Dynamical correlations in the electronic structure of BiFeO$_{3}$, as revealed by dynamical mean field theory

Using local density approximation plus dynamical mean-field theory (LDA+DMFT), we have computed the valence band photoelectron spectra of highly popular multiferroic BiFeO$_{3}$. Within DMFT, the local impurity problem is tackled by exact diagonalization (ED) solver. For comparison, we also present result from LDA+U approach, which is commonly used to compute physical properties of this compound. Our LDA+DMFT derived spectra match adequately with the experimental hard X-ray photoelectron spectroscopy (HAXPES) and resonant photoelectron spectroscopy (RPES) for Fe 3$d$ states, whereas the other theoretical method that we employed failed to capture the features of the measured spectra. Thus, our investigation shows the importance of accurately incorporating the dynamical aspects of electron-electron interaction among the Fe 3$d$ orbitals in calculations to produce the experimental excitation spectra, which establishes BiFeO$_{3}$ as a strongly correlated electron system. The LDA+DMFT derived density of states (DOSs) exhibit significant amount of Fe 3$d$ states at the energy of Bi lone-pairs, implying that the latter is not as alone as previously thought in the spectral scenario. Our study also demonstrates that the combination of orbital cross-sections for the constituent elements and broadening schemes for the calculated spectral function are pivotal to explain the detailed structures of the experimental spectra.