Micro-magnetic structures of planar charged walls

The energy structure and internal magnetic field distributions for the cross section of a planar charged wall [1] have been calculated by direct numerical integration of the Landau-Lifshitz-Gilbert equation with minimal physical approximations [2]. Head-to-head (and tail-to-tail) charged wall structures have been computed for a wide range of material parameters. Results indicate that the charged wall structures depend on a non-dimensional film thickness D normalized by δo=π√ (A/K) which is the Néel or Bloch wall width for thin or thick film respectively. For thin films, the charged walls have features of the Néel wall in terms of wall width and energy. For thick films, the charged walls have complex structures with Néel wall features at the center, and Bloch wall features (Bloch spin) near the surfaces of the film. The Bloch spin increases with the film thickness D and is nearly independent of the value of Q. The charged wall width is equal to the Néel wall width δo for large Q and small D. The charged wall width increases rapidly with decreasing Q which causes some difficulties in defining the wall width and in estimating the wall energy. The charged wall energy is close to the Néel wall energy for large Q=5, and is constantly larger than that for small Q regardless of the value of D.