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Based on spin-dependent transport theory and thermodynamics, we develop ageneralized theory of the Joule heating in the presence of a spin current.Along with the conventional Joule heating consisting of an electric current andelectrochemical potential, it is found that the spin current and spinaccumulation give an additional dissipation because the spin-dependentscatterings inside bulk and ferromagnetic/nonmagnetic interface lead to achange of entropy. The theory is applied to investigate the dissipation due topure spin-current generated by spin pumping across aferromagnetic/nonmagnetic/ferromagnetic multilayer. The dissipation arises froman interface because the spin pumping is a transfer of both the spin angularmomentum and the energy from the ferromagnet to conduction electrons near theinterface. It is found that the dissipation is proportional to the enhancementof the Gilbert damping constant by spin pumping.

Dissipation due to pure spin-current generated by spin pumping