Stable topological textures in a classical 2D Heisenberg model

We show that stable localized topological soliton textures (skyrmions) with ${\pi }_2$ topological charge $\nu \ge 1$ exist in a classical 2D Heisenberg model of a ferromagnet with uniaxial anisotropy. For this model the soliton exist only if the number of bound magnons exceeds some threshold value $N_{\rm cr}$dependingon$\nu $andtheeffectiveanisotropyconstant$K_{\rm eff}$. We define soliton phase diagram as the dependence of threshold energies and bound magnons number on anisotropy constant. The phase boundary lines are monotonous for both $\nu =1$ and $\nu >2$, while the solitons with $\nu =2$ reveal peculiar nonmonotonous behavior, determining the transition regime from low to high topological charges. In particular, the soliton energy per topological charge (topological energy density) achieves a minimum neither for $\nu =1$ nor high charges, but rather for intermediate values $\nu =2$ or $\nu =3$.