Ab initio studies of phonons in CaTiO3

Using the local-density approximation, and calculating the Hellmann–Feynman forces, the stability of the perovskite-like structures of ${\mathrm{CaTiO}}_3$ have been studied by applying the direct method and deriving the phonon dispersion relations. The cubic $\text{Pm3̄m}$ phase shows dispersionless soft phonon branch spreading from R to M points of the cubic Brillouin zone. Low-symmetry phase $\text{I4/mcm}$ can be considered as a result of the soft mode condensation at R point. The experimentally observed $\mathrm{Pmnb}$ phase is a consequence of the intersection of $\mathrm{Imma}$ and $\text{P4/mbm}$ space groups, being the result of soft mode condensation at R and M points, respectively. Thus, the $\mathrm{Pmnb}$ can be regarded as simultaneous condensations of two soft modes. The phonon dispersion relations of $\mathrm{Pmnb}$ suggest that this phase is stable.