Origin of the increased resistivity in epitaxial ${\mathrm{Fe}}_3{\mathrm{O}}_4$ films

We report resistivity measurements on epitaxial ${\mathrm{Fe}}_3{\mathrm{O}}_4$ films between 3 and 100 nm thickness grown on polished MgO substrates. The resistivity of the films is larger than the bulk resistivity, and is increasing with decreasing film thickness. This can be explained by the significant decrease of antiphase domain size with decreasing film thickness, as observed by transmission electron microscopy. The domain size decreases from 40 nm for 100-nm-thick films, to 5 nm for 3-nm-thick films. The effective conductivity has been modeled as a function of the bulk and boundary conductivities using the effective medium approximation. It is suggested that the absence of the Verwey transition in the thinnest films is also related to the very small domain size, which inhibits long-range order.