3D polarization texture of a symmetric 4-fold flux closure domain in strained ferroelectric PbTiO₃ films

Although the strong coupling of polarization to spontaneous strain in ferroelectrics would impart a flux-closure with severe disclination strains, recent studies have successfully stabilized such a domain via a nano-scaled multi-layer growth. Nonetheless, the detailed distributions of polarizations in three-dimensions (3D) and how the strains inside a flux closure affect the structures of domain walls are still less understood. Here we report a 3D polarization texture of a 4-fold flux closure domain identified in tensile strained ferroelectric PbTiO₃/SrTiO₃ multilayer films. Ferroelectric displacement analysis based on aberration-corrected scanning transmission electron microscopic imaging reveals highly inhomogeneous strains with strain gradient above 10⁷/m. These giant disclination strains significantly broaden the 90° domain walls, while the flexoelectric coupling at 180° domain wall is less affected. The present observations are helpful for understanding the basics of topological dipole textures and indicate novel applications of ferroelectrics through engineering strains.