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

Using low-energy electron diffraction, we show that the room-temperature $(\sqrt{2}\times\sqrt{2})R45^\circ$ reconstruction of Fe$_3$O$_4$(100) reversibly disorders at $\sim$450 $^\circ$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 sub-surface Fe$^{3+}$ is replaced by Fe$^{2+}$ as the temperature is raised. This model reproduces the structure of antiphase boundaries previously observed with STM 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.