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Anisotropic optical properties of rhombohedral and tetragonal thin film BiFeO$_3$ phases

The anisotropic optical properties of multiferroic BiFeO$_3$ thin films have been determined with Mueller matrix ellipsometry at room-temperature. The full dielectric tensors of tetragonal-like and rhombohedral-like BiFeO$_3$ phases epitaxially grown on LaAlO$_3$ and SrTiO$_3$ single crystal substrates, respectively, within the spectral range of 0.6 and 6.5 eV are reported. Strain-driven anisotropy changes and transition shifts are observed as well as evidence of sub-band gap many-particle excitations are found. The transition shifts, mostly to higher energies for the highly strained tetragonal-like BiFeO$_3$ phase on LaAlO$_3$, are indicative of band structure differences. Additionally, optical modelling, confirmed by piezoelectric force microscopy studies, revealed that the average polarization direction of bivariant BiFeO$_3$ on LaAlO$_3$ is not parallel to the crystallographic [001] direction but tilted by about $7^{\circ}$. Spectral weight analyses reveal phase-dependent differences underlining that theoretical calculations of optical spectra need further improvement to appropriately account for electronic and excitonic correlations to fully understand multiferroic BiFeO$_3$.