相关论文: Hopfions emerge in ferroelectrics

Hopfions are an intriguing class of string-like solitons, named according to a classical topological concept classifying three-dimensional direction fields. The search of hopfions in real physical systems is going on for nearly half a…

Structured light fields embody strong spatial variations of polarisation, phase and amplitude. Understanding, characterization and exploitation of such fields can be achieved through their topological properties. Three-dimensional (3D)…

Two-dimensional topological solitons, commonly called Skyrmions, are extensively studied in solid-state magnetic nanostructures and promise many spintronics applications. However, three-dimensional topological solitons dubbed hopfions have…

3D topological solitons are marvels of mathematical physics that arise in theoretical models in elementary particle and nuclear physics, condensed matter, and cosmology. A particularly interesting type of them is described by the…

Magnetic hopfions are string-like three-dimensional topological solitons, characterised by the Hopf invariant. They serve as a fundamental prototype for three-dimensional magnetic quasi-particles and are an inspiration for novel device…

Topological solitons have been studied for decades in classical field theories, and have started recently to impact condensed matter physics. Among those solitons, magnetic skyrmions are two-dimensional particle-like objects with a…

Three-dimensional topological solitons attract a great deal of interest in fields ranging from particle physics to cosmology but remain experimentally elusive in solid-state magnets. Here we numerically predict magnetic heliknotons, an…

Spatial topology endows topological solitons, such as skyrmions and hopfions, with fascinating dynamics. However, the temporal dimension has so far provided a passive stage on which topological solitons evolve. Here we construct spacetime…

Topological solitons are relevant in several areas of physics [1]. Recently, these configurations have been investigated in contexts as diverse as hydrodynamics [2], Bose-Einstein condensates [3], ferromagnetism [4], knotted light [5] and…

Hopfions, higher-dimensional topological quasiparticles with sophisticated 3D knotted spin textures discovered in condensed matter and photonic systems, show promise in high-density data storage and transfer. Here we present crystalline…

Magnetic hopfions are three-dimensional topological solitons whose static stability has recently been confirmed in experiments, yet their dynamical modes remain largely unexplored. Here we combine micromagnetic simulations and analytical…

Magnetic hopfions are three-dimensional localized topological solitons in the volume of a magnet. In this work, starting with a classical free energy density of a helimagnet, an approximate variational model of hopfions is studied. The…

Several materials, such as ferromagnets, spinor Bose-Einstein condensates, and some topological insulators, are now believed to support knotted structures. One of the most successful base-models having stable knots is the Faddeev-Skyrme…

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…

Topological particle-like excitations such as skyrmions and hopfions offer rich opportunities for spintronic and photonic applications. While skyrmions have been extensively studied, the stabilization mechanisms and phase behavior of…

Magnetic hopfions are localized magnetic solitons with non-zero 3D topological charge (Hopf index). Here I present an analytical calculation of the toroidal magnetic hopfion vector potential, emergent magnetic field, the Hopf index, and the…

Magnetic hopfions in chiral magnets are topological solitons, localized in three dimensions. But is their localization strong? To address this question we derive an asymptotic expansion for the isolated hopfion's spatial profile. It becomes…

Hopfions, three-dimensional topological solitons characterized by nontrivial Hopf indices, represent a fundamental class of field configurations that emerge across diverse areas of physics. Despite extensive studies of isolated hopfions, a…

Topological solitons are knots in continuous physical fields classified by non-zero Hopf index values. Despite arising in theories that span many branches of physics, from elementary particles to condensed matter and cosmology, they remain…

Magnetic hopfions are topologically protected three-dimensional solitons that are constituted by a tube which exhibits a topologically nontrivial spin texture in the cross-section profile and is closed to a torus. Here we show that the…