Theoretical studies on a 2D quasi discrete Ferromagnetic spin system with NNN interactions

We present a new Hamiltonian for a two dimensional Ferromagnetic system with nearest neighbour (NN) and next nearest neighbour (NNN) exchange interactions along with anisotropic interactions. The Dyson–Maleev transformation (DM) is used to bosonize the Hamiltonian. The method of multiple scales accompanying the quasi discreteness approach is attuned to arrive at the cubic nonlinear Schrödinger equation (CNLSE). The effect of NNN interactions on localized excitations in the system is theoretically investigated and analysed using Sine–Cosine, Inverse scattering methods. The respective wave patterns are presented and studied. •Nonlinear spin dynamics in a 2D ferromagnetic spin system is studied.•Glauber’s coherent state is paired with Dyson–Maleev operators for the study.•CNLS equation is obtained using Quasi discreteness analysis.•Soliton excitation is exhibited through sine–cosine and inverse scattering method.•The obtained wave patterns are analysed and studied.