Collective modes of three-dimensional magnetic structures: A study of target skyrmions

Abstract

• We explored the three-dimensional (3D) collective modes of target skyrmion under different external magnetic fields. • The three regimes captured by the spectrum calculations directly reflect the ground states of the target skyrmion. • All the collective modes were spatially resolved. • 3D analysis is necessary to understand the collective modes of 3D magnetic structures. Three-dimensional magnetic textures present their richness not only in variety of ground state structures, but also in their dazzling collective modes. As an example, the target skyrmion, a topological spin texture with a central skyrmion and an extra concentric helical ring, has been enabled by confining a chiral magnet in a nanodisk geometry. In this work we investigate the collective spin wave modes of the target skyrmion in the external field region of −400 mT to 400 mT. Through micromagnetic simulations we reproduced three major phases of the target skyrmion, and derived resonance modes at varying external magnetic field by the power spectral density study. All typical modes were resolved in terms of their dynamical snapshots in temporal domain and the corresponding spatial Fourier transformations. Some modes are shown to behave similarly in-plane but differently out-of-plane, and vice versa. This suggests, on a broader scope, that both responses will be necessary to fully characterize collective modes of three-dimensional spin textures.