Thermally induced spin polarization in 2D systems with Rashba spin-orbit interaction

We present the theory of spin polarization induced by a temperature gradient (heat current) in a magnetized two-dimensional electron gas (2DEG) with a Rashba spin-orbit interaction. Within the Matsubara Green’s function formalism, we calculated the temperature dependence of the spin polarization not only in non-magnetic case but also in the presence of a nonzero exchange field oriented arbitrarily in the space. For the magnetic system, among others, we identified a term in the spin polarization that stems from the Berry curvature of the corresponding electronic bands.
Moreover, we show that the electrically induced and the thermally induced spin polarizations obey the Mott relation in a nonmagnetic 2DEG as well as in the magnetic system but in the latter case only for the spin polarization normal to the electric field and to the thermal gradient. The components along the driving forces in a magnetic system do not obey this relation. This is mainly due to the fact that these components are determined by the Berry curvature of the electronic bands in the presence of both spin-orbit and exchange interactions.
[PRB 98, 075307 (2018), PRB 95, 245302 (2017)]