Transverse electron transport in layered metallic systems: Giant magnetoresistance and injection of spins

The distribution functions for electrons differing in the sign of the spin projection and belonging to different layers (ferromagnetic and nonmagnetic) are determined from the system of Boltzmann kinetic equations. These functions make it possible to derive integral equations for electrochemical potentials for arbitrary ratios of characteristic lengths (layer thicknesses and momentum-and diffusion mean free paths) and to describe transverse electron transport both in the bulk and in the surface regions of the multilayer structure. The expressions for the effective contact resistance are derived and the value of the transverse ohmic resistance of the structure is found, as well as its spin-dependent part determined by the values of injection factors γ. The values of nonequilibrium spin polarizations, which are also connected with coefficients γ, are determined. The values of γ are calculated for various relations between the characteristic parameters of the given system and for various types of magnetic order.