Analytical approach to the Camley-Barnaś theory for giant magnetoresistance in magnetic layered structures

We present an analytical treatment of the Camley-Barnaś theory of the magnetoresistance (MR) in magnetic layered structures and obtain an exact and general expression for the MR. Particular attention is given to the multilayer effect for the enhancement of MR change. It is proposed that the MR formula obtained from a single sandwich system can be used to calculate the MR effect of a multilayer structure provided an effective specularity factor for the reflection by the surfaces is introduced as a function of the number of bilayers. The theoretical results are in good agreement with experimental data for the epitaxial (Fe/Cr${)}_{\mathit{n}}$/Fe multilayers.