The self-trapping transition of one-magnon excitations coupled to acoustic phonons

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 Schrodinger equation. We provide a detailed numerical study of the magnon self-trapping transition. We accurately determine the critical nonlinearity χ c 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 ∝ ( χ c - χ ) 1 / 2 . The return probability is shown to be discontinuous at χ c while the participation number displays a kink singularity.