Ab initio study of the phase diagram of epitaxial ${\text{BaTiO}}_3$

Using a combination of first-principles and effective-Hamiltonian approaches, we map out the structure of ${\text{BaTiO}}_3$ under epitaxial constraints applicable to growth on perovskite substrates. We obtain a phase diagram in temperature and misfit strain that is qualitatively different from that reported by Pertsev, Zembilgotov, and Tagantsev [Phys. Rev. Lett. 80, 1988 (1998)], who based their results on an empirical thermodynamic potential with parameters fitted at temperatures in the vicinity of the bulk phase transitions. In particular, we find a region of “$r$ phase” at low temperature where Pertsev et al. have reported an “$ac$ phase.” We expect our results to be relevant to thin epitaxial films of ${\text{BaTiO}}_3$ at low temperatures and experimentally achievable strains.

Figure 1

Phase diagrams of epitaxial ${\text{BaTiO}}_3$ as predicted by the theory of Pertsev et al. (see Ref. 9). (a) Using the parameters quoted in Ref. 9. (b) Using the parameters quoted in Ref. 11. The second- and first-order phase transitions are represented by thin and thick lines, respectively.

Figure 2

(Color online) Energies of the possible epitaxial ${\text{BaTiO}}_3$ phases for different misfit strains, as obtained from the full ab initio calculations. The vertical lines denote the phase transition points given by the stability analysis.

Figure 3

(Color online). Displacements of the atoms from the cubic perovskite cell positions, for the most energetically favorable configuration at a given misfit strain. The vertical lines denote the phase transition points obtained from the stability analysis. ${\Delta }_3\left(\text{Ti}\right)$ labels the displacement of the Ti atom in units the third lattice vector, etc.

Figure 4

Phase diagram of epitaxial ${\text{BaTiO}}_3$ obtained using the effective Hamiltonian of Zhong, Vanderbilt and Rabe (see Ref. 19).