Nonlinear generation modes in easy-axis anisotropy ferromagnetic spin chains with nearest-neighbor coupling

In this paper, we consider the Heisenberg ferromagnetic lattices with single-ion easy-axis anisotropy to show the effects of the nearest-neighbor coupling on discrete modulation instability and localized energy in the forbidden gap. We use the multi-scale scheme to establish the nonlinear Schrodinnger equation from where it was carried out the static breather equation together with the threshold amplitude. Thus, one end of the spin chains was submitted to an external periodic boundary. It results that the nearest-neighbor coupling parameter induced instability in the forbidden frequency gap by increasing the amplitude of the plane wave. The most important feature of this investigation is the fact that the driven amplitude is considered below the threshold amplitude and the nonlinear supratransmission phenomenon arises. These outcome shed light on the fact that the Heisenberg ferromagnetic spin chains with a single-ion easy-axis anisotropy could be used to generate both long-lived temporal localized solitons and nonlinear supratransmission phenomenon.