TRANSPORT IN MAGNETIC MULTILAYERS FROM THE QUANTUM BOLTZMANN-EQUATION

We describe a method for the computation of resistivity in a periodic or nonperiodic multilayer of magnetic materials. We show that the approach that leads to the well-known constant-relaxation-time solution to the Boltzmann equation in systems with spherical symmetry [J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, Cambridge, England, 1964)] can be generalized to cylindrical symmetry. The effects of interface scattering are included. For a layered system with a step-function potential, we have calculated scattering matrix elements from the exact quantum-mechanical wave functions. In the special case of two layers these are the well-known Kronig-Penney wave functions, but we have developed a transfer-matrix method for obtaining them in general, so our code will work for an arbitrary number of layers. We find that in realistic models there are often states trapped between high-potential layers, for which numerical divergences occur; we show how to handle these cases by a recursive procedure. The advantages of the quantum method over semiclassical ones are that (a) it includes interference effects exactly, and (b) it involves fewer free parameters. We give results for the ''giant magnetoresistance'' of a model of an FeCr sandwich structure for various numbers of layers. The approach to the result for an infinite periodic system is highly singular.