We study the Nernst effect and the spin Nernst effect, that a longitudinalthermal gradient induces a transverse voltage and a spin current. A mesoscopicfour-terminal cross-bar device having the Rashba spin-orbit interaction (SOI)under a perpendicular magnetic field is considered. For zero SOI, the Nernstcoefficient peaks when the Fermi level crosses the Landau Levels. In thepresence of the SOI, the Nernst peaks split, and the spin Nernst effect appearsand exhibits a series of oscillatory structures. The larger SOI is or theweaker magnetic field is, the more pronounced the spin Nernst effect is. Theresults also show that the Nernst and spin Nernst coefficients are sensitive tothe detailed characteristics of the sample and the contacts. In addition, theNernst effect is found to survive in strong disorder than the spin Nernsteffect does.
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