Universal scaling of the anomalous Hall effect

We have undertaken a detailed study of the magneto-transport properties of ultra-thin Fe films epitaxially grown on GaAs (1 0 0). A metal–semiconductor transition has been observed with a critical thickness of 1.25 nm, which was thought to be related to the thermally activated tunneling between metallic clusters. By fitting ${{\rho}_{\text{AH}}}$ versus $\rho _{xx}^{2}$ with the TYJ equation (Tian et al 2009 Phys. Rev. Lett. 103 087206), we found that the magnetization is negligible for the scaling of the anomalous Hall effect in ultra-thin Fe films. Furthermore, the intrinsic term, which is acquired by the linear fitting of ${{\rho}_{\text{AH}}}$ versus $\rho _{xx}^{2}$ , shows an obvious decrease when the film thickness drops below 1.25 nm, which was thought to be related to the fading of the Berry curvature in the ultra-thin film limit.