Extension of the semiclassical theory of current-perpendicular-to-plane giant magnetoresistance including spin flip to any multilayered magnetic structures

In the framework of the Valet and Fert theory of current perpendicular to plane (CPP) giant magnetoresistance (GMR) in metallic multilayers [Valet and Fert, Phys. Rev. B 48, 7099 (1993)], the calculation of the CPP resistance and magnetoresistance has been generalized to any multilayered stacks including spin valves with synthetic free layers, laminated free and pinned layers, and dual spin valves. The theory takes into account bulk and interfacial spin-dependent scattering as well as spin flip in all layers. It also considers the effect of scattering at lateral edges of submicron multilayered pillars which can be viewed as a current in plane effect intruding on CPP transport. This latter effect plays a role when the diameter of the pillar becomes of the order of the elastic mean-free paths (i.e., below $\text{∼30\hspace{0.17em}}\mathrm{nm}\mathrm{).}$ Based on the theory, a code has been developed to compute the CPP resistance and CPP magnetoresistance from the transport parameters of each material involved in the stack (spin-dependent resistivities, spin-dependent interfacial resistances, and spin-diffusion length in each layers). As examples, we compare the results of the calculations with various already published CPP experiments. In particular, we interpret experiments previously carried out on $(\mathrm{NiFe/Cu/Co/Cu}{)}_{\mathrm{N}}$ and $(\mathrm{Co}\text{\hspace{0.17em}6\hspace{0.17em}}\mathrm{nm/Cu/Co}\text{\hspace{0.17em}1\hspace{0.17em}}\mathrm{nm/Cu}{)}_{\mathrm{N}}$ multilayers in which the order of the layers in the stack had been shown to affect the CPP resistance and magnetoresistance, a property which could not be explained in a simple two-channel serial resistance model. We also investigate the influence of the thickness of the various layers and underline the key role of the spin diffusion length in these thickness variations. Unexpected predictions are made with this theory such as the existence of a maximum in CPP–MR as a function of the thickness of the antiferromagnetic pinned layer. This type of calculations should allow a faster optimization of CPP–GMR in metallic multilayers.