Absence of the ordinary and extraordinary Hall effects scaling in granular ferromagnets at metal-insulator transition

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.