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