An analysis of derivative absorption spectroscopy of multiferroic bismuth ferrite materials

The probability density function (PDF) and cumulative density function (CDF) of bulk BiFeO3, nanostructured BiFeO$_3$, and thick film of BiFeO$_{2.85}$ were studied in detail based on their experimental absorption data. The goal of this study was to investigate the electronic transitions and the Urbach tail band in three samples of the magnetoelectric multiferroic BiFeO$_3$. The PDF and CDF functions were derived from the absorption data of these substances in the UV-visible-NIR region of light spectrum. For the BiFeO$_3$-based materials, charge transfer (p-d and/or p-p) transitions in the energy range of 2.5 eV to 5.5 eV were identified through PDF and CDF analysis. Furthermore, spin-orbit and electron-lattice interactions along with a low-symmetry crystal field cause two doubly degenerate d-d transitions of Fe$^{3+}$ ions in the FeO$_6$ octahedra of the BiFeO$_3$ samples to occur between 1.5 eV and 2.5 eV. Additionally, the BiFeO3-based materials exhibited strong direct and weak indirect transitions near the band edge, which point to a complex band structure of BiFeO$_3$. Finally, the energy of the defect-induced Urbach tail band was directly calculated by examining the CDF function of the materials, yielding estimated values of approximately 0.40 eV, 0.31 eV, and 0.33 eV for the bulk, nanostructured, and film BiFeO$_3$ samples, respectively.