An alternative to the spin-coupled interface resistance for describing heat generation

Using a macroscopic approach, we studied theoretically the heat generation in a typical spin valve with nonmagnetic spacer layer of finite thickness. Our analysis shows that the spin-dependent heat generation cannot be interpreted as the Joule heating of the spin-coupled interface resistance except for some special segments. Moreover, the spin-coupled interface resistance can be negative in certain situation, and thus its "Joule heating" should be understood instead as the work done by the extra field in the ferromagnetic layers and at the spin-selective interfaces. Effective resistances are proposed as alternatives so that the spin-dependent heat generation can still be expressed in a form resembling Joule's law.