Related papers: Topological characterization of Hopfions in finite…

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…

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…

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…

Three-dimensional magnetic textures, such as Hopfions, torons, and skyrmion tubes, possess rich geometric and topological structure, but their detailed energetics, deformation modes, and collective behavior are yet to be fully understood.…

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…

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…

The Hopf index, a topological invariant that quantifies the linking of preimage fibers, is fundamental to the structure and stability of hopfions. In this work, we propose a new mathematical framework for modeling hopfions with high Hopf…

Magnetic hopfions are localized magnetic solitons with a nonzero 3D topological charge (Hopf index). Herein, an analytical calculation of the magnetic hopfion gyrovector is presented and it is shown that it does not vanish even in an…

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…

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 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.…

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…

An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in…

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…

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)…

Hopf insulators are intriguing three-dimensional topological insulators characterized by an integer topological invariant. They originate from the mathematical theory of Hopf fibration and epitomize the deep connection between knot theory…

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…

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…

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…

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…