Vortex rings in ferromagnets

Abstract

Vortex ring solutions are presented for the Landau-Lifshitz equation, which models the dynamics of a three-dimensional ferromagnet. The vortex rings propagate at constant speed along their symmetry axis and are characterized by the integer-valued Hopf charge. They are stable to axial perturbations, but it is demonstrated that an easy axis anisotropy results in an instability to perturbations which break the axial symmetry. The unstable mode corresponds to a migration of spin flips around the vortex ring that leads to a pinching instability and ultimately the collapse of the vortex ring. It is found that this instability does not exist for an isotropic ferromagnet. Similarities between vortex rings in ferromagnets and vortons in cosmology are noted.

13 pages, 6 figures

References in corpus (7)

• To be or knot to be?
• Solitons, Links and Knots
• Knots in the Skyrme-Faddeev model
• ``Smoke Rings'' in Ferromagnets
• Vorton Existence and Stability
• On the Behaviour and Stability of Superconducting Currents
• Localized Solutions in a 2 Dimensional Landau-Lifshitz Model

Cited by in corpus (21)

• Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles
• Stationary ring solitons in field theory - knots and vortons
• Vortex solitons: Old results and new perspectives
• Three-dimensional droplets of swirling superfluids
• Skyrmion knots in frustrated magnets
• Binding a Hopfion in Chiral Magnet Nanodisk
• Static Hopf Solitons and Knotted Emergent Fields in Solid-State Noncentrosymmetric Magnetic Nanostructures
• Topological Hall signatures of magnetic hopfions
• Torus knots as Hopfions
• Vorton construction and dynamics
• Winding Hopfions on R^2 x S^1
• Scattering of knotted vortices (Hopfions) in the Faddeev-Skyrme model
• Solitons in a continuous classical Haldane-Shastry spin chain
• Kinky Vortons
• Spacetime magnetic hopfions: from internal excitations and braiding of skyrmions
• Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy
• Numerical Calculation of the Hopf Index for 3D Magnetic Textures
• Leapfrogging vortex rings in the Landau-Lifshitz equation
• Stationary Precession Topological Solitons with Nonzero Hopf Invariant in a Uniaxial Ferromagnet
• Nontrivial Causal Structures Engendered by Knotted Solitons
• Three-dimensional topological orbital Hall effect caused by magnetic hopfions