Boltzmann-equation approach to the negative magnetoresistance of ferromagnetic–normal-metal multilayers

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Abstract
The Boltzmann equation is solved for a system consisting of a ferromagnetic–normal-metal–ferromagnetic metallic trilayer. The in-plane conductance of the film is calculated for two configurations: the ferromagnetic layers aligned (i) parallel and (ii) antiparallel to each other. The results explain the giant negative magnetoresistance encountered in these systems when an initial antiparallel arrangement is changed into a parallel configuration by application of an external magnetic field. The calculation depends on (a) geometric parameters (the thicknesses of the layers), (b) intrinsic metal parameters (number of conduction electrons, magnetization, and effective masses in the layers), (c) bulk sample properties (conductivity relaxation times), (d) interface scattering properties (diffuse scattering versus potential scattering at the interfaces), and (e) outer surface scattering properties (specular versus diffuse surface scattering). For perfect specular scattering at the surfaces the problem becomes identical to an infinite multilayer, periodic system. It is found that a large negative magnetoresistance requires, in general, considerable asymmetry in the interface scattering for the two spin orientations. All qualitative features of the experiments are reproduced. Quantitative agreement can be achieved with sensible values of the parameters. The effect can be conceptually explained based on considerations of phase-space availability for an electron of a given spin orientation as it travels through the multilayer sample in the various configurations.