Why isn't CsSnF$_3$ ferroelectric?

Complex fluorides are an interesting class of materials to explore for new ferroelectrics and multiferroics. The elucidation of design rules for new ferroelectric fluorides is challenging because polar fluorides tend to form in structures with a large number of atoms in the unit cell and the ferroelectricity is almost always of the geometric type. In this talk we will discuss our recent attempt to rationally design new polar fluorides from first principles. By exploring the relative stability of the subgroups of the perovskite manifold (using the phonons of the 5-atom cubic structure as a guide), we reveal the origin of ferroelectricity in R3c CsPbF$_3$, the only known polar ABF$_3$ compound. Comparison with CsSrF$_3$, which has a similar tolerance factor but no lone pair cation, reveals that the interplay between lone-pair localization and rotations stabilizes the rotation pattern most compatible with ferroelectricity, $i.e.$, a$^-$a$^-$a$^-$, rather than the more common a$^-$a$^-$c$^+$. Next we replace Pb$^{2+}$ with another lone pair cation, Sn$^{2+}$. Within a perovskite manifold of states CsSnF$_3$ is ferroelectric, yet synthesis of this compound by our experimental collaborators shows that not only isn't it ferroelectric, it isn't even a perovskite. Why?