Magnetoresistance of metallic magnetic multilayers in the ballistic regimefor a spacer

The role of a spin-dependent electronic structure in the giant magnetoresis tance effect (GMR) of metallic magnetic multilayers is considered. The gene ral transmission amplitude (coefficient) for an electron Bloch wave passing from one magnetic layer to another one through a nonmagnetic spacer in the ballistic regime is found for the case of perfect interfaces. The Boltzman n equation, which incorporates this transmission coefficient and spin depen dent scattering (SDS) in a hulk of magnetic layers, is solved for a magneti c multilayer in the current-in-plane (CIP) geometry. It is shown that, if t here is no spin asymmetry in an electron scattering by imperfections, an el ectron refraction (a difference in the electron velocities in different lay ers/different sheets of the Fermi surface) itself results in a negative mag netoresistance and thus can lead to an enhancement of the GMR. The interfer ence of electronic waves leads to the oscillations of the magnetoresistance as a function of the spacer thickness. These oscillations can survive an i ntegration over the Fermi surface and their periods are determined by the s tationary vectors of the spacer Fermi surface. The oscillating quantum corr ections are calculated explicitly. A new approach to accounting for imperfe ctions of the interfaces is proposed. The general formula for the magnetore sistance, which accounts for both the coherent and diffuse electron scatter ing at the interfaces, is obtained.