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Using first-principle calculations, we restrained the m=1 oxyfluorideAurivillius Bi$_2$TiO4F$_2$ to adopt three ordered key configurations, such astetragonal $I4/mmm$ phases with fluorine anions distributed either at theoctahedral apical sites or at the octahedral equatorial ones and orthorhombic$Pma2$ phase with fluorine anions distributed over both apical and equatorialsites. We explored the energetics of the metastable phases and their potentialfor ferroelectricity and found that the least favorable configuration isequatorial sites for fluorine and the most favorable one is the mixture betweenapical and equatorial sites for fluorine. Phonon calculations performed in thetetragonal $I4/mmm$ with fluorine at the apical sites showed a strong c-axispolar instability $\Gamma_{3}^{-}$ that co-exists with the ab-plane polarinstability $\Gamma_{5}^{-}$, commonly found in Aurivillius oxide phases. Thesetwo polar instabilities lead to $Pc$ phase that displays in-plane andout-of-plane spontaneous polarizations as large as 44 $\mu$c/cm$^{2}$ and 35$\mu$c/cm$^{2}$, respectively, opening new prospective design in thin filmsAurivillius FeRAM devices.

Ferroelectricity in oxyfluoride Aurivillius phase Bi$_2$TiO$_4$F$_2$ from first-principles