We consider the minimization problem of the Landau-Lifshitz energy with the Dzyaloshinskii-Moriya interaction term, including its coefficient as a parameter. This functional admits an explicit critical point with the vortex-type configuration, called (magnetic) skyrmion in physical context. In this talk, we show that there exists an explicit critical value of the parameter above which the skyrmion is unstable, while stable below this threshold. This is a mathematical result consistent with some experiments and numerical studies. This talk is based on the joint work [arXiv:2210.00892] with Slim Ibrahim (UVic).

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