Energetic and dynamic stability of kinks in planar ferromagnets

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Abstract
The static 360 degrees kink in a planar ferromagnet with an in-plane field becomes energetically unstable when the strength of the applied field exceeds one-third of the anisotropy field. The search for a soft dynamic eigenmode of the kink yields, however, a negative result. One finds that in the undamped chain the role of the soft eigenmode is taken over by the perturbation which carries the static kink into a neighbouring one, and the role of the soft-mode frequency is taken over by the velocity difference with respect to neighbouring kinks. When spin damping is included, one does find a soft relaxation mode: attenuation of the velocity of the neighbouring kinks gives rise to a perturbation which may be described as a superposition of the Goldstone mode and a relaxation mode. For the moving kinks a similar situation occurs, but in this case the inclusion of damping would make the kink nonstationary. It is therefore not obvious how the dynamic stability of a moving kink can be defined.