We performed a systematic full-potential density functional theory study with the generalized gradient and local density $\text{approximation}+U$ approaches on five possible $(1\times 1)$ 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 ${\mathrm{Fe}}_{\mathrm{oct}2}\text{−}{\mathrm{Fe}}_{\mathrm{tet}1}\text{−}\mathrm{O}1$-terminated surface is energetically favored, showing metallic properties. The ${\mathrm{Fe}}_{\mathrm{oct}1}\text{−}\mathrm{O}2$-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 ${\mathrm{Fe}}_{\mathrm{tet}1}\text{−}\mathrm{O}1$-terminated surface, the O-terminated surfaces, and the surfaces with vacancy defects all show metallic properties.

• Received 26 October 2005

DOI:https://doi.org/10.1103/PhysRevB.74.035409