Related papers: Magnetic hopfions in solids
Localized magnetic topological solitons with Hopf index of 1 in an unbounded bulk magnet are studied theoretically, starting with the classical micromagnetic Hamiltonian. It is shown analytically that (like Bloch and N\'eel walls in…
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 spin textures exhibit a hierarchical nature. For instance, magnetic skyrmions, which possess a particle-like nature, can aggregate to form superstructures such as skyrmion strings and skyrmion lattices. Magnetic hopfions are…
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…
A new type of three-dimensional magnetic soliton in easy-axis ferromagnets is predicted by taking simultaneous account of the Dzyaloshinsky-Moriya interaction and an external magnetic field. The numerically obtained static three-dimensional…
Magnetic hopfions are non-collinear spin textures that are characterized by an integer topological invariant, called Hopf index. The three-dimensional magnetic solitons can be thought of as a tube with a twisted magnetization that has been…
In this paper we construct explicitly an infinite number of Hopfions (static, soliton solutions with non-zero Hopf topological charges) within the recently proposed 3+1-dimensional, integrable and relativistically invariant field theory.…
Hopfions are localized and topologically non-trivial magnetic configurations that have received considerable attention in recent years. Through a micromagnetic approach, we analyze the scattering of spin waves by magnetic hopfions. We show…
Hopfions, as three-dimensional topologically nontrivial structures described by poloidal and toroidal winding numbers, hold promise as robust information carriers in spintronics, functional materials, and optical communications. Although…
Magnetic hopfions are three-dimensional topological solitons -- knotted, vortex-like spin configurations. In chiral magnets, hopfions can appear as isolated structures or they can be linked to skyrmion strings. Previous studies employed a…
Toroidal modes in the form of so-called Hopfions, with two independent winding numbers, a hidden one (twist, s), which characterizes a circular vortex thread embedded into a three-dimensional soliton, and the vorticity around the vertical…
Topological spin configurations, such as soliton-like spin texture and Dirac electron assemblies, have emerged in recent years in both fundamental science and technological applications. Achieving stable topological spin textures at…
This work provides the first experimental elucidation of quantum topological effects in individual hopfions, establishing their potential as building blocks for three-dimensional topological quantum spintronics. The observed Non-Abelian…
We find exact static soliton solutions for the unit spin vector field of an inhomogeneous, anisotropic three-dimensional Heisenberg ferromagnet. Each soliton is labeled by two integers $n$ and $m$. It is a (modified) skyrmion in the $z=0$…
Cubic chiral magnets exhibit a remarkable diversity of two-dimensional topological magnetic textures, including skyrmions. However, the experimental confirmation of topological states localized in all three spatial dimensions remains…
We extend the definition of hopfions to include a class of spin-$h$ fields and use this to introduce the electromagnetic and gravitational hopfions of different algebraic types. The fields are constructed through the Penrose contour…
In this paper, we study topological properties of 3D lattice dimer model. We demonstrate, that the dimer model on a bipartite lattice possesses topological defects, which are exactly characterized by Hopf invariant. We derive its explicit…
We present micromagnetic simulations on resonant spin wave modes of magnetic Hopfions up to 15 GHz driven by external magnetic fields. A sharp transition is found around 32 mT coinciding with a transition from Hopfions to magnetic torons.…
Pursuing topological phases in natural and artificial materials is one of the central topics in modern physical science and engineering. In classical magnetic systems, spin waves (or magnons) and magnetic solitons (such as domain wall,…
Knots and links play a crucial role in understanding topology and discreteness in nature. In magnetic systems, twisted, knotted and braided vortex tubes manifest as Skyrmions, Hopfions, or screw dislocations. These complex textures are…