Unique vortex and stripe domain structures in PbTiO3 epitaxial nanodots

The domain structures of PbTiO₃ epitaxial nanodots under the influences of depolarization fields and mismatch strains have been studied using three dimensional phase field simulations. The single-vortex structure and mixed domain configuration, which consisted of zigzag stripe domain and closure dipole flux near the interfaces, were found to be effective in annihilating the depolarization fields in the isotropically tensile and compressive ferroelectric nanodots, respectively. These domain structures were produced by the combined effect of electrostatic and mismatch elastic energies. The width of stripe domain was found to be related to the volume percentage of polarization dipoles along the z-axis, which varied remarkably with the change of compressive mismatch strain. In the case of nanodots under anisotropic mismatch strains, double-vortex domain patterns and stripe domains with nearly straight domain walls were formed. Moreover, the domain structures with electrostatic energy neglected were also studied.