Phenomenological spin transport theory driven by anomalous Nernst effect

Several experimental efforts such as material investigation and structure improvement have been made recently to find a large anomalous Nernst effect in ferromagnetic metals. Here, we develop a theory of spin transport driven by the anomalous Nernst effect in a diffusive ferromagnetic/nonmagnetic multilayer. Starting from a phenomenological formula of a spin-dependent electric current, the theoretical formulas of electric voltage and spin torque generated by the anomalous Nernst effect are derived. The magnitude of the electric voltage generated from the spin current via the inverse spin Hall effect is on the order of $0.1$ $\mu$V for currently available experimental parameter values. The temperature gradient necessary to switch the magnetization is quite larger than the typical experimental value. The separation of the contributions of the Seebeck and transverse spin Seebeck effects is also discussed.