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Unconventional Scaling of the Anomalous Hall Effect Accompanying Electron Localization Correction in the Dirty Regime

Scaling of the anomalous Hall conductivity to longitudinal conductivity, has been observed in the dirty regime of two-dimensional weak and strong localization regions in ultrathin, polycrystalline, chemically disordered, ferromagnetic FePt films. The relationship between electron transport and temperature reveals a quantitatively insignificant Coulomb interaction in these films while the temperature dependent anomalous Hall conductivity experiences quantum correction from electron localization. At the onset of this correction, the low-temperature anomalous Hall resistivity begins to be saturated when the thickness of the FePt film is reduced, and the corresponding Hall conductivity scaling exponent becomes 2, which is above the recent unified theory of 1.6 (σ_AH \propto σ^1.6_xx). Our results strongly suggest that the correction of the electron localization modulates the scaling exponent of the anomalous Hall effect.