Dynamics of two-magnon resonances in the absence of bound states

Spectral intensity distributions are calculated for different types of spin-pair excitations in a simple-cubic Heisenberg ferromagnet with next-nearest-neighbor (nnn) exchange interactions. The ratio of next-nearest- to nearest-neighbor (nn) exchange interaction ($\eta$) is chosen to be large enough to prevent the formation of bound states, by containing all pair excitations in the continuum, but without being too far removed from the nn case. Calculations have been performed using $\eta =\frac{1}{8}$ and $S=1\mathrm{}$ for single-ion, nn and nnn pair excitations for total pair wave vectors ($\overrightarrow{\mathrm{K}}$) along the [111] direction. An understandable picture of the excitations follows the study of resonance peaks in the computed spectra and their comparison with those of the nn case. The changes due to the relaxation of the exact Ising-like limit of the nearest-neighbor case at the zone boundary in the [111] direction are largely due to states which were formerly bound states having become resonances for all values of $\overrightarrow{\mathrm{K}}$.