Theory of PbTiO₃, BaTiO₃, and SrTiO₃ surfaces

First-principles total-energy calculations are carried out for (001) surfaces of the cubic perovskite ATiO₃ compounds PbTiO₃ , BaTiO₃ , and SrTiO₃. Both AO-terminated and TiO₂-terminated surfaces are considered, and fully-relaxed atomic configurations are determined. In general, BaTiO₃ and SrTiO₃ are found to have a rather similar behavior, while PbTiO₃ is different in many respects because of the partially covalent character of the Pb-O bonds. PbTiO₃ and BaTiO₃ are ferroelectrics, and the influence of the surface upon the ferroelectric distortions is studied for a tetragonal ferroelectric distortion parallel to the surface. The surface relaxation energies are found to be substantial, i.e., many times larger than the bulk ferroelectric well depth. Nevertheless, the influence of the surface upon the ferroelectric order parameter is modest, and is qualitatively as well as quantitatively different for the two materials. Surface energies and electronic properties are also computed. It is found that for BaTiO₃ and SrTiO₃ surfaces, both AO-terminated and TiO₂-terminated surfaces can be thermodynamically stable, whereas for PbTiO₃ only the PbO surface termination is stable.