Modulational instability and localized modes in Heisenberg ferromagnetic chains with single-ion easy-axis anisotropy

A semiclassical theoretical study on the property of the modulational instability of corresponding linear spin-waves and the presence of nonlinear localized excitations in a discrete quantum ferromagnetic spin chain with single-ion easy-axis anisotropy is reported. We consider the Glauber coherent-state representation combined with the Dyson-Maleev transformation for local spin operators as the basic representation of the system, and derive the equation of motion by means of the Ehrenfest theorem. Using a modulational instability analysis of plane waves, we predict the existence regions of bright envelope solitons and intrinsic localized spin-wave modes. Besides, with the help of a semidiscrete multi-scale method, we obtain analytical solutions for the bright envelope soliton and intrinsic localized spin-wave mode. Moreover, we analyze their existence conditions, which agree with the results of modulational instability analysis.