  We have performed micromagnetic simulations of the vortex gyrotropic mode
resonance in a range of disk geometries subject to spatially uniform
out-of-plane magnetic fields. For disks of small lateral dimensions, we observe
a drop-off in the mode's frequency for field amplitudes approaching the disk
saturation field. This non-linear frequency response is shown to be associated
with an increased vortex core deformation, which results from the demagnetizing
field created when the core is shifted laterally. Such deformation results in
an increase in the average out-of-plane magnetization of the displaced vortex
state, which through an exchange contribution, leads to a sharp decrease in the
vortex stiffness coefficient. It is this decrease in the vortex stiffness
coefficient which leads to the non-linear field dependence of the gyrotropic
mode frequency.
