Related papers: Nonequilibrium dynamics of magnetic hopfions drive…
Knots, characterized by topological invariants called the Hopf number $H$, arise from the intertwining of strings and exhibit diverse configurations. The knot structures have recently been observed in condensed matters, as examplified by a…
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…
Magnetic hopfion is three-dimensional (3D) topological soliton with novel spin structure that would enable exotic dynamics. Here we study the current driven 3D dynamics of a magnetic hopfion with unit Hopf index in a frustrated magnet.…
Magnetic hopfions are three-dimensional topological solitons with non-zero Hopf index ${\cal H}$ in the vector field of material's local magnetization. In this Letter elliptical stability of hopfions with ${\cal H}=1$ in a classical…
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…
Resonant spin dynamics of topological spin textures are correlated with their topological nature, which can be employed to understand this nature. In this study, we present resonant spin dynamics of three-dimensional topological spin…
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 magnetic textures have attracted considerable interest since they exhibit new properties and might be useful in information technology. Magnetic hopfions are three-dimensional (3D) spatial variations in the magnetization with a…
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…
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…
Hopfions are a class of three-dimensional (3D) solitons which are built as vortex tori carrying intrinsic twist of the toroidal core. They are characterized by two independent topological charges, \textit{viz}., vorticity $S$ and winding…
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 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…
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 $z=0$…
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…
Topological magnetic structures, such as Hopfions, are central to three-dimensional magnetism, but their characterization in complex geometries remains challenging. We introduce a robust finite-element method for calculating the Hopf index…
Spin-orbit torques (SOTs) are widely used to control magnetization in nanoscale electric systems and are typically assumed to drive skyrmion nucleation and motion in a deterministic manner, especially in materials with strong…
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…
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…
e study the solitons, stabilized by spin precession in a classical two--dimensional lattice model of Heisenberg ferromagnets with non-small easy--axis anisotropy. The properties of such solitons are treated both analytically using the…