经典二维Heisenberg模型的稳定拓扑结构
Stable topological textures in a classical 2D Heisenberg model
摘要：
我们证明了在具有单轴各向异性的铁磁体的经典二维海森堡模型中存在稳定的具有$π_2$拓扑荷$ν\geq 1$的局域拓扑孤子织构（skyrmions）。对于这个模型，孤子的存在，只有当束缚磁振子的数量超过某个阈值$N_{\rm cr}$依赖于$ν$和有效各向异性常数$K_{\rm eff}$。我们将孤子相图定义为阈值能量和束缚磁振子数对各向异性常数的依赖关系。$ν=1$和$ν>2$的相边界线都是单调的，而含$ν=2$的孤子表现出特殊的非单调行为，决定了从低拓扑荷到高拓扑荷的过渡区.特别地，每个拓扑电荷的孤子能量（拓扑能量密度）既不针对$ν=1$也不针对高电荷实现最小值，而是针对中间值$ν=2$或$ν=3$实现最小值。
英文摘要：
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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