Analytical and iterative semiclassical solutions for the giant magnetoresistance in magnetic multilayers

Abstract

Based on the semiclassical theory of Camley and Barnaś (C-B), the problem of solving the giant magnetoresistance in magnetic multilayers (Fi/Ni)n/Fn+1 is comprehensively discussed with both the bulk and interface spin-dependent scatterings being involved. The solution of this problem is attributed to the solution of G-coefficients (G's). First, we point out that for large n the analytical solution in close form is hard to obtain and a recent attempt made in the literature failed in general. Second, a new choice of local spin quantization-axes is adopted for reducing (in comparison with C-B) the number of G's and several exact inferences are drawn in order to further simplify the solution of G's. Finally, an iteration method for solving G's is developed, which, we believe, is the simplest one among the numerical methods in this area and leads naturally to the analytical solutions with close expression in the case of small n. Such solutions are given for symmetric sandwich as well as superlattice.