Comparative study of [001] surface relaxations of perovskite titanates

Surface relaxations of the cubic perovskite SrTiO₃ and BaTiO₃ crystals have been studied in the framework of the shell model. The positions of atoms in several surface layers embedded into the electrostatic field of the remainder of the crystal were calculated. Ti⁴⁺, Sr²⁺, Ba²⁺ and O^2- ions in six near-surface layers are displaced differently from their crystalline sites. Such effects create the so-called surface rumpling, a dipole moment and the electric field in the near-surface region. Calculated atomic displacements were compared with the LEED experimental data and showed good agreement. Our simulations have demonstrated that the cubic perovskite SrTiO₃ crystals reveal surface polarization and accompanied by the presence of relevant electric field. This arises due to a disturbed force balance accompanying the surface creation and affect 5-6 planes below the surface. In other words, the surface can serve as important factor imposing a long-range order in paraelectric SrTiO₃. As discussed in the literature, the [001] surface turns out to be ferroelectric with properties different from the bulk material.