Ab initio study of the phase diagram of epitaxial BaTiO₃

Using a combination of first-principles and effective-Hamiltonian approaches, we map out the structure of BaTiO₃ 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 BaTiO₃ at low temperatures and experimentally achievable strains.