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 crossover to a logarithmic divergence occurs. The shrinking dynamics of the antiskyrmion size is found to be accompanied by quadrupolelike oscillations. Numerical simulations on the lattice support the predictions from the continuum model.