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 Fetet1 (exposing tetrahedral coordinated iron) and Feoct2 (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.