Triangular frustration of ferroelectric domains

The recent discovery of chiral electric dipoles in PbTiO3 thin films, including vortices [1] and skyrmions [2], has attracted tremendous interest from both fundamental and practical points of view. To date, these textures have been exclusively produced in (001)-oriented films, where the tetragonal PbTiO3 exhibits three structural variants, namely a1/a2 and c domains with their polarization along the in-plane and out-of-plane directions, respectively. By contrast, the domain structures in (111)-oriented PbTiO3 films have not been systematically explored yet. Along the (111) orientation, PbTiO3 is expected to have three energetically degenerate structural variants, which constitute a markedly different situation for domain formation and its control. We propose a diffuse x-ray scattering study in which we will determine the nature of ferroelectric domain structures in a series of PbTiO3 films grown along the (111) orientation.