Three-magnon bound states in an S=1 linear chain with next-nearest-neighbour interaction

Abstract

The problem of three spin deviations from a fully aligned state is studied for the Heisenberg model with next-nearest-neighbour interactions for the case of spin 1. The method used is a straightforward generalization of the equation-of-motion method of Fukuda and Wortis, taking care of the unphysical states. The resulting integral equation is solved in one dimension and the dependence of the bound states on the next-nearest-neighbour interaction discussed. Numerical calculations have also been done for closed chains containing up to 40 spins. By using CN invariance of the Hamiltonian, the dimensionality of the space is substantially reduced. The results of the finite-chain calculation agree well with solutions obtained from the equation-of-motion method.

Multi-magnon excitations in Heisenberg spin-Schains with next-nearest-neighbour interactions

“…As β → ∞ (figure 8), the upper bound state emerges from the continuum at values of K closer to K = π/2a, and we simply have the β = 0 case with the lattice distance doubled. These results do not agree with those reported previously by Kadolkar et al [19]. For all β > 0, we find that only the lower bound-state branch exists for all K. The upper branch is present near K = π/a for small β and near K = π/2a for large values of β.…”

“…The shaded region is the scattering-state continuum (shading slanted to the left indicates the two-bound-onefree-magnon continuum, and shading slanted to the right indicates the three-free-magnons continuum), the solid lines below the continuum indicate the bound states, and the dashed line indicates a resonance. The energies of the bound states at K = π/a agree fairly well with the energies found by Millet and Kaplan [20] and Kadolkar, Ghosh and Sarma [19] using an integral equation approach. We find two bound states below the continuum: the lower state exists across the entire Brillouin zone but the upper enters the continuum near K = π/a and becomes a resonance.…”

“…This case was discussed in detail by Southern et al [1]. The shaded region is [20] and Kadolkar, Ghosh and Sarma [19] using an integral equation approach. We find two bound states below the continuum: the lower state exists across the entire Brillouin zone but the upper enters the continuum near K = π/a and becomes a resonance.…”

“…Bound states exist both below and above the scattering-state continuum. Kadolkar et al [19] have recently studied the three-magnon spectrum of the S = 1 Heisenberg model with NNN interactions. Their method is based upon the integral equation approach used by Millet and Kaplan [20].…”

Spin wave and spin flip in hexagonal LuMnO3 single crystal

“…For multiple spin flip in the spin-network of magnetic ion with spin state ≥ 1, different types of multiple spin flip states are possible [23]. In hexagonal manganites, the Mn 3+ ions (spin state of S = 2) forming triangular networks.…”