On soliton excitations in a one-dimensional Heisenberg ferromagnet

Abstract

Soliton excitations in a one-dimensional Heisenberg ferromagnet are studied by means of the Holstein-Primakoff representation. Writing the Hamiltonian and the equation of motion into dimensionless forms, the authors show that the relative ratio of epsilon to eta is important for the determination of the modified terms of the nonlinear Schrodinger equation; epsilon =1/ square root S (S is the spin length) is the small dimensionless parameter used in the semiclassical approximation and eta =a/ lambda 0 (a is the lattice space and lambda 0 is the characteristic wavelength of the excitations) is another small dimensionless parameter used in the long-wave approximation. The soliton solutions are given in three cases ( eta =O( epsilon ), eta =O( epsilon 32/) and eta =O( epsilon 2)) which correspond to the different physical conditions of the system. The results obtained by Pushkarov and Pushkarov (1977), de Azevedo et al. (1982), and Skrinjar et al. (1989) are included in this approach.