Leapfrogging vortex rings in the Landau-Lifshitz equation

Abstract

Vortex rings are ubiquitous in fluids, with smoke rings being a familiar example. The interaction of multiple vortex rings produces complex dynamical behaviour, such as the leapfrogging motion first analysed by Helmholtz more than a century and a half ago. Here we report on numerical investigations of vortex ring dynamics in a different setting from fluids, namely, as solutions of the Landau-Lifshitz equation that models the evolution of the local magnetization in a ferromagnetic medium. We present the results of the first study on the dynamics of interacting magnetic vortex rings and provide a novel link between fluids and magnetism, by showing that a range of phenomena familiar in fluids are reproduced in ferromagnets. This includes the leapfrogging motion of a pair of vortex rings and evidence for the chaotic dynamics of a trio of rings.

18 pages, 9 figures. Version to appear in Nonlinearity

References in corpus (4)

• Microscopic approach to current-driven domain wall dynamics
• Rotating vortex dipoles in ferromagnets
• Vortex rings in ferromagnets
• Scattering of knotted vortices (Hopfions) in the Faddeev-Skyrme model

Cited by in corpus (6)

• Scattering and leapfrogging of vortex rings in a superfluid
• Solitons in a continuous classical Haldane-Shastry spin chain
• Rings on strings in excitable media
• Perturbations of vortex ring pairs
• Chern-Simons Improved Hamiltonians for Strings in Three Space Dimensions
• Quantum Magnets and Matrix Lorenz Systems