Controlling the spin-wave modes in planar nanostructure with wire-ring morphology

We investigate the dynamic magnetic response of planar ferromagnetic nanostructures with wire-ring morphology using micromagnetic simulations. By systematically varying the inner ring diameter and thickness, we analyze how geometric confinement governs the accessibility of stable and metastable magnetic states and shapes the spin-wave spectra. The equilibrium configurations are found to depend strongly on the relaxation pathway, giving rise to bistability for intermediate ring diameters. Dynamic susceptibility calculations under microwave excitation reveal distinct resonance spectra associated with low- and high-energy magnetic states, which we classify in terms of two energy-evolution paths. Spatial Fourier analysis of the out-of-plane magnetization identifies wire-like, ring-localized, and hybrid spin-wave modes, whose localization and spectral complexity are controlled by geometry. Our results demonstrate that planar wire-ring nanostructures offer a versatile platform for tailoring spin-wave excitations through geometric design, with potential implications for reconfigurable magnonic and spintronic devices.