Evolution and stability of a magnetic vortex in small cylindrical   ferromagnetic particle under applied field
  The energy of a displaced magnetic vortex in a cylindrical particle made of isotropic ferromagnetic material (magnetic dot) is calculated taking into account the magnetic dipolar and the exchange interactions. Under the simplifying assumption of small dot thickness the closed-form expressions for the dot energy is written in a non-perturbative way as a function of the coordinate of the vortex center. Then, the process of losing the stability of the vortex under the influence of the externally applied magnetic field is considered. The field destabilizing the vortex as well as the field when the vortex energy is equal to the energy of a uniformly magnetized state are calculated and presented as a function of dot geometry. The results (containing no adjustable parameters) are compared to the recent experiment and are in good agreement. 
Konstantin Yu. Guslienko and Konstantin L. Metlov