Abstract
We study theoretically two-dimensional nanorings assumed to have the in-plane vortex magnetic configuration. Using a discrete dipole model we examine the spectrum of normal spin-wave modes vs. the dipolar-to-exchange interaction ratio. We systematize the spin-wave excitations by their azimuthal and radial wave numbers. The lowest-frequency mode, the fundamental (quasiuniform) mode, and the mode hybridization are analyzed; the discussion of the influence of effective pinning at the ring boundaries is provided as well. We study the stability of the in-plane vortex state and discuss the role of the size of the ring and the type of lattice arrangement of the magnetic moments within it. To facilitate comparison with our results we provide the relationships between microscopic parameters, used in our model, and those used in the case of continuous medium.
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