Computer simulation of two-dimensional vertical Bloch lines by direct integration of Gilbert equation

The Gilbert equation is solved numerically to obtain detailed structures of two-dimensional vertical Bloch lines. To avoid situations in which magnetization aligns parallel to the polar axis, the computing region is divided into three subregions, and two kinds of coordinates systems are used depending on the orientation of the magnetization in each subregion. The instability associated to the equation is suppressed completely by discretizing the equation according to the backward Euler method. The paper formulates the method of calculation, describes the derived structure of a plane-like wall with periodically-spaced VBL´s, and makes comparison with the results of simulations based on various modelings developed so far.