Order-disorder phase transition on the (100) surface of magnetite

Abstract

Using low-energy electron diffraction, we show that the room-temperature $(\sqrt{2}\ifmmode\times\else\texttimes\fi{}\sqrt{2})R{45}^{\ensuremath{\circ}}$ reconstruction of Fe${}_{3}$O${}_{4}$(100) reversibly disorders at $\ensuremath{\sim}$450${\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}$C. Short-range order persists above the transition, suggesting that the transition is second order and Ising-like. We interpret the transition in terms of a model in which subsurface Fe${}^{3+}$ is replaced by Fe${}^{2+}$ as the temperature is raised. This model reproduces the structure of antiphase boundaries previously observed with scanning tunneling microscopy, as well as the continuous nature of the transition. To account for the observed transition temperature, the energy cost of each charge rearrangement is 82 meV.