Critical behavior of resistivity and Hall resistivity in percolating fellomagnetic metal-insulator films

Resistivity rho(xx) and Hall resistivity rho(xy) were measured as functions of the magnetic field, temperature, and the metal volume fraction x, on a series of percolating Ni-SiO2 granular films. At 5 K, the data for the metallic samples were fitted to power law dependencies of the forms, rho(xx) proportional to [(x - x(c))/x(c)](-1) and rho(xy) proportional to [(x - x(c))/x(c)](-g), with x(c) = 0.6. The critical exponents of the resistivity t = 2.7 +/- 0.2, the extraordinary Hall resistivity g(s) = 2.0 +/- 0.2 and the ordinaIy Hall resistivity g(0) = 1.8 +/- 0.3 were found to be notably larger than the predictions for discrete percolation models (t approximate to 2 and g approximate to 0.4-0.5). We suggest that a percolation model incorporating localization can explain that contradiction. In the region of transition from metallic conduction to thermally activated tunneling, 0.53 < x < 0.6, the extraordinary Hall resistivity rho(xys) was found to be saturated at a value > 100 mu Omega cm, which is almost four orders of magnitude greater than that of pure Ni.