Thermodynamic description of heat and spin transport in magnetic nanostructures

Spin-dependent heat and charge transport perpendicular to the plane of magnetic Co/Cu multilayers was studied experimentally and interpreted in the framework of the thermodynamics of irreversible processes. The thermogalvanic voltage(TGV) is introduced. It measures the ac voltage response to a small temperature oscillation while a dc current is driven through the sample. TGV presents a magnetic response (MTGV) of 50%, much larger than magnetoresistance (GMR) and the magneto-thermoelectrical power (MTEP). The linear equations for transport of heat, charge, and spin-polarized currents in magnetic and nonmagnetic mediums are applied to a multilayer structure. The role of spin mixing in GMR, MTEP, and MTGV is shown. In particular, the asymmetry of the spin-mixing gives rise to spin-dependent effective Peltier coefficients. The three measurements can be accounted for with two parameters expressing the spin dependence of the transport coefficients.