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We have performed micromagnetic simulations of the vortex gyrotropic moderesonance in a range of disk geometries subject to spatially uniformout-of-plane magnetic fields. For disks of small lateral dimensions, we observea drop-off in the mode's frequency for field amplitudes approaching the disksaturation field. This non-linear frequency response is shown to be associatedwith an increased vortex core deformation, which results from the demagnetizingfield created when the core is shifted laterally. Such deformation results inan increase in the average out-of-plane magnetization of the displaced vortexstate, which through an exchange contribution, leads to a sharp decrease in thevortex stiffness coefficient. It is this decrease in the vortex stiffnesscoefficient which leads to the non-linear field dependence of the gyrotropicmode frequency.

physical review. b./physical review. b

Exchange-mediated, non-linear, out-of-plane magnetic field dependence of  the ferromagnetic vortex gyrotropic mode frequency driven by core deformation