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The energy of a displaced magnetic vortex in a cylindrical particle made ofisotropic ferromagnetic material (magnetic dot) is calculated taking intoaccount the magnetic dipolar and the exchange interactions. Under thesimplifying assumption of small dot thickness the closed-form expressions forthe dot energy is written in a non-perturbative way as a function of thecoordinate of the vortex center. Then, the process of losing the stability ofthe vortex under the influence of the externally applied magnetic field isconsidered. The field destabilizing the vortex as well as the field when thevortex energy is equal to the energy of a uniformly magnetized state arecalculated and presented as a function of dot geometry. The results (containingno adjustable parameters) are compared to the recent experiment and are in goodagreement.Comment: 4 pages, 2 figures, RevTe

Evolution and stability of a magnetic vortex in a small cylindrical ferromagnetic particle under applied field