Phenomenological thermodynamic potential for CaTiO${}_3$ single crystals

The antiferrodistortive (AFD) structural transitions of calcium titanate (CaTiO${}_3$) at ambient pressure have been extensively studied during the last few years. It has been found that none of the AFD polymorphs is polar or ferroelectric. However, it was recently shown theoretically and later experimentally confirmed that a ferroelectric transition in CaTiO${}_3$ can be induced by tensile strains. The ferroelectric instability is believed to be strongly coupled to the AFD soft modes. In this paper, we present a complete thermodynamic potential for describing the coupling between the AFD and ferroelectric phase transitions. We analyzed the dependence of transition temperatures on stress and strain condition. Based on this potential, a (001) CaTiO${}_3$ thin film diagram was constructed. The results show good agreement with available experimental observations. The strong suppression of ferroelectric transition by the AFD transition is discussed.

Figure 1

Crystal structure of CaTiO${}_3$: (a) projection along [100] direction, the TiO${}_6$ octahedra in consecutive two layers exhibit out-of-phase tilt, (the projection along [010] direction is similar); (b) projection along [001] direction, the TiO${}_6$ octahedra show in-phase tilt.

Figure 2

Tilt angle as a function of temperature. The discontinuities in the plot clearly show that there are three first-order transformations.

Figure 3

Relative free energy density of different structures: $I$4/mcm, Imma, Cmcm, and Pbnm. Note that $Pm\overline{3}m$ is set to be the reference state with free energy equal to zero. So the relative free energies of other structures are basically the energy difference from $Pm\overline{3}m$ structure.

Figure 4

The dielectric constant as a function of temperature. The saturation of dielectric constants occurs at very low temperature.

Figure 5

The temperature-constraint strain phase diagram of (001) CaTiO${}_3$ (a) with AFD and (b) without AFD. The transition point shown in (a) is measured by SHG experiment.[22]

Figure 6

The polariztation of (001) CaTiO${}_3$ thin film as a function of in-plain constraint strain of different temperatures. The void markers represent our calculations for different temperatures. And the solid diamonds denote the data from first-principles calculations (Ref. 21; solid diamond) for 0 K.