Magnetic skyrmion strings: how they bend, twist and vibrate

Magnetic skyrmions are smooth topological textures of the magnetization that are localized within a two-dimensional plane. They arise in magnetic systems that lack inversion symmetry where they are stabilized by the Dzyaloshinskii-Moriya interaction. In bulk materials, magnetic skyrmions extend in the third direction forming an effective string. Such skyrmion strings either arise as excitations or they condense and form a crystal. These strings can be dynamically excited resulting in various vibrational modes. We provide an overview of the dynamics of skrymion strings [1], that can be found in chiral magnets like MnSi or FeGe, and we compare theoretical predictions with magnetic resonance spectroscopy [2], spin-wave spectroscopy [3], inelastic neutron scattering [4] and Brillouin light scattering. At high energies, the spin-wave dynamics is governed by an emergent orbital magnetic field that is directly linked to the topological density of the skyrmions. As a result, magnon Landau levels emerge in skyrmion crystals. At low-energies the dynamics is determined by an effective elasticity theory of the strings. We show that a single string supports non-linear solitary waves [5] similar to vortex filaments in fluids. 

[1] M. Garst, J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50, 293002 (2017).

[2] T. Schwarze et al., Nat. Mater. 14, 478 (2015).

[3] S. Seki et al., Nat. Commun. 11, 256 (2020).

[4] T. Weber et al. Science 375, 1025 (2022).

[5] V. P. Kravchuk et al., Phys. Rev. B 102, 220408(R) (2020).