Topological charges are calculated for a number of exact three-dimensional analytical solutions to the Landau–Lifshitz equation, which describe the distributions of the vector fields for the vectors of antiferromagnetism and antiferromagnet magnetization. It is shown that in the case of samples with dimensions that are comparable to the characteristic scales of topological objects of the antiferromagnetism and magnetization vector fields, there are modified characteristics that depend not only on the topological properties of these objects, but also on the geometry of the sample. These modified characteristics in samples with finite dimensions may assume non-integer values.

中文翻译：

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具有 Dzyaloshinskii-Moriya 相互作用的反铁磁体畴壁中积木的拓扑特征

拓扑电荷是为朗道-利夫希茨方程的许多精确三维解析解计算的，这些方程描述了反铁磁性和反铁磁磁化矢量的矢量场分布。结果表明，在尺寸与反铁磁性和磁化矢量场的拓扑对象的特征尺度相当的样本的情况下，修改的特征不仅取决于这些对象的拓扑特性，还取决于几何形状的样本。具有有限维度的样本中的这些修改特性可以采用非整数值。