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A large, by a factor of ≈103−104, enhancement of Hall effect in cosputtered magnetic granular metals such as (NiFe)x-(SiO2)1−x near the metal-insulator transition has been termed giant Hall effect (GHE). It is associated with a high resistivity which increases slowly with decreasing temperature. We suggest that particle-size distribution which is singular at zero and quantum size effects may be responsible for these phenomena. From our scaling analysis of the relations between resistivity, and the ordinary and extraordinary Hall effects, it follows that the extraordinary Hall resistivity ϱxys scales with mobility as-ϱxys ∝ μ−y with the exponent γ ≈ 0.5, which is characteristically different from the predictions of both the skew scattering (γ ≈ 1) and the side jump (γ ≈ 2) theories in homogeneous ferromagnets.

Resistivity ϱxx and Hall resistivity ϱxy 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, ϱxx ∝ [(x − xc)/xc]−t and ϱxy ∝ [(x − xc)/xc]−g, with xc = 0.6. The critical exponents of the resistivity t = 2.7 ± 0.2, the extraordinary Hall resistivity gs = 2.0 ± 0.2 and the ordinary Hall resistivity g0 = 1.8 ± 0.3 were found to be notably larger than the predictions for discrete percolation models (t ≈ 2 and g ≈ 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 > 100μΩ cm , which is almost four orders of magnitude greater than that of pure Ni.