Emergent Magnetic Field and Nonzero Gyrovector of the Toroidal Magnetic Hopfion

Abstract

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 infinite sample. The calculation method is based on the concept of the emergent magnetic field. The particular case of the simplest nontrivial toroidal hopfion with the Hopf index $\Vert Q_H\Vert =1$ in the cylindrical magnetic dot is considered and dependencies of the gyrovector components on the dot sizes are calculated. Nonzero hopfion gyrovector is important in any description of the hopfion dynamics within the collective coordinate Thieles approach.

6 pages, 3 figures

References in corpus (8)

• Creation and confirmation of Hopfions in magnetic multilayer systems
• Particle-like topologies in light
• Topological Transformation and Free-Space Transport of Photonic Hopfions
• Three-dimensional dynamics of magnetic hopfion driven by spin transfer torque
• Topological Hall signatures of magnetic hopfions
• Classification of Electromagnetic and Gravitational Hopfions by Algebraic Type
• Emergent Magneto-multipoles and Nonlinear Responses of a Magnetic Hopfion
• Geometric transformation and three-dimensional hopping of Hopf solitons

Cited by in corpus (3)

• Emergent magnetic field and vector potential of the toroidal magnetic hopfions
• Three-dimensional topological orbital Hall effect caused by magnetic hopfions
• Dipolar-exchange spin waves in thin bilayers