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

The spin-coupled interface (SI) resistance plays a crucial role in the interpretation of the giant magnetoresistance with current perpendicular to the plane. Recently, a theoretical work showed that its Joule heat also equals the total spin-dependent heat generation in a conceptual spin valve. Here we reexamine this conclusion in a practical spin valve with a finite nonmagnetic spacer layer and spin-selective interfaces. It turns out that this conclusion does not hold except for some special segments. The SI resistance has a more serious limitation: it may be negative in certain situation. In-depth analysis shows that its "Joule heating" should be interpreted actually as the extra energy supplied only in the ferromagnetic layers and at the interfaces. This extra energy is stored in the chemical-potential splitting due to spin accumulation and only part of it converts into heat locally. The rest flows to other layers, especially the nonmagnetic layer, in which the inflowing energy compensates exactly for the spin-dependent heat generation. In essence, this kind of energy transport makes the SI resistance unsuitable for a simple description of the heat generation, and thus we propose a new effective resistance as an alternative to it.