Effects of ferroelectric displacement and octahedral rotations on the electronic structure of BiFeO₃

The ground state of multiferrioc BiFeO₃ has rhombohedral structure with space group R3c. Despite decades of research its band gap remains a subject of debate. Reported band gaps vary over a wide range of 2.5 – 3.1 eV, the reasons for which are yet unclear. Using hybrid density functional theory calculations, we find a band gap of 3.4 eV for R3c BiFeO₃, which is slightly larger than a recent reported band gap of 3.1 eV for BiFeO₃ single crystals based on optical absorption and photoluminescence measurements. We also computed the effects of the ferroelectric displacement and the antiferrodistortive rotations of the FeO₆ octahedra on the band edge positions and the band gap, going from the ferroelectric ground-state R3c structure, to a nonpolar R-3c structure containing only the octahedral rotations, and to cubic Pm-3m structure. We find the band gap decreases from 3.4 eV for the R3c, to 2.9 eV for the R-3c, and to 1.6 eV for the cubic BiFeO₃, by significant lowering of the conduction band and slight raising of the valence band. We also find that the Bi 6s-O 2p coupling notably increases with the ferroelectric displacement, not with the octahedral rotations. Our results explain the large variation of the reported band gaps between single crystals and partially relaxed thin films.