature dependence differs from the familiar one of the longitudinal resistivity. In the concrete example of Pt, we show that the change of the spin Hall conductivity with temperature can be as high as 50%. Experimentally accessible high-purity Pt is proposed to be suitable for observing this prominent variation below 80 K.