# Regensburg 2022 – wissenschaftliches Programm

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# KFM: Fachverband Kristalline Festkörper und deren Mikrostruktur

## KFM 30: Skyrmions 3 (joint session MA/KFM)

### KFM 30.3: Vortrag

### Freitag, 9. September 2022, 10:00–10:15, H37

**Generalization of the collective variables approach for skyrmion strings.** — •Volodymyr Kravchuk^{1,2} and Markus Garst^{1} — ^{1}Karlsruhe Institute of Technology, Germany. — ^{2}Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine

In a bulk saturated chiral magnet, the skyrmion core penetrates the ferromagnet volume forming a string-like object [1]. Here we describe the small-amplitude dynamics of the string, applying the generalized collective variable approach. For the collective variables, we use the coordinate- and time-dependent string position defined as the first moment of topological charge calculated for the continuously stacked horizontal cross-sections perpendicular to the applied magnetic field. The simplest "plane-wave" solution corresponds to the helix-shaped deformation of the string. In a nonlinear regime, this solution is unstable due to the Lighthill criterion, that results in a self-modulation of the wave. Using a multiscale analysis both in space and time, we show that this modulation is captured by a non-linear Schroedinger equation of focusing type. Two classes of non-linear periodic waves of skyrmion string (so-called dc- and cn-waves) are analytically predicted and numerically verified. The separatrix soliton solution just corresponds to the solitary wave found previously [1]. The developed approach is generalized for the case of arbitrary meaning of the collective variables. The latter enables us to describe the string excitations of various symmetries, e.g. breathing and elliptical modes in a nonlinear regime.

[1] V. Kravchuk, U. Rößler, J. van den Brink, M. Garst, PRB, 102, 220408(R) (2020).