The linear transport behavior of metallic multilayers is studied by using the real-space Kubo formula, for a model Hamiltonian consisting of zero-range spin-dependent impurity-scattering potentials. The resulting theory allows a direct comparison with the Boltzmann equation approach in the quasiclassical limit, which is expected to be a good approximation for most magnetic multilayers. Furthermore, the regimes for which quantum corrections might be needed are explicitly indicated. It is explicitly shown that: (i) periodicity is not required as a mechanism for giant magnetoresistance, and (ii) the two main geometries, current in the plane of the layers and perpendicular to the plane of the layers, exhibit very different size effects, the latter yielding the so-called series resistor model.
Camblong, Horacio E., "Linear Transport Theory of Magnetoconductance in Metallic Multilayers: A Real-space Approach" (1995). Physics and Astronomy. Paper 11.