We analyze the temperature dependence of conductivity in thick granular ferromagnetic compounds NiSiO2 and in thin weakly coupled films of Fe, Ni and Py in vicinity of metal-insulator transition. Development of resistivity minimum followed by a logarithmic variation of conductivity at lower temperatures is attributed to granular structure of compounds and thin films fabricated by conventional deposition techniques. Resistivity minimum is identified as a transition between temperature dependent intra-granular metallic conductance and thermally activated inter-granular tunneling.

We present our last results on anomalous Hall effect (AHE) in (Co 41 Fe 39 B 20 ) x (Al–O) 100-x nanocomposites focusing on the possible correlation between temperature dependence of AHE and resistivity. It is shown that the temperature dependence of conductivity G =1/ R xx , where R xx is resistivity, for compositions with x =49-56% at 10K< T < T k follows the relation, where the parameters A, , T k depend on x . For x =47% this relation changes to the exponential law “1/2” R xx ∝ exp (Т 0 /T) 1/2 . The correlation between AHE resistivity R H (T) and resistivity R xx (T) can be described as R H ∝ ( R xx ) m , where m increases from 0.38 to 0.58 with an increase of x from 49 to 56 %.

Universality of the extraordinary Hall effect scaling was tested in granular three-dimensional Ni-SiO2 films across the metal-insulator transition. Three types of magnetotransport behavior have been identified: metallic, weakly insulating, and strongly insulating. Scaling between both the ordinary and the extraordinary Hall effects and material's resistivity is absent in the weakly insulating range characterized by logarithmic temperature dependence of conductivity. The results provide compelling experimental confirmation for recent models of granular metals predicting transition from logarithmic to exponential conductivity temperature dependence when intergranular conductance drops below the quantum conductance value and loss of Hall effect scaling when intergranular conductance is higher than the quantum one. The effect was found at high temperatures and reflects the granular structure of the material rather than low-temperature quantum corrections.

The concentration dependence of the coefficient R s characterizing the anomalous Hall effect (AHE) has been studied by measuring the electrical resistivity ρ, magnetoresistance, and the magnetic field dependence of magnetization and Hall resistivity of (Co41Fe39B20) x (Al-O)100 − x nanocomposite thin films. It has been demonstrated that the AHE coefficient increases by more than an order of magnitude with a decrease in the percentage x of the amorphous ferromagnetic metal from 60 to 30 and its behavior is described by the relation R s ∼ ρ m , where m = 0.46 ± 0.1. At the same time, the coefficient characterizing the normal Hall effect grows by a factor of less than 10. The mechanisms underlying the giant Hall effect in nanocomposites have been discussed.