The spin accumulation due to the spin current induced by the perpendiculartemperature gradient (the spin Nernst effect) is studied in a two-dimensionalelectron system (2DES) with spin-orbit interaction by employing the Boltzmannequation. The considered 2DES is confined within a symmetric quantum well withdelta doping at the center of the well. A symmetry consideration leads to thespin-orbit interaction which is diagonal in the spin component perpendicular tothe 2DES. As origins of the spin current, the skew scattering and the side jumpare considered at each impurity on the center plane of the well. It is shownthat, for repulsive impurity potentials, the spin-Nernst coefficient changesits sign at the impurity density where contributions from the skew scatteringand the side jump cancel each other out. This is in contrast to the spin Halleffect in which the sign change of the coefficient occurs for attractiveimpurity potentials.
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