Dynamics of antiskyrmion shrinking

Antiskyrmions are unstable in ferromagnetic systems with isotropic bulk or interfacial Dzyaloshinskii-Moriya interaction (DMI). We develop a continuum model for the shrinking dynamics of antiskyrmions in bulk DMI systems, using the Landau-Lifshitz-Gilbert equation for the time derivative of the magnetization field. Owing to the structure of their azimuthal angle, or helicity, elliptic antiskyrmions are energetically favored over circular ones. To capture this feature, we parametrize the magnetization field with a triangular radial profile and an elliptic in-plane shape. This ansatz yields four coupled dynamical equations governing time evolution of the semi-axes, helicities, and rotation angles. In the absence of the DMI, circular antiskyrmions shrink isotropically, exhibiting a crossover from exponential decay to square-root collapse. Initially elliptic antiskyrmions are driven towards circularity. For finite DMI, the semi-axes dynamics couples to the helicity and rotation, where the theory predicts a rotation angle following by half of the slope of the helicity evolution which is linear in time. Only at small semi-axes a cross-over to a logarithmic divergence occurs. The shrinking dynamics of the antiskyrmion size is found to be accompanied by quadrupole-like oscillations. Numerical simulations on the lattice support the predictions from the continuum model.

💡 Research Summary

The paper investigates the collapse dynamics of antiskyrmions in ferromagnets that possess an isotropic bulk Dzyaloshinskii‑Moriya interaction (DMI). While skyrmions are stabilized by such DMI, antiskyrmions remain energetically unfavorable and eventually shrink to annihilation. To capture the essential physics, the authors develop a continuum description based on the Landau‑Lifshitz‑Gilbert (LLG) equation and introduce a collective‑coordinate ansatz that combines a triangular radial profile for the polar angle Θ with an elliptic in‑plane shape for the azimuthal dependence. The ellipse is characterized by two semi‑axes (a₀, b₀) and a rotation angle ω, while the helicity φ₀ enters the azimuthal angle Φ(φ)=−φ+φ₀. Substituting this parametrization into the energy functional (exchange, DMI, Zeeman terms) yields an explicit expression for the total energy E(a₀,b₀,φ₀,ω). Numerical evaluation shows that the energy landscape possesses π‑periodic minima along the line φ₀=2ω−(4ℓ+1)π/2, reflecting the strong influence of the DMI term sin(φ₀−2ω).

By applying the variational principle to the LLG equation with the collective coordinates, four coupled nonlinear ordinary differential equations are derived for a₀(t), b₀(t), φ₀(t) and ω(t). In the DMI‑free limit the semi‑axes decouple from φ₀ and ω, leading to isotropic shrinking: the radius first decays exponentially, then crosses over to a square‑root collapse as the core size approaches zero. Elliptic antiskyrmions are driven toward circularity (a₀≈b₀) during this process.

When a finite bulk DMI is present, the dynamics becomes richer. The helicity evolves linearly in time, φ₀(t)=φ₀(0)+κt, and the rotation angle follows with half that slope, ω(t)=ω(0)+κt/2. The semi‑axes are now coupled to φ₀ and ω, producing quadrupole‑like oscillations of the ellipse as it shrinks. Near the final collapse the helicity and rotation angle diverge logarithmically, while the semi‑axes rapidly approach zero. Thus the antiskyrmion collapse is not a simple radial contraction but a combined rotation‑deformation process dictated by the DMI‑induced anisotropy.

To validate the analytical framework, the authors perform micromagnetic simulations on a two‑dimensional lattice using the full LLG dynamics. The simulations reproduce the predicted behaviors: (i) simultaneous reduction of a₀·b₀, (ii) linear increase of φ₀, (iii) ω increasing at half the helicity rate, and (iv) the emergence of quadrupolar oscillations in the shape. The agreement confirms that the triangular‑profile, elliptic ansatz captures the dominant collective modes despite its simplifications.

Overall, the study provides a comprehensive theoretical picture of antiskyrmion shrinking, highlighting the crucial role of DMI‑induced anisotropy in coupling helicity, rotation, and shape. These insights are relevant for spin‑tronic applications where controlled annihilation of topological textures is required, and they suggest that engineering DMI strength and symmetry could be used to tailor the collapse dynamics of antiskyrmions.