Cross-tie walls in thin permalloy films

Cross-tie walls in permalloy films have been simulated as a function of thickness in the range 10-70 nm using direct integration of the Landau-Lifshitz-Gilbert equation in a Cartesian lattice with periodic boundary conditions along the length of the wall. A cross-tie wall is a Bloch-like transition along the wall [or vertical Bloch line (VBL)] between Neel Walls of opposite chirality in a film with in-plane magnetization. This transition is a low-energy state, which allows the long tails of Neel walls to partially close their magnetic flux in the vicinity of the walls. The magnetization configuration of these transitions is either elliptical (vortex) or hyperbolic (antivortex). The pi-VBL transitions are 50 nm in diameter and the distance from each other increases with film thickness. The cross-tie wall energy per unit area was lower than that of a pure Neel or Bloch wall between 15 and 50 nm film thickness.