Interplay of dipolar interactions and grain-size distribution in the giant magnetoresistance of granular metals

The giant magnetoresistance (GMR) of a granular metal containing interacting magnetic particles with disperse sizes and shapes is studied numerically using a tight binding Hamiltonian with spin-dependent potentials. Dipolar interactions between the magnetic particles are assumed and the equilibrium configuration of the system is obtained by a classical Monte Carlo simulation. The conductance of the system is calculated using the Kubo-Greenwood formula and real space Green function techniques. Due to the dipolar interactions acting between the grains the maximum GMR value is reduced and the saturation field is increased. When the coalescence between particles is introduced the concentration dependence of the GMR develops an optimum value close to the percolation threshold, where the effect of dipolar interactions is mostly pronounced, causing serious deviations from the predictions for noninteracting grains. Both dipolar interactions and grain size distribution are responsible for the deviations from the parabolic dependence of the GMR on the reduced magnetization at low fields. The relative importance of these two factors is investigated. Our numerical results are compared with experimental findings in ${\mathrm{Co}}_x{\mathrm{Cu}}_{1-x}$ granular alloys.