Gyrational modes of benzenelike magnetic vortex molecules

With scanning transmission x-ray microscopy we study six magnetostatically coupled vortices arranged in a ring that resembles a benzene molecule. Each vortex is contained in a ferromagnetic microdisk. When exciting one vortex of the ring molecule with an alternating magnetic high-frequency field, all six vortices perform gyrations around the equilibrium center positions in their disks. In a rigid particle model, we derive the dispersion relation for these modes. In contrast to carbon atoms, magnetic vortices have a core polarization that strongly influences the intervortex coupling. We make use of this state parameter to reprogram the dispersion relation of the vortex molecule experimentally by tuning a homogeneous and an alternating polarization pattern. In analogy to the benzene molecule, we observe motions that can be understood in terms of normal modes that are largely determined by the symmetry of the system.