Negative Thermal Expansion in Hybrid Improper Ferroelectric Ruddlesden-Popper Perovskites by Symmetry Trapping

We present new results on the microscopic nature of the ferroelectricity mechanisms in ${\mathrm{Ca}}_{3}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Ca}}_{3}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$. To the first approximation, we confirm the hybrid improper ferroelectric mechanism recently proposed by Benedek and Fennie for these Ruddlesden-Popper compounds. However, in ${\mathrm{Ca}}_{3}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ we find that there is a complex competition between lattice modes of different symmetry which leads to a phase coexistence over a large temperature range and the ``symmetry trapping'' of a soft mode. This trapping of the soft mode leads to a large uniaxial negative thermal expansion (NTE) reaching a maximum between 250 and 350 K ($3.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}\text{ }\text{ }{\mathrm{K}}^{\ensuremath{-}1}$) representing the only sizable NTE reported for these and related perovskite materials to date. Our results suggest a systematic strategy for designing and searching for ceramics with large NTE coefficients.