Topological polarization networking in uniaxial ferroelectrics

Discovery of topological polarization textures has put ferroelectrics at the frontier of topological matter science. High-symmetry ferroelectric oxide materials allowing for freedom of the polarization vector rotation offer a fertile ground for emergent topological polar formations, like vortices, skyrmions, merons, and Hopfions. It has been commonly accepted that uniaxial ferroelectrics do not belong in the topological universe because strong anisotropy imposes insurmountable energy barriers for topological excitations. Here we show that uniaxial ferroelectrics provide unique opportunity for the formation of topological polarization networks comprising branching intertwined domains with opposite counterflowing polarization. We report that they host the topological state of matter: a crisscrossing structure of topologically protected colliding head-to-head and tail-to-tail polarization domains, which for decades has been considered impossible from the electrostatic viewpoint. The domain wall interfacing the counterflowing domains is a multiconnected surface, propagating through the whole volume of the ferroelectric.