Fe3O4 surface electronic structures and stability from GGA + U

The electronic structures, stabilities and magnetic properties of the Fe₃O₄(111), (110) and (001) surfaces have been computed at the level of density functional theory by including the Hubbard parameter (U) for describing the on-site Coulomb interaction of iron 3d electrons. Among the six Fe₃O₄(111) terminations, the Fe_tet1 (exposing tetrahedral coordinated iron) and Fe_oct2 (exposing octahedral coordinated iron) terminations are more stable and have metallic character. For the Fe₃O₄(110) surface, strong surface distortion has been found; the A-layer termination (exposing tetrahedral coordinated iron) has metallic character, while the B-layer termination (exposing tetrahedral and octahedral coordinated iron) has half-metal character. For the Fe₃O₄(001) surface, both A-layer (exposing tetrahedral coordinated iron) and B-layer (exposing octahedral coordinated iron) terminations have half-metal character. The surface stability of (111) > (001) > (110) on the basis of the computed surface energies agrees well with the experimental findings, and explains reasonably the observed diversity and complexity of the experiments.