Soliton-like magnon localization and the two-magnon bound state in a Heisenberg ferromagnetic chain

Abstract

An inhomogeneous Heisenberg spin Hamiltonian with single-ion anisotropy is used to investigate the non-linear excitations in a ferromagnetic chain. By means of the Holstein-Primakoff transformation and Glauber's coherent-state representation, the equation of motion for the annihilation operator a(j) is reduced to a non-linear Schrodinger-like equation with variable coefficients. Its non-linear modified terms are strongly restricted by the relation between the continuum approximation ( eta =a/ lambda 0, where eta is the 'degree' of the long wavelength, a is the lattice constant and lambda 0 the characteristic wavelength of the excitation) and the semiclassical approximation ( in =1/ square root S, where in is the degree of truncation of the operator expansion and S is the spin length). When assuming that eta =O( in ) and after retaining the terms to O( in 4), the motion of the coherent amplitude for the homogeneous case satisfies the non-linear Schrodinger equation. The single-soliton and two-soliton bound-state solutions are given. The results show that the magnon localization and two-magnon bound state are possible in the chain. Other relations between eta and in ( eta =O( in 1/2), eta =O( in 3/2 and eta =O( in 2)) are also discussed.