CRITICAL VELOCITY OF MOTION OF DOMAIN WALLS IN MAGNETIC MATERIALS.

The study of motion of domain walls in different types of magnetic material is usually based on the solution of a system of second-order differential equations (the Landau-Lifshitz equations) whose analytic integration is, in most cases, impossible and numerical solutions are required. It is proposed to determine the critical velocity of motion of domain walls from the asymptotic behavior of the solutions of the Landau-Lifshitz equations. The proposed method is applied to a ferromagnet in an external magnetic field and to a rare-earth orthoferrite at temperatures for which 180 degree domain walls can exist. In the former case, the dependence of the critical velocity of motion of domain walls on the magnitude and orientation of the external magnetic field is calculated. In the second case, the critical velocity of motion of domain walls is shown to be greater than the Walker limit and it is found that the critical velocity depends only weakly on the relativistic constants. The nature of the solutions of nonlinear equations corresponding to velocities higher than the critical velocity of motion of domain walls is analyzed.