Abstract
We study the dynamics of one-magnon states coupled to the underlying harmonic oscillations of a linear lattice. We consider that small amplitude oscillations affect linearly the exchange couplings. Within an adiabatic approximation, the magnon dynamics is governed by an effective modified nonlinear Schrödinger equation. We provide a detailed numerical study of the magnon self-trapping transition. We accurately determine the critical nonlinearity χc above which a finite fraction of an initially localized spin excitation remains trapped. To this end, we analyze relevant quantities such as the return probability, participation number and Shannon entropy. We also follow the soliton dynamics showing that its velocity vanishes as v∝(χc-χ)1/2. The return probability is shown to be discontinuous at χc while the participation number displays a kink singularity.
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