Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy
A. B. Borisov, F. N. Rybakov
TL;DR
This paper reports the discovery and analysis of three-dimensional toroidal Hopfions in a uniaxial ferromagnet, characterized by their nonzero Hopf index and uniform motion along the anisotropy axis, using numerical solutions of the Landau-Lifshitz equation.
Contribution
It introduces a new class of moving toroidal Hopfions in ferromagnets and provides their structural and existence conditions through numerical analysis.
Findings
Identified stable toroidal Hopfions with nonzero Hopf index
Mapped the existence region of these solitons in parameter space
Demonstrated their uniform motion along the anisotropy axis
Abstract
Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.
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