A semi-analytical approach for studying the dynamics of magnetic vortices with Dzyaloshinskii-Moriya interactions*

The magnetic vortex provides a convenient system to investigate the effects of the Dzyaloshinskii Moriya interactions (DMIs) on the dynamics of patterned magnetic structures in confined geometries. Here we introduce a Landau-Lifshitz based diagonalization (LLD) method to calculate the effects of the DMI on radial-type modes in circular disks. The LLD method is a semi-analytical approach which diagonalize the magnetostatic kernel, exchange and DMI contributions to extract the system eigenfrequencies and eigenmodes. Our calculations show that the DMI leads to a frequency shift that is comparable to what is observed for extended films, however, only the down-shifted mode is observed. The excitation amplitudes are enhanced near the core and the structure edges, and modes with even symmetry that would normally be suppressed for a spatially uniform excitation field are present.