Fig. 3: HOI and curvature of the energy surface for the skyrmion.
From: Impact of higher-order exchange on the lifetime of skyrmions and antiskyrmions
Local part of the eigenvalue spectrum of the Hessian matrix of the skyrmion (a, blue) and the skyrmion saddle point (SP) (b, green and blue) in fcc-Pd/Fe/Ir(111) including HOI as a function of the magnetic field B⊥ − BC. Eigenvalues above the magnon gap are indicated by the orange painted area. For reference the corresponding local eigenvalue spectra in the model without considering HOI explicitly are shown as gray dashed lines. Selected eigenmodes are labeled while the number in brakets gives their multiplicity (see surrounding text). Curvature associated with the local eigenvalue spectrum (see Eq. (10)) for the skyrmion (blue, c) and the corresponding SP (blue, e) for the energy model including HOI (solid line). The local curvatures of the skyrmion and the SP for the model neglecting HOI are drawn with dashed gray lines. In e only the regime of the radial collapse is shown. d Energy along the seesaw eigenmodes of the SP including HOI (blue, SP in f) and of the SP excluding HOI (gray, SP in h). g Configuration obtained after displacing the SP in f along the indicated direction (black arrow) using the corresponding eigenvector of the seesaw mode. i Total curvature difference of the minimum and the SP for the regime of the radial collapse mechanism.
