Quasianalytical treatment of the spin Seebeck effect on the Na₂ molecule

In the field of spin caloric transport one seeks to both understand and utilize thermal effects to control spin and charge transport. The discovery of the spin-Seebeck effect (SSE), where a thermal gradient induces a spin-voltage difference parallel to the wire, has given a major impetus to the field of spin caloritronics [1].

Here we report an ab initio method to calculate the SSE on finite systems, and demonstrate it quasianalytically on Na₂. The system is coupled to two baths with different temperatures, described with a Lindblad superoperator. We mainly focus on how to divide any operator into spatially localized contributions and show that the spatial localization of the virtual excitations (i.e., splitting of the ladder operators into two sets of localized operators with different eigenbases) is the underlying reason for the SSE. We also analyze the precession angles on the localized spins, and find that a broadening of the temperature-induced transitions leads to noncollinear magnetism. Finally, we show the connection between the SSE and the electronic entanglement in the system [2].

[1] K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, and E. Saitoh, Nature (London) 455, 778 (2008)
[2] G. Lefkidis and S. A. Reyes, Phys. Rev. B 94, 144433 (2016)