Why hole polaron formation on oxygen is limiting the Fermi level in Fe acceptor doped BaTiO$_{3}$ under oxidizing conditions

Abstract

Oxidizing Fe-doped BaTiO$_3$ is commonly expected to convert substitutional Fe$^{3+}$ acceptors into formal Fe$^{4+}$ centers. Yet, the experimentally accessible picture based on electron-paramagnetic resonance (EPR) is dominated by Fe$^{3+}$-related signatures, while Fe$^{4+}$ is not a straightforward observable. Here we show that this apparent discrepancy reflects the preferred location of the oxidizing hole: not on Fe, but on oxygen. Using density-functional theory with with occupation-matrix control and a piecewise-linearity-based Hubbard correction (DFT+$U$) for O-2$p$ states, we find that an oxygen-centered hole polaron is forming a Fe$^{3+}$-O$^{-}$ complex that is lower in energy than the formal Fe$^{4+}$ configuration. Our results identify ligand-hole formation as a favorable charge-compensation mechanism in oxidized Fe-doped BaTiO$_3$ and provide an explanation for the predominance of Fe$^{3+}$-based centers in spectroscopy. More broadly, they show how oxygen polarons can limit Fermi-level shifts and control the electronic response of acceptor-doped ferroelectric perovskites.