First-principles study of ferroelectric and antiferrodistortive instabilities in tetragonal SrTiO3

We carry out first principles density-functional calculations of the antife rrodistortive (AFD) and ferroelectric (FE) soft-mode instabilities in tetra gonal SrTiO3, with the structural degrees of freedom treated in a classical , zero-temperature framework. In particular, we use frozen-phonon calculati ons to make a careful study of the anisotropy of the AFD and FE mode freque ncies in the tetragonal ground state, in which an R-point AFD soft phonon h as condensed. Because of the anharmonic couplings, the presence of this AFD distortion substantially affects both the AFD and FE mode frequencies. The AFD mode is found to be softer for rotations around a perpendicular axis ( E-g mode) than for rotations about the tetragonal axis (A(1g) mode), in agr eement with experimental results. The FE mode, on the other hand, is found to be softer when polarized perpendicular to the tetragonal axis (E-u, mode ) than parallel to it (A(Zu) mode). The sign of this frequency splitting is consistent with the experimentally reported anisotropy of the dielectric s usceptibility and other evidence. Finally, we present a discussion of the i nfluence of various types of structural distortions on the FE instability a nd its anisotropy.