Three-dimension calculation of vertical Bloch line and Bloch point

Detailed micromagnetic structures around a three-dimensional vertical Bloch line and Bloch points of circulation and contracirculation types are obtained from a first-principle calculation in which the Euler equation is solved using Newton´s method. The computing region consists of 21×21×21 cells extending in x (wall normal), y and z (film normal) directions. To avoid situations in which the polar angle θ of the magnetization vector approaches 0(mod π), a proper-coordinates frame is selected at each cell and each calculation step from the conventional system xyz and a subsidiary system XYZ with the Z axis lying in the film plane. The method of calculation and the results are presented