Path-integral approach to the quasiclassical theory for giant magnetoresistance in magnetic multilayers

We present a rigorous, analytical approach to the Camley-Barnas model of the magnetoresistance (MR) in magnetic multilayers with an arbitrary number of bilayers. Using a path-integral method, we solve the semiclassical Boltzmann-transport equation subject to boundary conditions at the surfaces and interfaces, and obtain analytical results for the MR of magnetic layered systems. Particular attention is given to the multilayer effect for the enhancement of the change in magnetoresistance, and good agreement with experimental data is found for the epitaxial (Fe/Cr${)}_{\mathit{n}}$/Fe samples.