Room-temperature measurements of magnetization and giant magnetoresistance were performed on rapidly solidified granular ${\mathrm{Cu}}_{100-x}{\mathrm{Co}}_x$ systems ($x=5, 10, 15$). The magnetoresistance of melt-spun ${\mathrm{Cu}}_{100-x}{\mathrm{Co}}_x$ ribbons was enhanced either by suitable furnace annealings or by exploiting the dc Joule-heating technique in the attempt of precipitating smaller magnetic particles. The particle-size distribution, the particle density, and mean distance are obtained for all compositions and heat treatments through a suitable analysis of the magnetic behavior of samples. The magnetoresistance is plotted as a function of the reduced magnetization, and a significant deviation from the quadratic behavior predicted by the independent-moment approach is observed at low fields. A simple theory taking explicitly into account the correlation existing among the magnetic particles is proposed. A general expression for the magnetoresistance in granular magnetic systems is obtained, and shown to accurately fit all the experimental curves, indicating that this effect is basically determined by the ratios between two distinct correlation ranges for the magnetic-moment fluctuations and the electronic mean free path.

• Received 10 May 1995

DOI:https://doi.org/10.1103/PhysRevB.52.15398