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 $\text{MgO}\left(001\right)//\text{Fe}\left(t\right)/\text{MgO}$ 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 ${\sigma }_{xx}$ and anomalous Hall conductivity ${\sigma }_{xy}$. In this way, we report a crossover from the intrinsic moderately dirty region of conductivities where ${\sigma }_{xy}=\text{const}$ to the dirty region of poorly conducting materials $\left({\sigma }_{xx}<{10}^4\text{S}/\text{cm}\right)$ where we have found that the relation ${\sigma }_{xy}\propto {\sigma }_{xx}^n$ with $n=1.66\left(4\right)$ holds, in good agreement, with the expected universal scaling relationship reported in other ferromagnetic compounds.

We study the enhanced magnetic moment observed in epitaxial magnetite (Fe3O4) ultrathin films (t<15$\hskip0.3em${}nm) grown on MgO (001) substrates by means of pulsed laser deposition. The Fe3O4 (001) thin films exhibit high crystallinity, low roughness, and sharp interfaces with the substrate, and the existence of the Verwey transition at thicknesses down to 4 nm. The evolution of the Verwey transition temperature with film thickness shows a dependence with the antiphase boundaries density. Superconducting quantum interference device (SQUID) and vibrating sample magnetometry measurements in ultrathin films show a magnetic moment much higher than the bulk magnetite value. In order to study the origin of this anomalous magnetic moment, polarized neutron reflectivity (PNR), and x-ray magnetic circular dichroism (XMCD) experiments have been performed, indicating a decrease in the magnetization with decreasing sample thickness. X-ray photoemission spectroscopy measurements show no metallic Fe clusters present in the magnetite thin films. Through inductively coupled plasma mass spectroscopy and SQUID magnetometry measurements performed in commercial MgO (001) substrates, the presence of Fe impurities embedded within the substrates has been observed. Once the substrate contribution has been corrected, a decrease in the magnetic moment of magnetite thin films with decreasing thickness is found, in good agreement with the PNR and XMCD measurements. Our experiments suggest that the origin of the enhanced magnetic moment is not intrinsic to magnetite but due to the presence of Fe impurities in the MgO substrates.

We report a systematic study of the anomalous Hall effect in epitaxial thin films of magnetite grown on $\mathrm{MgO}\left(001\right)$ substrates as a function of film thickness (from 5 to $150\mathrm{nm}$) and temperature $(60\mathrm{K}<T<300\mathrm{K})$. The Hall resistivity was found to be negative for all the measured temperature range, presenting a huge enhancement at temperatures below the Verwey transition, reaching values above $1\mathrm{m}\mathrm{\Omega }\mathrm{cm}$. The anomalous Hall conductivity scales as ${\sigma }_H\propto {\sigma }_{xx}^{1.6}$ over four decades of the longitudinal conductivity ${\sigma }_{xx}$ in all the samples, in agreement with a recent unified theory for the anomalous Hall effect.