Quasi discreteness analysis of a 2-dimensional Heisenberg ferromagnetic spin system with biquadratic interactions

Abstract

The dynamical theory of soliton excitations in two-dimensional ferromagnets is studied by introducing a Hamiltonian that includes biquadratic interaction along with uniaxial anisotropy. To obtain a dynamical equation of motion, we use the Dyson-Maleev transformation and the coherent state ansatz. We obtain a Nonlinear Schrdinger equation by applying the multiple-scale and quasi-discreteness methods. For the more general nonintegrable case, we perform a multiple scale perturbation analysis to determine the discreteness effect on the soliton excitations. Finally, we examine modulational instability (MI) under the influence of small perturbations.