Stability of uniformly driven domain walls

Abstract

An infinite ferromagnetic medium with orthorombic crystal field anisotropy and with a constantdc field applied along the easy axis is considered in the framework of micromagnetics. It is shown that in the presence of Gilbert damping the uniformly driven plane domain wall (“Walker wall”) with positive Doring mass is linearly stable for any strengthH of the applied field below a critical valueH0, where it connects to an unstable wall configuration with negative Doring mass. The critical fieldH0 is lower than the existence limitH W (‘Walker limit”) of the solitary travelling-wave type domain wall solutions, and represents the threshold of the field regionH0<H<H W where negative wall mobilities occur. The instability atH=H0 is associated with a nonuniform localized relaxation mode (“corrugating mode”) of the plane domain wall. If coupling to the external circuit is taken into account, negative-mobility walls also become unstable against uniform perturbations for sufficiently small circuit resistance.