Domain wall instability in biaxial ferromagnets

The energetic and dynamic stability of domain walls (DW's) in a 1D Heisenberg ferromagnet with orthorhombic anisotropy is examined in the framework of classical continuum theory. It is shown that in the undamped chain the critical slowing-down accompanying the energetic instability of the static DW's at a critical ratioa _c of the anisotropy fields is not marked (as one might expect) by a localized soft dynamic mode of the DW's, but it is realized by a mechanism which may be termed softening of the velocity change. The role of the soft eigenmode is taken over by the perturbation which carries the static DW into a moving one with infinitesimal velocity, and the role of the soft-mode frequency is taken over by the velocity change induced by the perturbation. When spin damping is included, one does find a soft relaxation mode: Attenuation of the velocity of moving DW's gives rise to a perturbation which may be described as a superposition of the Goldstone mode and a relaxation mode. This behaviour is not a special feature of the system under consideration, but a similar situation arises in general, when a static DW becomes unstable with respect to a perturbation connecting it with a family of other static DW's. For moving DW's the softening of the velocity change also occurs, but here no energetic stability criterion is available and inclusion of spin damping makes the DW motion nonstationary. Thus, in the case of moving DW's no possibility seems to exist to define stability and instability in the usual terms of linear analysis.Work supported by the Swiss National Science Foundation