180° Domain-Wall Energies in BaTiO3

Calculations of the energies and thicknesses of four possible 180° domain walls in BaTi${\mathrm{O}}_3$ are reported, two perpendicular to $〈100〉$ and two perpendicular to $〈110〉$, based on a microscopic model which accounts for the internal fields in the wall region in a self-consistent fashion. The Ti shifts are determined by an energy-minimization procedure, and the nonlinearity of the oxygen polarizability is included in the treatment. All four walls are found to have essentially zero thickness, and wall energies of 1.52, 10.3, 45.3, and 47.9 erg/${\mathrm{cm}}^2$ for the (100), (220), (110), and (200) domain walls, respectively. An exact solution of the Miller-Weinreich nucleation model of 180° domain-wall motions admits a (220) wall energy no larger than 1.22 erg/${\mathrm{cm}}^2$, although this model is shown to predict that the (100) wall energy is less than the (220) wall energy, contrary to Miller and Weinreich's original analysis. The calculated wall-energy anisotropy is in quantitative agreement with estimates derived from experimental studies of the equilibrium domain structure of BaTi${\mathrm{O}}_3$ at room temperature.