Electronic structure and lattice dynamical properties of different tetragonal phases ofBiFeO3

From first-principles calculations based on the plane-wave pseudopotential method within the density-functional $+U$ scheme, we have investigated the atomic geometry, electronic band-structure, and lattice dynamical properties of four tetragonal phases of the multiferroic ${\text{BiFeO}}_3$. In contrast to the indirect Kohn-Sham band gap of the rhombohedral phase, the most stable of the single-phase stable tetragonal structure is semiconducting with a smaller and direct band gap. It is found that the highest optical phonon branch is split from the rest of the phonon continuum by a small gap. The presently calculated zone-center optical modes have been compared and contrasted with the available polarized Raman-scattering studies and previous calculations based on a simple short-range force-constant method. The highest phonon mode with frequency $\sim 662{\text{cm}}^{-1}$ of $A_1$ representation in the tetragonal phase $\left(P4mm\right)$ can be readily distinguished from the frequency $\sim 590{\text{cm}}^{-1}$ of $A_2$ representation in the rhombohedral phase $\left(R3c\right)$.