Ab initio study of the phase diagram of epitaxial 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.