Untangling the effects of octahedral rotation and ionic displacements on the electronic structure of BiFeO3

Abstract

The electronic structure and related properties of perovskites ${\mathrm{ABO}}_{3}$ are strongly affected by even small modifications in their crystalline structure. In the case of ${\mathrm{BiFeO}}_{3}$, variations in the octahedral rotations and ionic displacements lead to significant changes in the band gap. This effect can possibly explain the wide range of values (2.5--3.1 eV) reported in the literature, obtained from samples of varied structural qualities, including polycrystalline films, epitaxial films grown by pulsed-laser deposition and molecular beam epitaxy, nanowires, nanotubes, and bulk single crystals. Using hybrid density-functional calculations, we investigate the dependence of the electronic structure on the crystal lattice distortions of the ferroelectric-antiferromagnetic ${\mathrm{BiFeO}}_{3}$, disentangling the effects of the ferroelectric ionic displacements and the antiferrodistortive octahedral rotations on the band gap and the band-edge positions. The band gap is shown to vary from 3.39 eV for the rhombohedral ground-state (R3c) structure down to 1.58 eV for the perfect cubic (Pm$\overline{3}$m) structure, with changes in the conduction band being much more prominent than in the valence band. The gap varies linearly with the ferroelectric ionic displacements, but nonlinearly with the octahedral rotations around the pseudocubic [111${\mathrm{]}}_{c}$ axis, and this is explained in terms of the different interactions between Bi $6s, 6p$, Fe $3d$, and O $2p$ bands. We argue that such large variation of the band gap with structural changes may well explain the large scattering of the reported values, especially if significant deviations from the equilibrium crystal structure are found near domain boundaries, extended defects, or grain boundaries in polycrystalline films.