Entangled polarizations in ferroelectrics: A focused review of polar topologies

Ferroelectric crystals feature asymmetric or polar structures that are switchable under an external electric field, holding promise for information storage. Nanoscale ferroelectrics might exhibit various exotic domain configurations and polar topologies, such as full flux-closure, vortex, skyrmion, and meron. These topological domains were theoretically switchable and may give rise to an unusually high density of memory bits. They would also undergo unusual phase transitions and form hidden, collective polar topological states under external stimulations. Similar domains and spin topologies are well known in ferromagnetic materials, and their topological properties and dynamics are under intensive investigation. However, in ferroelectric materials, the coupling of polarizations to spontaneous strains would be so pronounced that the formations of polar topologies were believed to be impossible. How to stabilize the polar topologies in ferroelectrics, especially in nanoscale ferroelectrics, was known as a big challenge. In this overview, we summarize the recent progress in polar topologies in ferroelectric oxides. We start from a review the discovery of polar topologies, including flux-closure quadrant, vortex, bubble, skyrmion, meron lattice, polar waves, and center-type domains. We also focus on the effects of mechanical and electrical boundary conditions and sample size on the formation of topological structures. In the meanwhile, we emphasize the use of aberration-corrected transmission electron microscope which enables to visualize the ion displacement at a sub-Ångström resolution in real space. And at the end, we envision several aspects to be considered in the future, such as imaging three dimensional (3D) atomic morphology of the topological polar structures, exploring novel polar topologies in other possible systems, and addressing the coupling of polar topologies with flexoelectricity by a combination of quantitative transmission electron microscopy and relevant theoretical approaches.