Redox behaviour of Fe impurities in BaTiO$_3$ based on many-body calculations

Based on detailed electronic structure and spectroscopy obtained using DFT-based many-body techniques, the redox behavior of Fe impurities in BaTiO$_3$ is investigated. It is observed that Fe impurities exhibit a mixed valence nature, comprising mostly Fe$^{2+}$ ($3d^6$) and Fe$^{3+}$ ($3d^5$) configurations, and such configurations can be tuned via oxygen vacancies which favor Fe$^{2+}$. The origin of such a redox behavior can be attributed to the charge transfer caused by shifting of the $d_{3z^2-r^2}$ orbitals. Furthermore, x-ray photoemission spectroscopy is evaluated by solving the Wannier function-derived local atomic Hamiltonian using the crystal field multiplet approach, with good agreements with recent experimental measurements.