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We present a theoretical study of compact magnetic skyrmions in ferromagnetic films with perpendicular magnetic anisotropy that accounts for the full stray field energy in the thin film and low interfacial Dzyaloshinskii-Moriya interaction (DMI) regime. In this regime, the skyrmion profile is close to a Belavin-Polyakov profile, which yields analytical expressions for the equilibrium skyrmion radius and energy. The obtained formulas provide a clear identification of DMI and long-range dipolar interaction as two physical mechanisms determining skyrmion size and stability.
Bernand-Mantel et al. (Tue,) studied this question.