Direct observation of continuous electric dipole rotation in flux-closure domains in ferroelectric Pb(Zr, Ti)O₃

Low-dimensional ferroelectric structures are a promising basis for the next generation of ultrahigh-density nonvolatile memory devices. Depolarization fields, created by incompletely compensated charges at the surfaces and interfaces, depress the polarization of such structures. Theory suggests that under conditions of uncompensated surface charges, local dipoles can organize in flux-closure structures in thin films and vortex structures in nano-sized ferroelectrics, reducing depolarization fields. However, the continuous rotation of the dipoles required in vortex structures and the behavior of unit cell dipoles in flux-closure structures have never been experimentally established. By aberration-corrected transmission electron microscopy, we obtained experimental evidence for continuous rotation of the dipoles closing the flux of 180° domains in a ferroelectric perovskite thin film.