Soliton spin excitations and their perturbation in a generalized inhomogeneous Heisenberg ferromagnet

Abstract

We investigate the nonlinear spin dynamics of a generalized inhomogeneous anisotropic Heisenberg ferromagnetic spin chain with bilinear and biquadratic exchange, octupole-dipole, and weak interactions in the semiclassical limit by using Glauber's coherent state method in combination with Holstein-Primakoff bosonic representation of spin operators. The dynamics is found to be governed by a generalized nonlinear Schroedinger equation in the continuum limit. We have identified several completely integrable spin models with soliton spin excitations for specific parametric choices. Finally, we carry out a multiple scale perturbation analysis to find the effect of discreteness and inhomogeneity on the soliton excitations in a more general case. The results show that the discreteness effect introduces symmetric fluctuations in the localized region of the soliton without altering its amplitude and velocity. On the other hand, the inhomogeneity introduces asymmetric fluctuations in the localized region with a decrease in the amplitude and velocity of the soliton with time. Further, the inhomogeneity reverses the velocity of the soliton after some time.