Hopfions emerge in ferroelectrics

Abstract: Paradigmatic knotted solitons, Hopfions, that are characterized by topological Hopf invariant, are widely investigated in the diverse areas ranging from high energy physics, cosmology and astrophysics to biology, magneto- and hydrodynamics and condensed matter physics. Yet, while holding high promise for applications, they remain elusive and under-explored. Here we demonstrate that Hopfions emerge as a basic configuration of polarization field in confined ferroelectric nanoparticles. Our findings establish that Hopfions govern a wealth of novel functionalities in the electromagnetic response of composite nanomaterials opening route to unprecedented technological applications.