Solution to the Boltzmann equation for layered systems for current perpendicular to the planes

Present theories of giant magnetoresistance (GMR) for current perpendicular to the planes (CPP) are based on an extremely restricted solution to the Boltzmann equation that assumes a single free electron band structure for all layers and all spin channels. Within this model only the scattering rate changes from one layer to the next. This model leads to the remarkable result that the resistance of a layered material is simply the sum of the resistances of each layer. We present a solution to the Boltzmann equation for CPP for the case in which the electronic structure can be different for different layers. The problem of matching boundary conditions between layers is much more complicated than in the current in the planes (CIP) geometry because it is necessary to include the scattering-in term of the Boltzmann equation even for the case of isotropic scattering. This term couples different values of the momentum parallel to the planes. When the electronic structure is different in different layers there is an interface resistance even in the absence of intermixing of the layers. The size of this interface resistance is affected by the electronic structure, scattering rates, and thicknesses of nearby layers. For Co-Cu, the calculated interface resistance and its spin asymmetry is comparable to that measured at low temperature in sputtered samples. (C) 2000 American Institute of Physics. [S0021-8979(00)71908-6].