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We carry out first-principles density-functional calculations of theantiferrodistortive (AFD) and ferroelectric (FE) soft-mode instabilities intetragonal SrTiO3, with the structural degrees of freedom treated in aclassical, zero-temperature framework. In particular, we use frozen-phononcalculations to make a careful study of the anisotropy of the AFD and FE modefrequencies in the tetragonal ground state, in which an R-point AFD soft phononhas condensed. Because of the anharmonic couplings, the presence of this AFDdistortion substantially affects both the AFD and FE mode frequencies. The AFDmode is found to be softer for rotations around a perpendicular axis (Eg mode)than for rotations about the tetragonal axis (A1g mode), in agreement withexperimental results. The FE mode, on the other hand, is found to be softerwhen polarized perpendicular to the tetragonal axis (Eu mode) than parallel toit (A2u mode). The sign of this frequency splitting is consistent with theexperimentally reported anisotropy of the dielectric susceptibility and otherevidence. Finally, we present a discussion of the influence of various types ofstructural distortions on the FE instability and its anisotropy.

physical review. b, condensed matter

First-principles study of ferroelectric and antiferrodistortive instabilities in tetragonal<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">SrTiO</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

First-principles study of ferroelectric and antiferrodistortive instabilities in tetragonalSrTiO3