First-principles calculations of lattice dynamics in CdTiO${}_3$ and CaTiO${}_3$: Phase stability and ferroelectricity

First-principles calculations of various phases of CdTiO${}_3$ carried out with the aim of obtaining insights into the mechanism of the ferroelectric phase transition and the structure of the low-temperature ferroelectric phase are reported. The results indicate that the preferred symmetry of the low-temperature phase is Pna2${}_1$, rather than $P$2${}_{1}ma$, corresponding to a small relative shift of the Ti and O ions in the paraelectric Pnma phase with the polarization axis parallel to the long axis. Calculated phonon dispersion curves show a distinct soft mode at the Γ point of the Pnma phase, which vanishes in the Pna2${}_1$ phase, confirming that the transition to the ferroelectric phase is of the soft-mode displacive type. Calculations of perovskite CaTiO${}_3$, which also has an orthorhombic Pnma structure at room temperature but, unlike CdTiO${}_3$, does not exhibit a ferroelectric phase transition down to 4.2 K, were also carried out to help characterize the factors controlling ferroelectric phase transitions in perovskite titanates.

Figure 1

Crystal structures of possible polymorphs of CdTiO${}_3$: (a) $Pm\overline{3}m$, (b) Pnma, (c) Pna2${}_1$, and (d) $P$2${}_{1}ma$ phases.

Figure 2

Phonon dispersion curves for the $Pm\overline{3}m$ phases of (a) CdTiO${}_3$ and (b) CaTiO${}_3$.

Figure 3

Phonon dispersion curves for the Pnma phases of (a) CdTiO${}_3$ and (b) CaTiO${}_3$.

Figure 4

Directions of ion displacements in the Pnma structure corresponding to (a) $B_{2u}$ and (b) $B_{3u}$ modes associated with transformations to the Pna2${}_1$ and $P$2${}_{1}ma$ phases, respectively.

Figure 5

Phonon dispersion curves for the Pnma phase of CdTiO${}_3$ when the volume is uniformly (a) expanded by 2%, and (b) contracted by 2% relative to the equilibrium value.

Figure 6

Change in energy as a function of ion displacement for the $B_{2u}$ mode in the Pnma structure. The displacement has been normalized to the atomic positions of the polar (Pna2${}_1$) structure.

Figure 7

Phonon dispersion curves for the ferroelectric Pna2${}_1$ phase of CdTiO${}_3$.