Abstract
The existence and properties of intrinsic localized spin-wave modes in a ferromagnetic XXZ spin chain with Dzyaloshinsky—Moriya interaction are investigated analytically in the semiclassical limit. The model Hamiltonian is quantized by introducing the Dyson—Maleev transformation and the coherent state representation is chosen as the basic representation of the system. By making use of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is shown that a bright intrinsic localized spin-wave mode whose eigenfrequency lies below the bottom of the magnon frequency band can exist in the ferromagnetic system. We also show that the system can produce a dark intrinsic localized spin-wave mode, i.e., nonpropagating kink, whose eigenfrequency is below the upper of the magnon frequency band. In addition, we find that the introduction of the Dzyaloshinsky—Moriya interaction changes wave numbers in the Brillouin-zone corresponding to the appearance of intrinsic localized spin-wave modes.
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