Stable topological textures in a classical 2D Heisenberg model

We show that stable localized topological soliton textures (skyrmions) with $π_2$ topological charge $ν\geq 1$ 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 $N_{\rm cr}$ depending on $ν$ and the effective anisotropy constant $K_{\rm eff}$. 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 $ν=1$ and $ν>2$, while the solitons with $ν=2$ 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 $ν=1$ nor high charges, but rather for intermediate values $ν=2$ or $ν=3$.

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