The renormalization of large-wave-vector magnons in Cr${\mathrm{Br}}_3$ has been carefully studied using inelastic neutron scattering. The results are in disagreement with the first-order approximation to Dyson's spin-wave theory, which predicts that the spin-wave energy shift $\frac{\Delta E}{E}$ is independent of wave vector. Over part of the Brillouin zone our data can be fitted to a constant $\frac{\Delta E}{E}$. However, in the region $q=0.4\mathrm{}$ to 0.6 ${\mathrm{\AA }}^{-1\mathrm{}}$ in the $\Delta$ direction, there is strong evidence for a wave-vector dependence of $\frac{\Delta E}{E}$, such as would arise from the higher-order spin-wave interactions, i.e., spin-wave correlation effects. Qualitative comparison is made to the predictions of $t$-matrix calculations, which treat the interactions to all orders (and are thus capable of reproducing Dyson's results). The observed $q$ dependence agrees with these (qualitative) predictions, giving evidence for the direct observation of the effect of correlations between spin waves. Unfortunately, quantitative comparisons between theory and experiment are not possible at present, because of the difficulty of calculating the two-spin-wave $t$ matrix for this system.

• Received 14 May 1971

DOI:https://doi.org/10.1103/PhysRevB.4.2280