Soliton instabilities in the easy plane ferromagnet Heisenberg chain with out-of-plane spin deviation

Abstract

In this paper we investigate the presence of out-of-plane spin deviation $% \rho (\xi )$ in the easy-plane ferromagnetic Heisenberg chain by using the coupled-boson operators together with the Schwinger transformation for the spin operator; this method allows us to conclude that the critical behaviour of the instability is due to the velocity of the nonlinear excitations (solitons) only for an appropriate range of the magnetic field. In this case, when the velocity becomes lower, the stable soliton corresponding to $\rho (\xi )$ is distorted by magnons and loses stability. If we increase the velocity of $\rho (\xi )$, it then decays into high frequency-oscillations. Nevertheless, we find an opposite competence effect produced by the velocity and the magnetic field on $\rho (\xi )$.