Three-dimensional dynamics of solitary vertical Bloch lines in domain walls of garnets

Abstract

The results of a simulation of vertical Bloch lines (VBL) dynamics in garnet films are presented using the three-dimensional Landau–Lifshitz equation. The behavior of VBLs depends especially on the magnetic field driving the domain wall. At small driving fields the motion of VBL under the influence of a gyroscopic force is similar to the one obtained with the help of the one-dimensional Slonczewski equations. At large driving magnetic fields horizontal Bloch lines (HBLs) are generated in the domain wall. This fact leads to decay of a vertical Nπ-Bloch line into a packet of N separated π-lines. The motion of the horizontal Bloch line provides an annihilation of the leading π-VBL and the simultaneous generation of a π-line behind the packet. The velocity of the packet as a whole is lower than that of the one-dimensional Nπ-VBL. The results of the simulation of VBL dynamics using the three-dimensional Landau–Lifshitz equations and two-dimensional Slonczewski equations look very similar. Based on this fact the head-on collisions of two packets of 2π and −2π VBLs were investigated with the help of two-dimensional Slonczewski equations. After collisions of two ±2π VBLs, two with charge ±π move in the initial directions in some interval of the driving magnetic field. The partial restoration of the packets of ±2π takes place. Outside this interval the full annihilation of the colliding packets ±2π-VBLs takes place.