We study the structure of an axially symmetric magnetic skyrmion in a ferromagnet with the Dzyaloshinskii–Moriya interaction. We examine the regime of large skyrmions and we identify rigorously the critical value of the dimensionless parameter at which the skyrmion radius diverges to infinity, while the skyrmion energy converges to zero. This critical value coincides with the expected transition point from the uniform phase, which accommodates the skyrmion as an excited state, to the helical phase, which has negative energy. We give the profile field at the skyrmion core, its outer field, and the intermediate field at the skyrmion domain wall. Moreover, we derive an explicit formula for the leading asymptotic behavior of the energy as well as the leading term and first asymptotic correction for the value of the critical parameter. The key leading to the results is a parity theorem that utilizes exact formulae for the asymptotic behavior of the solutions of the static Landau–Lifshitz equation centered at the skyrmion domain wall. The skyrmion energy is shown to be an odd function of the radius and the dimensionless parameter to be an even function.

我们研究了具有Dzyaloshinskii-Moriya相互作用的铁磁体中的轴对称磁性skyrmion的结构。我们研究了大型天敌的状态，并严格确定了无量纲参数的临界值，在该无量纲参数处，天敌的半径发散到无穷大，而天敌的能量收敛到零。该临界值与预期的过渡点重合，该过渡点是从均匀相（该过渡相将天蝎子作为激发态容纳）到具有负能量的螺旋相。我们在skyrmion核心处给出轮廓场，在其外部区域给出一个轮廓，并在skyrmion畴壁处给出中间场。此外，我们导出了能量的超前渐近行为以及临界参数值的超前项和第一个渐近校正的显式公式。导致该结果的关键是奇偶性定理，该奇偶性定理利用精确公式来确定以skyrmion畴壁为中心的静态Landau–Lifshitz方程的解的渐近行为。示出了天rm子能量是半径的奇函数，而无量纲参数是偶函数。