Crossover from diffusive to ballistic transport properties in magnetic multilayers

We develop a theoretical model for computing the spin-dependent transport properties of magnetic multilayers in the presence of ballistic scattering at the interfaces and diffusive scattering within the layers for currents perpendicular to the plane of the layers. The local chemical potentials are found to be momentum and spin dependent in the vicinity of regions with ballistic scattering. We have derived the approximate macroscopic equations from the Boltzmann equation by taking into account both ballistic and diffusive scattering. With these equations, realistic data of the reflection coefficients from ab initio calculations can be explicitly included in computing magnetotransport properties. We apply our formulation to a number of interesting magnetic multilayer structures.