Phenomenological model of a 90° domain wall inBaTiO3-type ferroelectrics

The properties of ferroelectric-ferroelastic twin boundaries in tetragonal $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$-like crystals are analyzed in the framework of the phenomenological Ginzburg-Landau-Devonshire model. Special attention is paid to the introduction and appreciation of the gradient and dipole-dipole terms, which depends on inhomogeneous polarization. An adjustment of the model parameters to the bulk properties of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$ allows us to make quantitative predictions for domain-wall profiles and widths (at ambient conditions, $3.6\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and $0.6\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ for fully relaxed 90\ifmmode^\circ\else\textdegree\fi{} and 180\ifmmode^\circ\else\textdegree\fi{} domain walls).