Order-disorder phase transition of the subsurface cation vacancy reconstruction on $Fe_{3}O_{4}$ (001)

We present surface X-ray diffraction and fast scanning tunneling microscopy results to elucidate the nature of the surface phase transition on magnetite (001) from a (√2 x √2) R45° reconstructed to a non-reconstructed surface around 720 K. In-situ surface x-ray diffraction results at a temperature above the phase transition, at which long range order is lost, give evidence that the subsurface cation vacancy reconstruction still exists as a local structural motif, inline with the characteristics of a 2D second-order phase transition. Fast scanning tunneling microscopy results across the phase transition underpin the hypothesis that the reconstruction lifting is initiated by surplus Fe ions occupying subsurface octahedral vacancies. The reversible near-surface iron enrichment and reduction of the surface is further confirmed by in-situ low-energy ion scattering, as well as ultraviolet and X-ray photoemission results