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 ($3.6\times {10}^{-6}{\mathrm{K}}^{-1}$) 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.

Figure 1

(a) Rotating and tilting of the $B{\mathrm{O}}_6$ octahedra under the various distortion modes of symmetry $X_1^{-}$, $X_2^{+}$, and $X_3^{-}$ discussed in the Letter. (b) The relationship between the various symmetries of the high-temperature and low-temperature phases of ${\mathrm{Ca}}_3{\mathrm{Mn}}_2{\mathrm{O}}_7$ and ${\mathrm{Ca}}_3{\mathrm{Ti}}_2{\mathrm{O}}_7$, basis, and origin shift along with further details are given in Supplemental Material [16].

Figure 2

Evolution of the distortion modes of symmetry $X_1^{-}$, $X_2^{+}$, and $X_3^{-}$ (hexagonal, square, and circular symbols, respectively) with temperature. (a) Evolution of modes in the $A{2}_{1}am$ phase of ${\mathrm{Ca}}_3{\mathrm{Ti}}_2{\mathrm{O}}_7$; (b) evolution of the modes $X_2^{+}$ and $X_3^{-}$ in the low-temperature ($A{2}_{1}am$) phase and of the $X_1^{-}$ mode in the high-temperature ($Acaa$) phase of ${\mathrm{Ca}}_3{\mathrm{Mn}}_2{\mathrm{O}}_7$.

Figure 3

Evolution of the polarization of ${\mathrm{Ca}}_3{\mathrm{Ti}}_2{\mathrm{O}}_7$ (green squares) and ${\mathrm{Ca}}_3{\mathrm{Mn}}_2{\mathrm{O}}_7$ (red circles, in the low-temperature $A{2}_{1}am$ phase only) as a function of temperature.

Figure 4

(a) Evolution of the phase fraction in ${\mathrm{Ca}}_3{\mathrm{Mn}}_2{\mathrm{O}}_7$ as a function of temperature. (b) Negative thermal expansion along the $c$-axis of ${\mathrm{Ca}}_3{\mathrm{Mn}}_2{\mathrm{O}}_7$ at high temperatures consistent with a soft mode mechanism (shown in inset) (c) positive thermal expansion of the $c$-axis in ${\mathrm{Ca}}_3{\mathrm{Ti}}_2{\mathrm{O}}_7$ and in ${\mathrm{Ca}}_3{\mathrm{Mn}}_2{\mathrm{O}}_7$. Circle and square symbols represent data collected on cooling and warming respectively, and all e.s.u. are small than the size of the symbols.