Time-resolved x-ray diffraction and photoelectron spectroscopy investigation of the reactive molecular beam epitaxy of Fe$_3$O$_4$ ultrathin films

We present time-resolved high-energy x-ray diffraction, time-resolved hard-x-ray photoelectron spectroscopy (tr-HAXPES), and time-resolved grazing incidence small-angle x-ray scattering (tr-GISAXS) data of the reactive molecular beam epitaxy of $\mathrm{Fe_3O_4}$ ultrathin films on various substrates. Reciprocal space maps are recorded during the deposition of $\mathrm{Fe_3O_4}$ on $\mathrm{SrTiO_3}(001)$, $\mathrm{MgO}(001)$, and $\mathrm{NiO/MgO}(001)$ in order to observe the thickness-dependent evolution of Bragg reflections sensitive to the octahedral and tetrahedral sublattices of the inverse spinel structure of $\mathrm{Fe_3O_4}$. Rock salt and spinel-exclusive reflections appear at different thicknesses, revealing that first, the iron oxide film grows with $\mathrm{Fe_{1-\delta}O}$ rock salt structure with exclusive occupation of octahedral lattice sites. After reaching a film thickness of 1.1$\,$nm, further growth of the iron oxide film proceeds in the inverse spinel structure, with both octahedral and tetrahedral lattice sites being occupied. In addition, iron oxide on SrTiO3(001) initially grows with none of these structures. Here, the formation of the rock salt structure starts when reaching a film thickness of 1.5$\,$nm. This is confirmed by tr-HAXPES data obtained during growth of iron oxide on $\mathrm{SrTiO_3}(001)$, which demonstrate an excess of $\mathrm{Fe^{2+}}$ cations compared to $\mathrm{Fe_3O_4}$ in growing films thinner than 3.2$\,$nm. This rock salt phase only appears during growth and vanishes after the supply of the Fe molecular beam is stopped. Thus, it can be concluded that the rock salt structure of the interlayer is a property of the dynamic growth process while the film is still exposed to oxygen. The tr-GISAXS data link these structural results to an island growth mode of the first 2–3$\,$nm on both $\mathrm{MgO}(001)$ and $\mathrm{SrTiO_3}(001)$ substrates