Two-body problem of core-region coupled magnetic vortex stacks

The dynamics of all four combinations of possible polarity and circularity states in a stack of two vorticesis investigated by time-resolved scanning transmission x-ray microscopy. The vortex stacks are excited byunidirectional magnetic fields leading to a collective oscillation. Four different modes are observed that dependon the relative polarizations and circularities of the stacks. They are excited to a driven oscillation. We observe arepulsive and attractive interaction of the vortex cores depending on their relative polarizations. The nonlinearityof this core interaction results in different trajectories that describe a two-body problem

Collective modes in three-dimensional magnonic vortex crystals

Collective modes in three-dimensional crystals of stacked permalloy disks with magnetic vortices areinvestigated by ferromagnetic resonance spectroscopy and scanning transmission X-ray microscopy.The size of the arrangements is increased step by step to identify the different contributions to theinteraction between the vortices. These contributions are the key requirement to understand complexdynamics of three dimensional vortex crystals. Both vertical and horizontal coupling determine thecollective modes. In-plane dipoles strongly influence the interaction between the disks in the stacks andlead to polarity-dependent resonance frequencies. Weaker contributions discern arrangements withdifferent polarities and circularities that result from the lateral coupling of the stacks and the interactionof the core regions inside a stack. All three contributions are identified in the experiments and areexplained in a rigid particle model