Soft spin modes and magnetization reversal in submicrometric rings

The reversal of the magnetization in submicrometric magnetic particles is of great interest for practical applications, due to its role in any process for storing information in magnetic memories. In addition, during the process of reorientation fundamental phenomena; such as magnetic phase transitions and singularities in the spin wave spectrum occur. Here we wish to investigate the relationship between magnetization reversal and soft mode dynamics. We present a joint experimental and theoretical investigation of the magnetization reversal process in an array of circular rings. A squared array of 20 nm thick ring-shaped dots of Permalloy was fabricated by a combination of e-beam lithography, e-beam evaporation, and lift-off processes. The rings have outer radius R=355 nm and width w=200 nm. The measured Kerr longitudinal hysteresis loop exhibits the typical two-step switching behavior corresponding to transition from the onion to the vortex state and vice versa. The frequencies of the spin excitations in these configurations have been measured by Brillouin light scattering. We have used the dynamical matrix method to calculate the magnetic normal modes of a ring. The method allows us to evaluate directly both eigenvalues (mode frequencies) and eigenvectors (amplitude of precession) of the modes. Several types of spin modes are found, localized in different regions of the rings. It is found that the onion-to-vortex and the vortex-to-onion transitions are triggered by soft spin modes. The shape and symmetry of the dynamic magnetization profile of these soft modes induce the initial modifications of the magnetization at the onset of the transitions, providing a microscopic explanation why one reversal mechanism is preferred to another when the system undergoes a transition between equilibrium states under the action of the applied field. In particular the onion-to-vortex transition is driven by an anti-symmetric end-mode localized at the outer border of the ring in the direction of the applied field, while the vortex-to-onion transition is due to an azimuthal mode localized in one arm of the ring due to the non homogeneous internal field.