Coupling of surface relaxation and polarization in PbTiO₃ from atomistic simulation

Molecular dynamics simulations are used to characterize ferroelectricity on the (001) surfaces of PbTiO₃ (PT), one of the most widely studied ferroelectric materials. Two different empirical interatomic shell model potentials are used. Both PbO and TiO₂ surface terminations in PT under open circuit electrical boundary conditions are characterized. The results are found to be in good agreement with the results of density functional theory calculations. The atomic relaxations, interlayer spacings and surface rumplings of each of the four possible surface terminations are analyzed. The deviation of the polarization from the bulk value is observed to be larger when the polarization points out of the surface than when it points into the surface. Analysis of the surface energies for free-standing films shows that polarization parallel to the surface is energetically more favorable than the polarization normal to the surfaces.