Related papers: Three-Dimensional Domain-Wall Membranes

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…

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…

Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic…

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…

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…

To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterisation has proven essential. In particular, while the skyrmion number is a well-established topological invariant for 2D…

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…

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…

Three-dimensional topological spin textures have attracted growing interest due to their rich geometry and potential for functional magnetic phenomena. In this work, we propose the concept of symmetry-transforming magnetic models as a novel…

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.…

We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…

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…

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)…

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 (3D) topological states resemble truly localised, particle-like objects in physical space. Among the richest such structures are 3D skyrmions and hopfions that realise integer topological numbers in their configuration via…

Magnetic skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number describing the rotation of spins across the skyrmion. However, in real systems with a finite thickness of the…

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…

Magnetic skyrmions are chiral spin textures which have attracted intense research for their fundamentally novel physics and potential applications as spintronic information carriers. The stability which makes them so potentially useful is a…

Hopfions are three-dimensional (3D) topological textures characterized by the integer Hopf invariant $Q_H$. Here, we present the realization of a zero--field, stable hopfion spin texture in a magnetic system consisting of a chiral magnet…

Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to initiate and control their motion has opened a new field of research, skyrmionics,…