Chiral skyrmions are stable particle-like solutions of the Landau-Lifshitz equation for ferromagnets with the Dzyaloshinskii-Moriya (DM) interaction, characterized by a topological number. We study the profile of an axially symmetric skyrmion and give exact formulas for the solution of the corresponding far-field and near-field equations, in the asymptotic limit of small DM parameter (alternatively large anisotropy). The matching of these two fields leads to a formula for the skyrmion radius as a function of the DM parameter. The derived solutions show the different length scales which are present in the skyrmion profiles. The picture is thus created of a chiral skyrmion that is born out of a Belavin-Polyakov solution with an infinitesimally small radius, as the DM parameter is increased from zero. The skyrmion retains the Belavin-Polyakov profile over and well-beyond the core before it assumes an exponential decay; the profile of an axially-symmetric Belavin-Polyakov solution of unit degree plays the role of the universal core profile of chiral skyrmions.

中文翻译：

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小半径手性skyrmions的轮廓

手性斯格明子是具有 Dzyaloshinskii-Moriya (DM) 相互作用的铁磁体的 Landau-Lifshitz 方程的稳定粒子状解，以拓扑数为特征。我们研究了轴对称斯格明子的轮廓，并在小 DM 参数（或者大的各向异性）的渐近极限下给出了相应远场和近场方程解的精确公式。这两个字段的匹配导致了作为 DM 参数函数的斯格明子半径的公式。派生的解决方案显示了存在于斯格明子剖面中的不同长度尺度。因此，当 DM 参数从零增加时，该图片是由 Belavin-Polyakov 解产生的手性斯格明子产生的，半径极小。在呈指数衰减之前，斯格明子在核心上方并远远超出了贝拉文-波利亚科夫的轮廓；单位度的轴对称 Belavin-Polyakov 解的轮廓起到手性斯格明子的通用核心轮廓的作用。