Planar ferromagnets: Low-velocity kink dynamics near to the easy plane and static solitary spin structures bifurcating from the azimuthal kink

Abstract

Ferromagnetic spin chains with planar single ion anisotropy, exchange anisotropy and with an external fieldb applied in the easy plane are considered in classical continuum approximation. It is pointed out that in the static case the sine-Gordon approximation is only accidentally exact: it breaks down in the neighborhood of the easy plane already for infinitesimal kink velocities, unlessb→0. It is also shown that at certain valuesb n ,n=0, 1, 2, 3, ... of the applied field there bifurcate from the static in-plane kink (“azimuthal kink”) other static out-of-plane kink solutions. The azimuthal kink is linearly stable below the critical strengthb 0 of the applied field. For increasingb, there occurs at each of the bifurcation fieldsb 1<b 2<b 3... an instability with respect to an additional mode. In the undamped system the instabilities atb 2k ,k=0, 1, 2, ... are associated with the recently discovered “soft-velocity change” mechanism of the critical slowing-down, whereas atb 2k+1 , soft localized dynamic modes occur. If phenomenological spin damping is included, soft relaxation modes occur in the neighborhood of all the bifurcation fields.