Mechanisms of spin-dependent heat generation in spin valves

The extra heat generation in spin transport is usually interpreted in terms of the spin relaxation. By reformulating the heat generation rate, we found alternative current-force pairs without cross effects, which enable us to interpret the product of each pair as a distinct mechanism of heat generation. The results show that the spin-dependent part of the heat generation includes two terms. One of them is proportional to the square of the spin accumulation and arises from the spin relaxation. However, the other is proportional to the square of the spin-accumulation gradient and should be attributed to another mechanism, the spin diffusion. We illustrated the characteristics of the two mechanisms in a typical spin valve with a finite nonmagnetic spacer layer.