First-principles study of the polar (111) surface ofFe3O4

We performed a systematic full-potential density functional theory study with the generalized gradient and local density $\text{approximation}+U$ approaches on five possible $(1\ifmmode\times\else\texttimes\fi{}1)$ terminations of the low-index polar (111) surface of ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$. Applying the concepts of first-principles thermodynamics, we analyze the composition, the structure, and the stability of the ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ (111) orientation at equilibrium with an arbitrary oxygen environment. The densities of states of the unrelaxed and relaxed ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ (111) surfaces were calculated and compared with that of bulk ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$. The calculations reveal that the ${\mathrm{Fe}}_{\mathrm{oct}2}\text{\ensuremath{-}}{\mathrm{Fe}}_{\mathrm{tet}1}\text{\ensuremath{-}}\mathrm{O}1$-terminated surface is energetically favored, showing metallic properties. The ${\mathrm{Fe}}_{\mathrm{oct}1}\text{\ensuremath{-}}\mathrm{O}2$-terminated surface is more active than the other two Fe-terminated surfaces, showing half-metallic properties, similar to bulk ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$. The ${\mathrm{Fe}}_{\mathrm{tet}1}\text{\ensuremath{-}}\mathrm{O}1$-terminated surface, the O-terminated surfaces, and the surfaces with vacancy defects all show metallic properties.