# A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree $\pm1$ harmonic maps from $\mathbb{R}^2$ to $\mathbb{S}^2$

@inproceedings{BernandMantel2019AQD, title={A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree \$\pm1\$ harmonic maps from \$\mathbb\{R\}^2\$ to \$\mathbb\{S\}^2\$}, author={Anne Bernand-Mantel and Cyrill B. Muratov and Thilo M. Simon}, year={2019} }

We characterize skyrmions in ultrathin ferromagnetic films as local minimizers of a reduced micromagnetic energy appropriate for quasi two-dimensional materials with perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction. The minimization is carried out in a suitable class of two-dimensional magnetization configurations that prevents the energy from going to negative infinity, while not imposing any restrictions on the spatial scale of the configuration. We first…

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