Spin-Wave Approach to Two-Magnon Raman Scattering in a Simple Antiferromagnet

A spin-wave theory of two-magnon Raman scattering for a simple antiferromagnet at low temperatures is presented. The treatment is based on the Dyson-Maleev boson representation of the localized spin operators. At zero temperature, the theory yields results for the Raman cross section which are in excellent agreement with those which obtain from the Green's-function equation-of-motion method developed by Elliott and Thorpe. In the present theory, we derive an approximate cross-section formula in terms of renormalized one-magnon propagators and a vertex function which satisfies a general Bethe-Salpeter equation. Taking into consideration the lowest-order interaction processes, it is found that the experimentally observed shift of the Raman peak to lower energies with increasing temperature can satisfactorily be accounted for. However, it is also found that this lowest-order theory is inadequate for explaining the observed thermal broadening of the Raman spectra. The possibility that the observed broadening is due to damping of the one-magnon states is examined using a phenomenological width $\Gamma$ for a zone-edge magnon. It is found that the necessary width is surprisingly large, although more accurate calculations of the damping of a zone-edge magnon are needed to eliminate this possibility. Higher-order irreducible vertex corrections in the two-magnon Bethe-Salpeter equation are also considered. An approximate cross-section formula which includes these higher-order corrections is obtained using a variational principle. The effect of these corrections on the Raman line shape has not yet been determined.