Iterative semiclassical solutions of CIP giant magnetoresistance in magnetic multilayers with mixed layers taken into account

The problem of solving semiclassically the current in-plane (CIP) giant magnetoresistance in magnetic multilayers with mixed layers taken into account is comprehensively studied. The solution of this problem is attributed to the solution of G-coefficients. A new choice of local spin quantization-axes is adopted so that the number of G-coefficients is reduced from Johnson-Camley's 4(5n + 1) to our 4(4n + 1). Furthermore, we show that actually only a half number of G-coefficients need be sloved for the symmetric structure and a superlattice can be simplified to a symmetric penta-layered structure. The main result of this paper is the establishment of the iteration method for solving the G-coefficients. Associating this method with that of numerical integration, for which a formulism is developed, the GMR can be conveniently calculated.