管状和闭合磁畴壁的拓扑分类

本文从拓扑学角度,对管状磁畴壁和闭合磁畴壁静态结构的分类问题,做了统一处理。这两种磁畴壁的同伦类集合G_W⁽ⁿ⁾和G_W⁽ⁿ⁾,分别与S²→S²和S³→S²的n+1基点连续映射的相对同化类集合是一一对应的,因而构成同构于整数加群Z的群,分别称为n式管壁群和n式闭壁群。重新讨论了Slonczewski等人定义的“绕数”,找出了用它表征管壁 关键词：

TOPOLOGICAL CLASSIFICATION OF THE MAGNETIC DOMAIN WALLS OF TUBE-AND ENVELOPE-TYPE

The classification of the static magnetic domain wall structures of tube- and envelope-type is made in an unified way using the homotopy theory. The sets of topological classes for such two kinds of magnetic domain walls, G_Wⁿ and G_Wⁿ, are corresponding respectively one-by-one to the sets of homotopy classes relative to n + l base points for the S²→S² and S³→S⁴ continuous maps. Either G_W⁽ⁿ⁾ ro G_W⁽ⁿ⁾, therefore, can be constructed into group isomorphic to Z, the additive group of integers. (Then we call them the tube-wall group and the envelope-wall group of type n, respectively). The ‘winding number' introduced by Slon-czewski et al. is considered anew. The sufficient and necessary conditions under which the ‘winding number' is allowed to be taken as the index of tube-wall class are obtained. Finally, the topological classification of the magnetization states with M tube-walls and N envelope-walls coexisting is discussed. It is shown that the set of the corresponding topological classes, G_W^(M,N), can be constructed into group isomorphic to Z^M+N, the M + N dimensional lattice vector group. (It is then referred to as the mix-wall group of type M, N] ).