Domain wall structure in Permalloy films with decreasing thickness at the Bloch to Néel transition

The Bloch to Néel wall transition is investigated in Permalloy films between 160 and 10 nm thickness using direct integration of the Landau–Lifshitz–Gilbert equation in a three-dimensional Cartesian lattice. At 80 nm, the wall is a symmetric Bloch wall characterized by two adjoining vortices with the magnetization at the wall center pointing perpendicular to the plane of the material throughout the thickness. The Bloch to Néel transition takes place between 35 and 30 nm, below which the wall becomes a symmetric Néel wall. For the Bloch walls, our wall energy per unit area calculations match reasonably well the results of A. Hubert’s Ritz method calculations [Magnetic Domains (Springer, New York, 1998), p. 251] and A. E. Labonte’s numerical calculations [J. Appl. Phys. 40, 2450 (1969)]. For the Néel walls, however, our results indicate an approximately 70% higher energy for thicknesses of 30 nm and below, since the Néel wall tails are included. For thicknesses below 160 nm, the anisotropy energy component is low, and both C-shaped and symmetric Bloch walls are dominated by exchange interaction. As the wall transforms from Bloch to Néel below 35 nm, the energy contribution changes from 76% exchange and 24% demagnetization to 70% demagnetization and 30% exchange, respectively. Wall widths are computed for thicknesses between 10 and 640 nm along with the out-of-plane magnetization due to the presence of the vortex. © 2001 American Institute of Physics.