Finite-temperature properties and the hidden ferroelectric $R3c$ phase of bulk CaTiO$_3$ from second principles

A second-principles effective interatomic potential is introduced for the prototypical perovskite CaTiO$_3$ (CTO), relying on a Taylor polynomial expansion of the Born-Oppenheimer energy surface around the cubic reference structure, in terms of atomic displacements and macroscopic strains. This model captures various phases of bulk CTO and successfully reproduces, in particular, the structure, energy, and dynamical properties of the nonpolar $Pbnm$ ground state as well as of the hidden ferroelectric $R3c$ phase. Finite-temperature simulations suggest that the still debated sequence of structural phase transitions over heating is $Pbnm \ (a^-a^-c^+) \rightarrow C2/m \ (a^-b^-c^0) \rightarrow I4/mcm \ (a^-c^0c^0) \rightarrow Pm\bar{3}m \ (a^0a^0a^0)$, a sequence during which the oxygen-octahedra rotations around the three pseudocubic axes vanish successively. Although never experimentally observed in bulk, the ferroelectric $R3c$ phase appears to be metastable and at an energy only slightly above the $Pbnm$ ground state at 0 K. The simulations confirm that, if induced in some way, the $R3c$ phase remains stable up to about 300 K and shows ferroelectric properties. Furthermore, we find that the minimum energy path connecting the $Pbnm$ and $R3c$ phases involves localized layer-by-layer flipping of octahedral rotations, a mechanism which is shown to be at play during the thermal destabilization process of the $R3c$ phase toward the $Pbnm$ ground state. The proximity of the $R3c$ phase with the $Pbnm$ ground state suggests that the former could be stabilized under electric field. However, due to the large energy barrier, the field required for the $Pbnm$-to-$R3c$ transition appears to be extremely large, consistent with the fact that bulk CTO was never reported to be ferroelectric nor antiferroelectric.