First-principles Study of the Structural Instabilities in Hexagonal Barium Titanate: Coupling between the Soft Optical and the Acoustic Modes

Hexagonal BaTiO3 undergoes a structural phase transition to an orthorhombic C2221 phase at T0 = 222 K. The transition is driven by a soft optical mode with E2u symmetry whose couplings force the appearance of a spontaneous E2g strain (improper ferroelastic character). Staying within the same E2u subspace, the system could in principle settle into a second (not observed) orthorhombic phase (Cmc21). We have carried out a first-principles investigation of these questions, studying the structure of the existing C2221 and the virtual Cmc21 phases, and describing the spontaneous E2g strain in accord with the experimental observations. In addition, we show that the occurrence of C2221 instead of Cmc21 cannot be explained by the E2u soft modes themselves and, therefore, must be related to their couplings with secondary order parameters. A more detailed analysis proves that the E2g strains do not account for the experimental preference.