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

The Bloch to Neel wall transition is investigated in Permalloy films betwee n 160 and 10 nm thickness using direct integration of the Landau-Lifshitz-G ilbert equation in a three-dimensional Cartesian lattice. At 80 nm, the wal l is a symmetric Bloch wall characterized by two adjoining vortices with th e magnetization at the wall center pointing perpendicular to the plane of t he material throughout the thickness. The Bloch to Neel transition takes pl ace between 35 and 30 nm, below which the wall becomes a symmetric Neel wal l. For the Bloch walls, our wall energy per unit area calculations match re asonably 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 Neel walls, however, our results indicate an approximately 70% higher energy for thicknesses of 30 nm and below, since the Neel wall tails are included. For thicknesses b elow 160 nm, the anisotropy energy component is low, and both C-shaped and symmetric Bloch walls are dominated by exchange interaction. As the wall tr ansforms from Bloch to Neel below 35 nm, the energy contribution changes fr om 76% exchange and 24% demagnetization to 70% demagnetization and 30% exch ange, respectively. Wall widths are computed for thicknesses between 10 and 640 nm along with the out-of-plane magnetization due to the presence of th e vortex. (C) 2001 American Institute of Physics.