Self-trapping at a nonlinear impurity in a Heisenberg ferromagnetic chain

Abstract

We study the problem of a linearized Heisenberg ferromagnetic chain in the presence of a nonlinear impurity. The exchange coupling of the impurity to its nearest-neighbour spins is anisotropic and expanded to the fourth order of the magnon operators, while the rest of the couplings are isotropic and linearized. We show that, in a parameter region, a magnon bound state trapped at the impurity exists with energy higher than the magnon band of the linearized chain. The calculation of the transmission coefficient of plane waves through such an impurity reveals the existence of completely unscattered modes with transmission equal to unity. We also demonstrate a corresponding dynamical self-trapping phenomenon at the non-linear impurity by a numerical study of the time-integrated autocorrelation function.