Solitonlike excitations in a spin chain with a biquadratic anisotropic exchange interaction

Abstract

Nonlinear solitonlike excitations in a spin chain with a biquadratic anisotropic exchange interaction are investigated using the coherent-state method combined with the Holstein-Primakoff bosonic representation of the spin operators. It is argued that the modified terms of the nonlinear Schr\"odinger equation are strongly restricted by the relation between the continuum approximation (\ensuremath{\eta}=d/\ensuremath{\lambda}, the degree of the long-wavelength approximation, where d is the lattice constant and \ensuremath{\lambda} is the characteristic wavelength of excitation) and the semiclassical approximation (\ensuremath{\epsilon}=1/ \ensuremath{\surd}S , the degree of the truncation of the operator expansion, where S is the spin length). When assuming that \ensuremath{\eta} and \ensuremath{\epsilon} have the same order (\ensuremath{\eta}\ensuremath{\sim}\ensuremath{\epsilon}) after retaining terms of equivalent order O(${\mathrm{\ensuremath{\epsilon}}}^{6}$), the motion of the Bose operator for the anisotropic case satisfies the nonlinear Schr\"odinger equation with cubic nonlinearity, and solitonlike excitations are obtained. The other two cases of the relations between \ensuremath{\eta} and \ensuremath{\epsilon}(\ensuremath{\eta}\ensuremath{\sim}${\mathrm{\ensuremath{\epsilon}}}^{3/2}$ and \ensuremath{\eta}\ensuremath{\sim}${\mathrm{\ensuremath{\epsilon}}}^{2}$) are also discussed.