Shrinking dynamics of skyrmions and antiskyrmions

Abstract

Magnetic skyrmions and antiskyrmions are topologically nontrivial spin textures occurring in various magnetic systems. In chiral magnets, they emerge from the competition between Heisenberg exchange interaction, Dzyaloshinskii-Moriya interaction (DMI), and external magnetic fields. Owing to their nanoscale size, topological stability, and the possibility of their controlled manipulation by electric currents, magnetic fields, or thermal gradients, they are considered promising candidates for future spintronic technologies. Understanding their dynamical stability and collapse mechanisms is therefore of both fundamental and technological relevance. Unstable skyrmions and antiskyrmions shrink in size until their eventual collapse, while sufficiently strong isotropic DMI can stabilize skyrmions. The detailed shrinking dynamics remain insufficiently understood and therefore, this thesis develops an analytical continuum model for the nonequilibrium shrinking and breathing dynamics of both textures.

For skyrmions, a collective-coordinate approach is employed in which the radius and the helicity are treated as time-dependent variables. Using a triangular ansatz for the skyrmion profile together with the Landau-Lifshitz-Gilbert equation, we derive coupled nonlinear differential equations governing the shrinking dynamics. Our analysis reveals a crossover from a Zeeman-dominated exponential decay at large skyrmion sizes to an exchange-driven square-root behavior near the critical collapse time. If the DMI is too small to stabilize the skyrmion, the shrinking is accompanied by rotational breathing dynamics, whereas a sufficiently strong DMI stabilizes damped, oscillatory breathing modes around a finite equilibrium size. The critical collapse time is found to depend logarithmically on the lattice constant and sensitively on the magnetic field, DMI strength, and Gilbert damping.

For antiskyrmions, the continuum framework is extended to include elliptical deformations. These are incorporated to account for the antiskyrmions intrinsic twofold symmetry that gives rise to direction-dependent anisotropic energy contributions in systems with isotropic DMI. The set of collective coordinates is therefore expanded to include the two semi-axes, the helicity, and the in-plane rotation angle of the texture. The resulting theory reveals that elliptic antiskyrmions are energetically favored over circular ones, although they remain unstable. At large sizes they shrink exponentially and in the regime of small antiskyrmion sizes, the exchange interaction drives the antiskyrmion towards circularity and leads again to a square-root-like collapse dynamics. This overall behavior is then superimposed with coupled shrinking, deformation, rotation, and helicity dynamics, that give rise to a characteristic rotational quadrupole breathing mode.

The analytical predictions are systematically validated through micromagnetic simulations on a discrete lattice. Overall, this work establishes an analytical framework for the shrinking, breathing, and deformation dynamics of skyrmions and antiskyrmions, providing a basis for predicting and controlling topological spin textures in future spintronic applications.