  Magnetic skyrmions have been the subject of extensive experimental studies in
ferromagnetic thin films and multilayers, revealing a diversity in their size,
stability and internal structure. While the orthodox skyrmion theory focuses on
the Dzyaloshinskii-Moryia interaction (DMI) and neglects higher-order energy
terms, it is becoming clear that the full stray field energy needs to be taken
into account to understand these recent observations. Here we present a
micromagnetic study based on rigorous mathematical analysis which allows to
account for the full stray field energy in the thin film and low 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 Dzyaloshinskii-Moryia
and long-range dipolar interactions as two physical mechanisms determining
skyrmion size and stability, a consideration of importance for the optimization
of skyrmion characteristics for spintronic applications.
