The Properties of Isolated Magnetic Vortices

Abstract

Isolated magnetic vortices are stabilized by an antisymmetric exchange interaction, the so‐called Dzyaloshinsky interaction, which can be represented as an energy contribution linear in the first spatial derivatives of the magnetization vector. In contrast, vortex lines are demonstrated to be unstable in the bulk of regular uniaxial ferromagnets. They collapse spontaneously under the influence of anisotropy or an applied magnetic field. In reduced units the differential equation for isolated vortices contains two parameters: the reduced magnetic field h along the crystal axis and the material parameter \documentclass{article}\pagestyle{empty}\begin{document}$ \overline \chi $\end{document} which describes the relative contribution of the Dzyaloshinsky interaction term. Isolated vortices turn out to be always metastable for large fields, independent of \documentclass{article}\pagestyle{empty}\begin{document}$ \overline \chi $\end{document} as long as this parameter is positive. At low or negative fields they become unstable by two different mechanisms depending on the \documentclass{article}\pagestyle{empty}\begin{document}$ \overline \chi $\end{document}‐value, but altogether these micromagnetic structures turn out to be stable in a remarkably wide range of parameters. At the end possible applications are considered.