Abstract

Chiral magnetic skyrmions are topological solitons which can be stabilized in magnetically ordered systems with chiral Dzyaloshinskii-Moriya interaction. In magnetic films, skyrmions are commonly treated as topologically stable particle-like excitations which can be effectively controlled by spin-polarized currents. For this reason, they are considered as promising bit carriers in novel logic and memory devices. So, the understanding of dynamical properties of skyrmions has both applied and fundamental values. Here we consider skyrmions in uniaxial ferro- and antiferromagnetic films. In both cases, we provide a complete theoretical study of the spectrum of the skyrmion spin eigen-excitations. Additionally, we introduce effective models for ferro- and antiferromagnetic domain walls considering them as 2D topological strings. The string-models reproduce skyrmion spectra in the limit case of large skyrmion radii when the skyrmions can be treated as closed string loops. The topological density of a small-radius skyrmion in a bulk magnet is exponentially localized within a thin cord -- the 3D topological string. We propose a general dynamical model for such strings and study their linear and nonlinear excitations. We found a class of two-parametric solitary waves which travel with velocities 10^2 -- 10^3 m/s (data for FeGe) along the string. All theoretical predictions are verified by means of full-scale micromagnetic simulations.