Localized magnetic fields enhance the field-sensitivity of the gyrotropic resonance frequency of a magnetic vortex

We have carried out micromagnetic simulations of the gyrotropic resonance mode of a magnetic vortex in the presence of spatially localized and spatially uniform out-of-plane magnetic fields. We show that the field-induced change in the gyrotropic mode frequency is significantly larger when the field is centrally localized over lengths which are comparable to or a few times larger than the vortex core radius. When aligned with the core magnetization, such fields generate an additional confinement of the core. This confinement increases the vortex stiffness in the small displacement limit, leading to a resonance shift which is greater than that expected for a uniform out-of-plane field of the same amplitude. Fields generated by uniformly magnetized spherical particles having a fixed separation from the disk are found to generate analogous effects except that there is a maximum in the shift at intermediate particle sizes where field localization and stray field magnitude combine optimally to generate a maximum confinement.