Domain walls of ferroelectric BaTiO3 within the Ginzburg-Landau-Devonshire phenomenological model

Mechanically compatible and electrically neutral domain walls in tetragonal, orthorhombic, and rhombohedral ferroelectric phases of BaTiO3 are systematically investigated in the framework of the phenomenological Ginzburg-Landau-Devonshire model with parameters of J. Hlinka and P. Marton, Phys. Rev. B 74, 104104 (2006). Polarization and strain profiles within domain walls are calculated numerically and within an approximation leading to the quasi-one-dimensional analytic solutions applied previously to the ferroelectric walls of the tetragonal phase [W. Cao and L. E. Cross, Phys. Rev. B 44, 5 (1991)]. Domain-wall thicknesses and energy densities are estimated for all mechanically compatible and electrically neutral domain-wall species in the entire temperature range of ferroelectric phases. The model suggests that the lowest-energy walls in the orthorhombic phase of BaTiO3 are the 90 degrees and 60 degrees walls. In the rhombohedral phase, the lowest-energy walls are the 71 degrees and 109 degrees walls. All these ferroelastic walls have thickness below 1 nm except for the 90 degrees wall in the tetragonal phase and the 60 degrees S wall in the orthorhombic phase, for which the larger thickness on the order of 5 nm was found. The antiparallel walls of the rhombohedral phase have largest energy and thus they are unlikely to occur. The calculation indicates that the lowest-energy structure of the 109 degrees wall and few other domain walls in the orthorhombic and rhombohedral phases resemble Bloch walls known from magnetism.