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.

The Two-Soliton Bound-State Solution in an Order-Parameter-Preserving Antiferromagnet

“…Introducing the Dyson-Maleev transformation and the coherent state ansatz, we have investigated two-soliton bound-state solution in an OPP-AFM by using the method of multiple scales combined with the long-wavelength approximation, and avoided the inconsistence of the two-parameter theory of solitons in ferromagnetic system^1 [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] !. For studying the solitonin ferromagnets and antiferromagnets, the approach, developed above, is self-consistent and systematic.…”

“…where V"i i V4 are functions of all Xj and tj (j = 0,1,2,3,...), but these arguments will not be written explicitly. In the previous workst [15][16][17][18][19][20][21] ^ V,-is neglected. In order to consider this problem perfectly, V>, -is retained in this paper.…”

Localized spin excitations in a site-dependent antiferromagnetic spin system with D-M interaction

“…The AFM has two interpenetrating sublattices A and B which is denoted by the superscripts A and B respectively. Now, the spin Hamiltonian (1) is expressed in the dimensionless form [48] by introducing the dimensionless spin. The Hamiltonian now becomes…”

Nonlinear Excitation in Antiferromagnet RbFeCl 3

“…In order to get the slow varying ipi and V>2, the method of multiple scales is used to change Eqs (11) and (12) to another solvable nonlinear equations.' 8 '^ The method of multiple scales requires different spatial scales Xj -\s?x and time scales tj = piH (fi <C l,j = 0,1, 2, • • •).…”