Variational calculus for vertical bloch lines.

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Abstract
Magnetization distributions around vertical Bloch lines (VBL's) in the wall-center plane are calculated by direct minimization of the energy of the system. A successive approximation method using the Newton's method has been developed to solve the Euler equation numerically. The method has been found very effective to obtain equilibrium configurations in small iteration steps as compared with the dynamic calculation based on the so-called equation of wall motion. The calculation includes two-dimensional VBL's in which variations along the Z-axis are neglected and three-dimensional VBL's in which surface-to-surface magnetization twist is taken into consideration. Effective interaction field between two VBL's is calculated as a function of the VBL separation in both cases. The paper descibes the formulation of the problem, method of numerical calculation, and results.