Influence of NNN interaction and existence of breathers in a quasi-discrete Heisenberg helimagnetic spin system

Abstract

In this work, we investigate the existence and properties of discrete bright and dark breathers in a one-dimensional Heisenberg helimagnet incorporating bilinear, helical, NNN and anisotropic interactions. The Hamiltonian is bosonized using the Dyson–Maleev transformation and the coherent state representation is selected as the fundamental representation of the system. With the help of multiple scales combined with quasi-discreteness approximation, the dynamical equation is reduced to a nonlinear Schrödinger equation (NLSE). By employing the solution of NLSE derived using inverse scattering technique (IST), the bright and dark type breather solutions are constructed. The effect of helicity and NNN interactions on these breather modes is also analysed.