Anomalous Hall effect and ordinary Hall effect in variable range hopping regime of inhomogeneous ferromagnetic semiconductor

Anomalous Hall effect (AHE) and ordinary Hall effect (OHE) in variable range hopping regime of ferromagnetic semiconductor are important for understanding the localized impurity states at different energy levels within the band gap, and provides insight into the specific percolation networks of the thermally excited spin-polarized carriers. Here we report the experiments of both OHE and AHE in Mott and Efros variable range hopping regimes of inhomogeneous In_0.27Co_0.73O_1-v ferromagnetic semiconductor films with the tunable localized electron density and localization length. We found an unusual scaling relation between the AHE coefficient R_AH and the longitudinal resistivity ρ_xx, R_AH∝ρ_xx^β with β>2, which contrasts the scaling relation of OHE coefficient R_OH∝ρ_xx^α with α<1. More strikingly, the sign of AHE coefficient reverses with decreasing temperature for specific electron density. We argue that these surprising results are related to the specific impurity energy band structure of the oxygen vacancies within the band gap of inhomogeneous In_0.27Co_0.73O_1-v ferromagnetic semiconductor films.