Spin splitting Nernst effect in altermagnets

Altermagnet is a distinctive magnet phase, which has spin-split energy band but with zero net magnetic moment. In this paper, we propose that altermagnet behaves spin splitting Nernst effect: Under a longitudinal temperature gradient, the electrons with opposite spins tend to split oppositely in the transverse direction, thus generating a transverse spin current. The spin splitting Nernst effect is understood from the contribution of the longitudinal wave vector to the transverse group velocity. Using the nonequilibrium Green's function method, we calculate the spin-dependent transmission coefficient in the four-terminal altermagnet device. From the spin-dependent transmission coefficient, the nonzero transverse spin current from longitudinal temperature gradient is obtained, and the spin splitting Nernst effect is verified. We systematically study the parameter dependence of the spin splitting Nernst effect, while also performing symmetry analysis. The spin splitting Nernst effect can be easily regulated by Fermi surface energy, temperature, transport direction, and system size. Furthermore, in altermagnet, the $xy$-response and $yx$-response spin splitting Nernst coefficients are equal with $N_{s,xy}=N_{s,yx}$, different from the conventional spin Nernst effect where they are opposite. Meanwhile, the spin splitting Nernst effect require neither spin-orbit coupling nor net magnetism.