${\mathrm{NO}}_2$-assisted molecular-beam epitaxy of ${\mathrm{Fe}}_3{\mathrm{O}}_4,$ ${\mathrm{Fe}}_{3-\delta }{\mathrm{O}}_4,$ and $\gamma -{\mathrm{Fe}}_2{\mathrm{O}}_3$ thin films on MgO(100)

We report on the molecular beam epitaxial growth of single-crystalline, stoichiometric ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and $\gamma -{\mathrm{Fe}}_2{\mathrm{O}}_3$ films on MgO(100), using ${\mathrm{NO}}_2$ as the oxidizing agent. Mössbauer spectroscopy on ${}^{57}\mathrm{Fe}$ probe layers is used to determine accurately the stoichiometry of the films. It is found that also all intermediate nonstoichiometric ${\mathrm{Fe}}_{3-\delta }{\mathrm{O}}_4$ phases can be obtained. The formation of the metastable compound $\gamma -{\mathrm{Fe}}_2{\mathrm{O}}_3$ clearly demonstrates the large oxidizing power of ${\mathrm{NO}}_2.$ Although the shape anisotropy dictates that the zero-field magnetization direction should lie entirely in the plane of the film, this is never observed. Stoichiometric ${\mathrm{Fe}}_3{\mathrm{O}}_4$ has large out-of-plane components and only in the case of highly oxidized ${\mathrm{Fe}}_{3-\delta }{\mathrm{O}}_4$ does the magnetization approach the film plane. Upon further oxidation to stoichiometric $\gamma -{\mathrm{Fe}}_2{\mathrm{O}}_3,$ however, it rotates back, and finally becomes almost completely perpendicular to the plane of the film. Furthermore, in the case of (near-) stoichiometric ${\mathrm{Fe}}_3{\mathrm{O}}_4,$ the magnetizations of the A and B sublattices are not completely coupled antiparallel. On average, the magnetization of the B site ions is $4°$ closer to the film plane than the magnetization of the A site ions. All the as-grown films exhibit a $(\sqrt{2}\times \sqrt{2})\mathrm{R}45°$ surface reconstruction, independent of the stoichiometry. Using simple electrostatic considerations, we propose three possible surface terminations: a half-filled A layer, a B layer with oxygen vacancies and a B layer with hydroxyl groups. Upon annealing, the $(\sqrt{2}\times \sqrt{2})\mathrm{R}45°$ reconstruction irreversibly transforms to a $3\times 1$ reconstruction, caused by Mg outdiffusion from the substrate. Strong reflection high-energy electron diffraction intensity oscillations give direct, unambiguous evidence that ${\mathrm{Fe}}_3{\mathrm{O}}_4$ has a two-dimensional layer-by-layer growth mode over the entire temperature range studied, i.e., from 273 to 723 K, guaranteeing atomically flat surfaces and interfaces in multilayer structures. The largest oscillations are obtained on ex situ cleaved, UHV-annealed MgO(100) substrates, or on in situ annealed ${\mathrm{Fe}}_3{\mathrm{O}}_4/\mathrm{MgO}\mathrm{}\left(100\right)\mathrm{}$ films. Deposition above $\sim 700\mathrm{K}$ is accompanied by rapid Mg outdiffusion.