  We study the spin Nernst effect of a mesoscopic four-terminal cross-bar
device with the Rashba spin-orbit interaction (SOI) in the absence of a
magnetic field. The interplay between the spin Nernst effect and the seebeck
coefficient is investigated for a wide range of the Rashba SOI. When no peaks
appeared in the seebeck coefficient, an oscillatory spin Nernst effect still
occurs. In addition, the disorder effect on the spin Nernst effect is also
studied. We find that the spin Nernst effect can be enhanced up to threefold by
disorder. Besides, due to the interface effect, the counter propagating of the
charge current to the direction of the temperature gradient is possible for a
nonuniform system.
