Ferroelectricity ind0double perovskite fluoroscandates

Ferroelectricity in strain-free and strained double perovskite fluorides, ${\mathrm{Na}}_{3}{\mathrm{ScF}}_{6}$ and ${\mathrm{K}}_{2}{\mathrm{NaScF}}_{6}$, is investigated using first-principles density functional theory. Although the experimental room temperature crystal structures of these fluoroscandates are centrosymmetric, i.e., ${\mathrm{Na}}_{3}{\mathrm{ScF}}_{6}$ ($P{2}_{1}/n$) and ${\mathrm{K}}_{2}{\mathrm{NaScF}}_{6}$ ($Fm\overline{3}m$), lattice dynamical calculations reveal that soft polar instabilities exist in each prototypical cubic phase and that the modes harden as the tolerance factor approaches unity. Thus the double fluoroperovskites bear some similarities to $AB{\mathrm{O}}_{3}$ perovskite oxides; however, in contrast, these fluorides exhibit large acentric displacements of alkali metal cations (Na, K) rather than polar displacements of the transition metal cations. Biaxial strain investigations of the centrosymmetric and polar ${\text{Na}}_{3}{\text{ScF}}_{6}$ and ${\text{K}}_{2}{\text{NaScF}}_{6}$ phases reveal that the paraelectric structures are favored under compressive strain, whereas polar structures with in-plane electric polarizations ($\ensuremath{\sim}5--18\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{C}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$) are realized at sufficiently large tensile strains. The electric polarization and stability of the polar structures for both chemistries are found to be further enhanced and stabilized by a coexisting single octahedral tilt system. Our results suggest that polar double perovskite fluorides may be realized by suppression of octahedral rotations about more than one Cartesian axis; structures exhibiting in- or out-of-phase octahedral rotations about the $c$ axis are more susceptible to polar symmetries.