Heteroanionic Ruddlesden-Popper ferroelectrics from anion order and octahedral tilts

We describe a strategy to design ferroelectric heteroanionic materials based on the coupling of anion order and octahedral tilts in $n=1$ Ruddlesden-Popper structures, which allows noncentrosymmetric and polar compounds to arise from centrosymmetric anion-ordered structures. We investigate the relative phase stabilities of the polymorphs of ${\mathrm{Sr}}_{2}{\mathrm{ScO}}_{3}\mathrm{F}$ and ${\mathrm{Ca}}_{2}{\mathrm{ScO}}_{3}\mathrm{F}$ derived from this coupling using electronic structure calculations. We find that large degrees of octahedral tilting can stabilize different anion orders derived from assembly of $[{\mathrm{ScO}}_{5}{\mathrm{F}]}^{8\ensuremath{-}}$ octahedra. To further understand the link between octahedral tilting and anion order, we quantitatively separate the contributions of electrostatics and covalent interactions to the stability of tilts. We find that the tilts are driven primarily by covalent interactions and that local out-of-plane polar displacements, induced from the anion order, further stabilize the octahedral tilts through the pseudo-Jahn-Teller effect.