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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 (GLD) model with parameters of Ref. [Hlinka and Marton, Phys. Rev. 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. 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-degree and 60-degree walls. In the rhombohedral phase, the lowest energy walls are the 71-degree and 109-degree walls. All these ferroelastic walls have thickness below 1 nm except for the 90-degree wall in the tetragonal phase and the 60-degree S-wall in the orthorhombic phase, for which the larger thickness of the order of 5 nm was found. The antiparallel walls of the rhombohedral phase have the largest energy and thus they are unlikely to occur. The calculation indicates that the lowest energy structure of the 109-degree wall and few other domain walls in the orthorhombic and rhombohedral phases resemble Bloch-like walls known from magnetism.

There are two types of domain walls, O120 and R180{110}, for which the polarization profiles shown in Figs. 7 and 9(b) were not correctly calculated in the paper. 1 The polarization profiles were obtained numerically from constrained Euler-Lagrange equations. These equations can be written in the formwhere G rsrs , G rsts , and G tsts are components of the rotated gradient tensor. By mistake, G rsts terms were omitted in the paper. The correct profiles of polarization across the O120 and R180{110} domain walls, which do take into account the G rsts terms, are displayed here in Figs. 1 and 2. In all other domain walls considered in the paper, G rsts terms are zero for symmetry reasons. This Erratum does not affect any other result or the conclusion of the paper. FIG. 1. Trajectories of O120 (a) and R180{110} (b) domain walls superimposed with corresponding Euler-Lagrange energy surfaces. These two panels should replace the corresponding panels in the Fig. 7 of the paper. FIG. 2. Polarization profiles across the R180{110} domain wall, which should replace Fig. 9(b). 1 P. Marton, I. Rychetsky, and J. Hlinka, Phys. Rev. B 81, 144125 (2010). 139906-1

The piezoelectric properties of tetragonal BaTiO(3) crystals with a very high density of 90 degrees twin domain boundaries are analyzed in the framework of the Ginzburg-Landau-Devonshire theory. Computer simulations predict a considerable enhancement of piezoelectric coefficients for domain thicknesses below 50 nm. This enhancement is much larger than the effect of the domain wall broadening mechanism of Rao and Wang (2007 Appl. Phys. Lett. 90 041915), but it is still a too weak effect to explain the domain density enhancement observed in the experiments of Wada and Tsurumi (2004 Br. Ceram. Trans. 103 93). The phenomenon observed here should nevertheless manifest in materials with nanoscopic domains, such as relaxor ferroelectrics and artificial ferroelectric nanostructures.

The seminal paper by Zhirnov (1958 Zh. Eksp. Teor. Fiz. 35 1175-80) explained why the structure of domain walls in ferroelectrics and ferromagnets is drastically different. Here we show that the antiparallel ferroelectric walls in rhombohedral ferroelectric BaTiO(3) can be switched between the Ising-like state (typical for ferroelectrics) and a Bloch-like state (unusual for ferroelectric walls but typical for magnetic ones). Phase-field simulations using a Ginzburg-Landau-Devonshire model suggest that this symmetry-breaking transition can be induced by a compressive epitaxial stress. The strain-tunable chiral properties of these domain walls promise a range of novel phenomena in epitaxial ferroelectric thin films.

Ferroelectric domain walls (FDWs) are usually considered to be of Ising type, but there have been suggestions in recent years that Bloch-type FDWs are also possible in some cases, e.g., in the rhombohedral phase of BaTiO3. The mechanically compatible and electrically neutral FDWs in rhombohedral BaTiO3 are of 71 • , 109 • , and 180 • type. We have investigated these FDWs based both on first-principles calculations and on a Ginzburg-Landau-Devonshire (GLD) model [P. Marton, I. Rychetsky, and J. Hlinka, Phys. Rev. B 81, 144125 (2010)]. The results from both approaches confirm the Ising nature of the 71 • FDW and the Bloch nature of the 180 • FDW, and predict both Ising-type and Bloch-type FDWs are possible for the 109 • case. Considering the relatively small rhombohedral strain in BaTiO3, the competition between the energies of Bloch and Ising FDWs can be discussed in terms of a picture in which a Bloch wall is regarded as being composed of a pair of smaller-angle Ising ones. A reduction by 40% in the parameters describing the gradient term in the GLD model brings it into better agreement with the first-principles results for detailed properties such as the energies and widths of the FDWs.

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