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We investigate the variational formulation and corresponding minimizingenergies for the detection of energetically favorable magnetization states ofthin cylindrical magnetic nanodots. Opposed to frequently used heuristicprocedures found in the literature, we revisit the underlying governingequations and construct a rigorous variational approach that takes bothexchange and demagnetization energy into account. Based on a combination ofRitz's method and a Fourier series expansion of the solution field, we are ableto pinpoint the precision of solutions, which are given by vortex modes orsingle-domain states, down to an arbitrary degree of precision. Furthermore,our model allows to derive an expression for the demagnetization energy inclosed form for the in-plane single-domain state, which we compare to resultsfrom the literature. A key outcome of the present investigation is an accuratephase diagram, which we obtain by comparing the vortex mode's energy minimizerswith those of the single-domain states. This phase diagram is validated withdata of two- and three-dimensional models from literature. By means of thephase diagram, we particularly find the critical radius at which the vortexmode becomes unfavorable with machine precision. All relevant data and codesrelated to the present contribution are available athttp://dx.doi.org/10.18419/darus-3103.

Thin cylindrical magnetic nanodots revisited: variational formulation, accurate solution and phase diagram