Strain{\textendash}Induced Geometric Ferroelectricity in Perovskite{\textendash}structured Fluoroscandates

Using first-principles density functional theory calculations we investigate geometric ferroelectricity in epitaxially strained double-perovskite fluorides, Na$_3$ScF$_6$ and K$_2$NaScF$_6$. The experimental room temperature crystal structures of the fluoroscandates are centrosymmetric, i.e. Na$_3$ScF$_6$ ($P2_1/n$) and K$_2$NaScF$_6$ ($Fm\bar{3}m$). However, in their prototypical cubic geometry, we identify soft infrared active modes that are strongly sensitive to pressure: Ferroelectric instabilities are found for negative hydrostatic pressures $\sim\!$ -6 GPa. For Na$_3$ScF$_6$ we observe octahedral rotations ($a^-a^-c^+$ tilt system) are in strong competition with acentric polar distortions, and as a result exceedingly large tensile strain above 8\% are required to stabilize a Pm polar phase. We demonstrate that the strain mismatch required to stabilize the ferroelectric phase can be reduced to approximately 4\% with chemical substitution in ($a^0a^0a^0$) K$_2$NaScF$_6$ by reducing the tendency to octahedral rotations. Our study provides new insights that may prove useful in guiding experimental efforts towards identifying functional polar fluoroperovskites.