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

We have performed micromagnetic simulations of low-amplitude gyrotropic dynamics of magnetic vortices in the presence of spatially uniform out-of-plane magnetic fields. For disks having small lateral dimensions, we observe a frequency drop-off when approaching the disk's out-of-plane saturation field. This nonlinear frequency response is shown to be associated with a vortex core deformation driven by nonuniform demagnetizing fields that act on the shifted core. The deformation results in an increase in the average out-of-plane magnetization of the displaced vortex state (contrasting the effect of gyrofield-driven deformation at low field), which causes the exchange contribution to the vortex stiffness to switch from positive to negative. This generates an enhanced reduction of the core stiffness at high field, leading to a nonlinear field dependence of the gyrotropic mode frequency