The stability of vortex-like structures in uniaxial ferromagnets

Two-dimensional localized states in the form of isolated vortices are studied systematically in uniaxial ferromagnets with an antisymmetric `Dzyaloshinsky’ exchange interaction. In addition to previously investigated π-vortices, new types of localized solutions were found. Their structure and equilibrium parameters were calculated by numerically solving the differential equations. We studied the stability of all solutions with respect to small radial distortions by solving the eigenvalue problem for the perturbation energy. It turned out that single vortices as well as multiple vortices with a magnetization rotation kπ(k=2,3,…) are stable in certain parameter regions, while other solutions of the differential equations such as vortices with nodes and large or blown-up vortices are always radially unstable. The stability analysis also answered the question of the decay modes of the stable solutions at their stability limits.