First-principles self-consistent phonon approach to the study of the vibrational properties and structural phase transition of BaTiO3

Abstract

We investigate the cubic-to-tetragonal ferroelectric phase transition temperature ${T}_{c}$ of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$ through a first-principles self-consistent phonon scheme. This method extends the harmonic approximation by incorporating anharmonic effects due to thermalized displacements, which are simultaneous excitations of phonons with a temperature-dependent random amplitude. The calculated forces are analyzed with an effective harmonic force constant model, which serves as the basis for a new set of thermalized displacements until self-consistency has been reached. The phonons with imaginary frequencies at $T=0$ K are stabilized due to anharmonic effects in the temperature range where the corresponding phase is stable and the dynamical instabilities disappear. Using the calculated free energies at various temperatures, volumes, and $c/a$ ratios, we obtain a thermal expansion in good agreement with the experimental values. Comparing the free energies of the tetragonal and cubic phases at different temperatures, we predict ${T}_{c}\ensuremath{\approx}455\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. This is in reasonable agreement with the experimental value of $\ensuremath{\approx}393$ K in view of the strong influence of the particular density functional theory approximation on the unstable phonon modes.