Understanding electronic excited states in BiFeO₃ via ab initio calculations and symmetry analysis

BiFeO₃ is a technologically relevant multiferroic perovskite featuring ferroelectricity and antiferrromagnetism. Optical excitations in BiFeO₃ can couple with its lattice, magnetic and ferroelectic degrees of freedoms, and hold potential of probing and controlling them. In this work, ab initio density functional theory and GW-BSE methods are combined with an extensive symmetry and atomic orbital analysis of electronic states to describe the electronic structure and the optical spectra of BiFeO₃ with quantitative accuracy and qualitative insights. We find that spin-flip $d-d$ transitions localized on Fe atomic sites contribute to several in-gap features in the optical spectra of BiFeO₃. Our analysis provides a nuanced description of the crystal field splitting of Fe-$3d$ orbitals in the context of a specific crystal symmetry and its effect on the composition of these exciton states. Using symmetry analysis, we thoroughly explain how the spin-content and the splitting of energies of these excitons are dictated by an interplay between crystal symmetry, excitonic effects, and spin-orbit coupling.