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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

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