Bloch-type domain walls in rhombohedral BaTiO ₃

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 BaTiO ₃. The mechanically compatible and electrically neutral FDWs in rhombohedral BaTiO ₃ are of 71 ^a, 109 ^a, and 180 ^a type. We have investigated these FDWs based both on first-principles calculations and on a Ginzburg-Landau-Devonshire (GLD) model. The results from both approaches confirm the Ising nature of the 71 ^a FDW and the Bloch nature of the 180 ^a FDW, and predict both Ising-type and Bloch-type FDWs are possible for the 109 ^a case. Considering the relatively small rhombohedral strain in BaTiO ₃, 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.