The stability of the vortex magnetization state in circular cylindrical soft magnetic dots is calculated analytically and by micromagnetic simulations. For the cases considered the dot thickness is comparable to the material exchange length and dot radii are in the submicron range. The equation for the vortex magnetization distribution is analyzed taking exact account of the magnetostatic field inside dot. The limitations and applicability of a previously proposed “exchange-dominated” vortex ansatz are discussed. It is shown that for the transition from the vortex to perpendicular single-domain state the magnetization distribution changes continuously while retaining the axial symmetry. The zero-field critical line of the transition is calculated analytically as a function of dot size and is compared with micromagnetic simulations of the vortex magnetization profile.
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Guslienko et al. (2004) studied this question.
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