Theory of a dynamical coercive force in magnets with microscopic defects

The peculiar dynamical drag force F_c can arise at the domain wall motion in a magnet with microscopic defects, such that it cannot pin the domain wall in the usual way. The value of F_c is finite as the domain wall velocity v goes to zero. The reason for such behavior is the emission of bending waves of the domain wall. The calculations for different types of impurities as well as for both bulk ferromagnet and ultrathin magnetic layers are presented. In 3D ferromagnet the F_c value is finite at v→0 and this is interpreted as the dynamical coercive force. In the 2D case (e.g. in monolayer films) the drag force diverges at small velocities as F_c ∝1/v^1/2. In the film with a finite thickness and very small v the force has a viscous character: F_c∝v