The anharmonicity of the potential well confining the position of the magnetic vortex core is measured dynamically with a Magnetic Resonance Force Microscope (MRFM). The stray field of the MRFM tip is used to displace the core position away from the well minimum. Anharmonicity is then inferred from the relative frequency shift induced on the eigen-frequency of the vortex core translational mode. Traces of these shifts are recorded while scanning the tip above an isolated nanodot, patterned out of a single crystal FeV film. An analytical framework is proposed to analyze the data. It results in a quantitative measurement of the anharmonic coefficient found to be positive and 50% of the parabolic contribution. This calibrates the tunability of the gyrotropic mode by external magnetic fields. In our sample, we observe a variation of the eigen-frequency as high as +10% for a displacement of the vortex core to about one third of the nanodot radius.
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