Dynamic susceptibility of eccentric nanorings

Magnetic nanorings have potential applications in devices based on spintronics concepts. In this work, through micromagnetic simulations, we analyze the impact of changes in the size and position of the ring's hole on magnetization resonant modes in Permalloy eccentric nanorings. Our results show that the magnetization ground state forms a vortex centered either on the hole or on the geometric center of the nanoring, depending on the hole's position. The observed magnetic patterns yield spin wave modes that split when increasing the ring eccentricity. The new resonant frequencies are associated with hybridized radial and azimuthal modes, which form butterfly-like patterns, which are also observed in magnetic field-driven deviations of vortices from the center of nanodots. These findings offer a deeper understanding of the interplay between geometry and magnetization dynamics, which is crucial for designing magnetic nanostructures with specific functional properties.