Oxygen-Terminated (1x1) Reconstruction of Reduced Magnetite Fe$_3$O$_4$(111)

The (111) facet of magnetite (Fe$_3$O$_4$) has been studied extensively by experimental and theoretical methods, but controversy remains regarding the structure of its low-energy surface terminations. Using density functional theory (DFT) computations, we demonstrate three reconstructions that are more favorable than the accepted Fe$_{\rm oct2}$ termination in reducing conditions. All three structures change the coordination of iron in the kagome Fe$_{\rm oct1}$ layer to tetrahedral. With atomically-resolved microscopy techniques, we show that the termination that coexists with the Fe$_{\rm tet1}$ termination consists of tetrahedral iron capped by three-fold coordinated oxygen atoms. This structure explains the inert nature of the reduced patches.