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Iron oxides play an increasingly prominent role in heterogeneous catalysis, hydrogen production, spintronics and drug delivery. The surface or material interface can be performance limiting in these applications, so it is vital to determine accurate atomic-scale structures for iron oxides and understand why they form. Using a combination of quantitative low-energy electron diffraction, scanning tunneling microscopy, and density functional theory calculations, we show that an ordered array of subsurface iron vacancies and interstitials underlies the well-known (rt2xrt2)R45{\deg} reconstruction of Fe3O4(001). This hitherto unobserved stabilization mechanism occurs because the iron oxides prefer to redistribute cations in the lattice in response to oxidizing or reducing environments. Many other metal oxides also achieve stoichiometric variation in this way, so such surface structures are likely commonplace.

The surfaces of metal oxides often are reconstructed with a geometry and composition that is considerably different from a simple termination of the bulk. Such structures can also be viewed as ultrathin films, epitaxed on a substrate. Here, the reconstructions of the SrTiO3 (110) surface are studied combining scanning tunneling microscopy, transmission electron diffraction, and X-ray absorption spectroscopy, and analyzed with density functional theory calculations. While SrTiO3 (110) invariably terminates with an overlayer of titania, with increasing density its structure switches from nx1 and 2xn. At the same time the coordination of the Ti atoms changes from a network of corner-sharing tetrahedra to a double layer of edge-shared octahedra with bridging units of octahedrally coordinated strontium. This transition from the nx1 to 2xn reconstructions is a transition from a pseudomorphically stabilized tetrahedral network towards an octahedral titania thin film with stress-relief from octahedral strontia units at the surface.

Surfaces and interfaces offer new possibilities for tailoring the many-body interactions that dominate the electrical and thermal properties of transition metal oxides. Here, we use the prototypical two-dimensional electron liquid (2DEL) at the SrTiO$_3$(001) surface to reveal a remarkably complex evolution of electron-phonon coupling with the tunable carrier density of this system. At low density, where superconductivity is found in the analogous 2DEL at the LaAlO$_3$/SrTiO$_3$ interface, our angle-resolved photoemission data show replica bands separated by 100\,meV from the main bands. This is a hallmark of a coherent polaronic liquid and implies strong long-range coupling to a single longitudinal optical phonon mode. In the overdoped regime the preferential coupling to this mode decreases and the 2DEL undergoes a crossover to a more conventional metallic state with weaker short-range electron-phonon interaction. These results place constraints on the theoretical description of superconductivity and allow for a unified understanding of the transport properties in SrTiO$_3$-based 2DELs.