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.

References in corpus (13)

• Knots and Particles
• Reconfigurable knots and links in chiral nematic colloids
• Domain walls of ferroelectric BaTiO3 within the Ginzburg-Landau-Devonshire phenomenological model
• Ultrathin films of ferroelectric solid solutions under residual depolarizing field
• Abrupt appearance of the domain pattern and fatigue of thin ferroelectric films
• Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures
• Toroidal ferroelectricity in PbTiO3 nanoparticles
• Topological phase transformations and intrinsic size effects in ferroelectric nanoparticles
• Electrodynamics of ferroelectric films with negative capacitance
• Collective behavior of active topological solitons, knotted streamlines, and transport of cargo in liquid crystals
• Classification of Electromagnetic and Gravitational Hopfions by Algebraic Type
• Harnessing ferroelectric domains for negative capacitance
• Electromechanical control of polarization vortex ordering in an interacting ferroelectric-dielectric composite dimer

Cited by in corpus (28)

• Topological Transformation and Free-Space Transport of Photonic Hopfions
• Review: Topology of solitons and singular defects in chiral liquid crystals
• Magnetic hopfions in solids
• Chiral ground states of ferroelectric liquid crystals
• Ferroelectric nematic liquids with conics
• Spontaneous electric-polarization topology in confined ferroelectric nematics
• Ferroelectric Solitons Crafted in Epitaxial Bismuth Ferrite Superlattices
• Current Advances in Magnetoelectric Composites with Various Interphase Connectivity Types
• Vector, Bidirector and Bloch Skyrmion Phases Induced by Structural Crystallographic Symmetry Breaking
• Electronic scattering off a magnetic hopfion
• Dynamical manipulation of polar topologies from acoustic phonon pumping
• Topological solitonic macromolecules
• Emergent magnetic field and vector potential of the toroidal magnetic hopfions
• Ferroelectric texture of individual barium titanate nanocrystals
• Splay-bend elastic inequalities shape tactoids, toroids, umbilics, and conic section walls in paraelectric, twist-bend, and ferroelectric nematics
• Vortex states in a PbTiO${}_3$ ferroelectric cylinder
• Terahertz-field activation of polar skyrons
• Exact Hopfion Vortices in a 3D Heisenberg Ferromagnet
• Emergent Magnetic Field and Nonzero Gyrovector of the Toroidal Magnetic Hopfion
• Strain dependence of the Bloch domain component in 180${}^{\circ }$ domains in bulk PbTiO${}_3$ from first-principles
• Poincaré sphere engineering of dynamical ferroelectric topological solitons
• Topological protection breakdown: a route to frustrated ferroelectricity
• Tip-induced domain protrusion in ferroelectric films with in-plane polarization
• Controllable skyrmion chirality in ferroelectrics
• Theory of Polar Skyrmions in Layered Structure of Ferroelectric Perovskites
• Unconventional criticality in $O(D)$-invariant loop-constrained Landau theory
• Deformed states in paraelectric and ferroelectric nematic liquid crystals
• Construction of Hopfion Crystals