Magnetic Gap Solitons as the Intrinsic Self-Localized Magnons in Heisenberg Antiferromagnetic Chain

A magnetic gap soliton theory for the intrinsic self-localized magnon modes in one-dimensional Heisenberg antiferromagnets is developed in this paper. It is shown that these solitons have zero group velocity in the magnetic lattice and that the frequency of carrier wave is within the gap of magnon band. Different from the results obtained recently by lattice Green's function, our approach demonstrates that only the antisymmetric two-spin bound state can exist. We also show that the system can produce a new type of intrinsic self-localized magnon mode, a nonpropagating kink, whose oscillatory frequency is just below the upper cut-off of the magnon band.