Electron transport in magnetic inhomogeneous media

Giant magnetoresistance has been observed in both magnetic multilayers and magnetic granular solids. We develop a framework for unifying these particular realizations of inhomogeneous magnetic media, based on the real-space Kubo formula. It constitutes a spin-dependent form of linear response theory, associated with internal spin-dependent fields arising from spin accumulation; moreover, we discuss the physical meaning of these spin dependences. For magnetic multilayers we discuss the particular cases of collinear and noncollinear configurations, and we consider limiting cases of the elastic mean-free path to inhomogeneity-scale ratio for granular solids. Furthermore, we introduce the concept of magnetically self-averaging systems, which include the current perpendicular to the plane geometry of multilayers and granular solids. In the limit of no spin-flip scattering, we show that there are no length scales associated with the magnetoresistance of self-averaging structures.