Influence of the distribution of magnetic moments on the magnetization and magnetoresistance in granular alloys

In granular solids, the magnetoresistance is directly related to the macroscopic magnetization, but this relationship is extremelly complex due to the distribution of grain sizes and the intergranular magnetic interactions. The dependence of the magnetoresistance on the magnetization is here investigated by means of a theoretical model that is developed taking explicitly into account the magnetic moment distribution and the spin-dependent electron-impurity scattering within magnetic grains and at the interface between the grains and the metallic matrix. Using this model, one can explain large experimental deviations from the parabolic behavior of the magnetoresistance vs magnetization curves that are typically expected for equal noninteracting superparamagnetic grains. The expressions for the magnetization and magnetoresistance, obtained for general distribution funtions, are tested considering a log-normal-type distribution function by fitting on data obtained from melt-spun Cu${}_{90}$Co${}_{10}$ ribbons after annealing by dc Joule heating. The experimental data are well traced using just three parameters that determine the particle size distribution, the particle density, and the ratio of the scattering cross section at the boundaries of the grains to the scattering cross section within the grains.