We report Hall-effect measurements of epitaxial Fe (001) thin films grown on MgO (001). We have focused on the dependence of the anomalous Hall effect (AHE) in heteroepitaxial structures MgO (001)//Fe(t)/MgO with $t=10$, 2.5, 2, 1.8, and 1.3 nm. Our results have been interpreted in terms of a recent unified theory of the AHE. We have demonstrated that the thickness and roughness of the Fe layer are control parameters to tune both the longitudinal conductivity σₓₓ and anomalous Hall conductivity σxy. In this way, we report a crossover from the intrinsic moderately dirty region of conductivities where σxy=const to the dirty region of poorly conducting materials (σₓₓ<10⁴ S/cm) where we have found that the relation σxy∝σₓₓⁿ with $n=1.66(4)$ holds, in good agreement, with the expected universal scaling relationship reported in other ferromagnetic compounds.
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Sangiao et al. (2009) studied this question.