Dissipation due to pure spin current generated by spin pumping
Wayne M. Saslow, Tomohiro Taniguchi
Based on spin-dependent transport theory and thermodynamics, we develop a generalized theory of the Joule heating in the presence of a spin current. Along with the conventional Joule heating consisting of an electric current and electro-chemical potential, it is found that the spin current and spin accumulation give an additional dissipation because the spin-dependent scatterings inside bulk and ferromagnetic/nonmagnetic interface lead to a change of entropy. The theory is applied to investigate the dissipation due to pure spin current generated by spin pumping in a ferromagnetic/nonmagnetic/ferromagnetic multilayer. The dissipation arises from an interface because the spin pumping is a transfer of both the spin angular momentum and the energy from the ferromagnet to conduction electrons near the interface. It is found that the dissipation is proportional to the Gilbert damping constant enhanced by spin pumping.