Bistability of vortex core dynamics in a single perpendicularly magnetized nano-disk

Microwave spectroscopy of individual vortex-state magnetic nano-disks in a perpendicular bias magnetic field, $H$, is performed using a magnetic resonance force microscope (MRFM). It reveals the splitting induced by $H$ on the gyrotropic frequency of the vortex core rotation related to the existence of the two stable polarities of the core. This splitting enables spectroscopic detection of the core polarity. The bistability extends up to a large negative (antiparallel to the core) value of the bias magnetic field $H_r$, at which the core polarity is reversed. The difference between the frequencies of the two stable rotational modes corresponding to each core polarity is proportional to $H$ and to the ratio of the disk thickness to its radius. Simple analytic theory in combination with micromagnetic simulations give quantitative description of the observed bistable dynamics.