Theory of Two-Magnon Raman Scattering in the Ordered Region for Cubic Antiferromagnets

A Green's-function theory is applied to a study of two-magnon (2M) Raman scattering in cubic antiferromagnets in the ordered region. In addition to the first-order Hartree-Fock renormalization of the magnon energies together with 2M-interaction effects, a second-order theory gives additional contributions to the magnon self-energies. In particular, damping terms arising at this order are approximately evaluated for zone-boundary magnons, i.e., the ones relevant to the 2M Raman scattering Process. Using a second-order expression for the 2M Raman cross section, this magnon damping is seen to eliminate the discrepancies of first-order theories. Quantitative comparison with experimental 2M Raman spectra gives a satisfactory agreement, both for the peak and the width of the spectra of KNi${\mathrm{F}}_3$ and RbMn${\mathrm{F}}_3$, at least in the greatest part of the ordered region. The use of a simplified theory for the scattering cross section suggests the possibility of a simple estimation of zone-boundary magnon damping directly from experimental 2M spectra.