Unconventional scaling of the anomalous Hall effect accompanying electron localization correction in the dirty regime

Scaling of the anomalous Hall conductivity to longitudinal conductivity ${\sigma }_{\mathrm{AH}}\propto {\sigma }_{xx}^2$ 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 (${\sigma }_{\mathrm{AH}}\propto {\sigma }_{xx}^{1.6}$). Our results strongly suggest that the correction of the electron localization modulates the scaling exponent of the anomalous Hall effect.

Figure 1

(a) The normalized sheet resistance as a function of $\ln T$ for FePt films with 20, 12, 6, 3, 2.2, 1.8, 1.6, 1.4, 1.3, and 1.2 nm thicknesses. Inset: Log-log plot of the sheet resistance as a function of the FePt thickness at 300 K. (b) Sheet conductance versus the logarithm of temperature for a 1.8 nm FePt film. (c) Logarithm of sheet conductance as a function of $T^{-1/3}$ for a 1.2-nm-thick FePt film. The straight lines in (b) and (c) are the linear fit to the data between 2 and 20 K.

Figure 2

(a) $\ln T$ dependence of normalized relative changes in the sheet resistance $R_{xx}$, anomalous Hall resistance $R_{\mathrm{AH}}$, and anomalous Hall conductance $G_{\mathrm{AH}}$ for a 1.8 nm FePt film. The straight lines are the linear fit to the data between 2 and 20 K. (b) Prefactors $A_{\mathrm{R}}$, $A_{\mathrm{AH}}$, and $2A_{\mathrm{R}}-A_{\mathrm{AH}}$ as a function of sheet resistance $R_{xx}$ of 2 K in the weak localization region.

Figure 3

The normalized relative changes as a function of $\ln T$ for a 1.2 nm strongly localized film. The straight lines are the linear fit to the data between 2 and 20 K. Inset: Logarithm of the anomalous Hall resistance as a function of $T^{-1/3}$ for the same sample.

Figure 4

(a) The anomalous Hall resistivity as a function of $\ln T$ for FePt films with 100, 12, 6, 3, 1.6, 1.3, and 1.2 nm thicknesses. (b) The anomalous Hall resistivity as a function of electrical resistivity at 5 and 2 K. The solid lines are guides to the eye. (c) Log-log plot of the anomalous Hall conductivity as a function of the longitudinal conductivity at 2 K. The dashed straight line represents the power law fit to the experimental data of 3–1.2 nm films, and the solid curve sketches the crossover from the intermediate disorder regime to the high disorder regime.