Topological textures and their bifurcation processes in 2D ferromagnetic   thin films
  In this paper, by the use of the topological current theory, the topological structures and the dynamic processes in thin-film ferromagnetic systems are investigated directly from viewpoint of topology. It is found that the topological charge of a thin-film ferromagnetic system can be changed by annihilation or creation processes of opposite polarized vortex-antivortex pairs taking place at space-time singularities of the normalized magnetization vector field of the system, the variation of the topological charge is integer and can further be expressed in terms of the Hopf indices and Brouwer degrees of the magnetization vector field around the singularities. Moreover, the change of the topological charge of the system is crucial to vortex core reversal processes in ferromagnetic thin films. With the help of the topological current theory and implicit function theorem, the processes of vortex merging, splitting as well as vortex core 
Jinl\"u Cao, Guo-Hong Yang, Ying Jiang
cond-mat.mes-hall cond-mat.other