Effect of Biquadratic Exchange on Two Magnon States of Heisenberg Ferromagnets: Other Neighbor Exchange

Abstract

We have investigated the two magnon localized states of a one dimensional Heisenberg ferromagnet the Hamiltonian of which is made up of nearest neighbor and next nearest neighbor isotropic bilinear and biquadratic exchange terms, and a single ion anisotropy term. We have restricted our choice of parameters so that the ground state at T = 0 is the fully aligned ferromagnetic state and we have used the thermodynamic Green functions where the averages have been evaluated in the ground state so that our results are good for [Formula: see text]. We have evaluated the probabilities of finding two spin deviations a distance n apart when the system is in a localized state described by total wave vector q. We have (a) compared the effects of ferromagnetic and antiferromagnetic next nearest neighbor exchange, (b) found that localized modes can lie below or above the two free magnon band depending upon the sign and magnitude of the biquadratic exchange, (c) found that in certain cases two spin deviations appear to behave like objects interacting only via a soft core, and (d) found that modes can have a large single ion component when the single ion anisotropy is zero.