Novel insight reveals topological tangle in unexpected corner of the universe

Scientists from the U.S. Department of Energy’s Argonne National Laboratory, in collaboration with the University of Picardie in France and the Southern Federal University in Russia, have discovered the presence of a Hopfion structure in ferroelectric nanoparticles. A Hopfion structure, first proposed by Austrian mathematician Heinz Hopf in 1931, emerges in a wide range of physical constructs, and one of its defining characteristics is that any two lines within the Hopfion structure must be linked, constituting knots ranging in complexity from a few interconnected rings to a mathematical rat’s nest. According to the current study, the polarization structure in a spherical ferroelectric nanoparticle takes on this same knotted swirl.