Abstract We study the recently introduced ‘critically coupled’ model of magnetic Skyrmions, generalising it to thin films with curved geometry. The model feels keenly the extrinsic geometry of the film in three-dimensional space. We find exact Skyrmion solutions on spherical, conical and cylindrical thin films. Axially symmetric solutions on cylindrical films are described by kinks tunnelling between ‘vacua’. For the model defined on general compact thin films, we prove the existence of energy minimising multi-Skyrmion solutions and construct the (resolved) moduli space of these solutions.

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关于薄膜上磁性 Skyrmions 的几何结构

摘要 我们研究了最近引入的磁性 Skyrmions 的“临界耦合”模型，将其推广到具有弯曲几何形状的薄膜。该模型敏锐地感受到了电影在三维空间中的外在几何形状。我们在球形、锥形和圆柱形薄膜上找到了精确的 Skyrmion 解决方案。圆柱形薄膜上的轴对称解决方案由“真空”之间的扭结隧道描述。对于在一般致密薄膜上定义的模型，我们证明了能量最小化多 Skyrmion 解的存在，并构造了这些解的（已解析）模空间。