中国物理B ›› 1996, Vol. 5 ›› Issue (8): 561-567.doi: 10.1088/1004-423X/5/8/001

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TOPOLOGICAL CLASSIFICATION OF 3D AND 2D SPIN STATES IN THE FERROMAGNETS CONTAINING ANNULUS- AND CYLINDER-TYPE CAVITIES

高亭1, 阎凤利2, 李伯臧3   

  1. (1)Department of Mathematics, Hebei Normal University, Shijiazhuang 050016, China; (2)Department of Physics, Hebei Normal University, Shijiazhuang 050016, China; (3)Institute of Physics, Academia Sinica, Beijing 100080, China
  • 收稿日期:1995-06-02 出版日期:1996-08-20 发布日期:1996-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China, and the Hebei Provincial Natural Science Foundation, China.

TOPOLOGICAL CLASSIFICATION OF 3D AND 2D SPIN STATES IN THE FERROMAGNETS CONTAINING ANNULUS- AND CYLINDER-TYPE CAVITIES

GAO TING (高亭)a, YAN FENG-LI (阎凤利)b, LI BO-ZANG (李伯臧)c   

  1. a Department of Mathematics, Hebei Normal University, Shijiazhuang 050016, China; b Department of Physics, Hebei Normal University, Shijiazhuang 050016, China; c Institute of Physics, Academia Sinica, Beijing 100080, China
  • Received:1995-06-02 Online:1996-08-20 Published:1996-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China, and the Hebei Provincial Natural Science Foundation, China.

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摘要： Methods of algebraic topology have been employed to classify ordinary (3D) and planar (2D) spin states in the ferromagnets containing annulus- and cylinder-type cavities. The main result of this paper is that the sets of homotopy classes of 3D and 2D spin states in a ferromagnet containing m non-winding up annulus-type cavities threaded by k cylinder-type cavities can be constructed into groups isomorphic to Zm and Zm+k, respectively. Here m,k = 0, 1, 2,…,Zl denotes the l-dimensional discrete vector group.

Abstract: Methods of algebraic topology have been employed to classify ordinary (3D) and planar (2D) spin states in the ferromagnets containing annulus- and cylinder-type cavities. The main result of this paper is that the sets of homotopy classes of 3D and 2D spin states in a ferromagnet containing m non-winding up annulus-type cavities threaded by k cylinder-type cavities can be constructed into groups isomorphic to Zm and Zm+k, respectively. Here m,k = 0, 1, 2,…,Zl denotes the l-dimensional discrete vector group.

中图分类号:  (Generation of magnetic fields; magnets)

  • 07.55.Db
75.10.-b (General theory and models of magnetic ordering)