Abstract

A perturbation-theoretic diagrammatic scheme is developed for systematically studying the two-magnon Raman scattering in a Mott-Hubbard antiferromagnet. The fermionic structure of the magnon interaction vertex is obtained at order-$\frac{1}{\mathcal{N}}$ level in an inverse-degeneracy expansion, and the relevant two-magnon propagator is obtained by incorporating magnon interactions at a ladder-sum level. Evaluation of the magnon interaction vertex in the large-$U$ limit yields a nearest-neighbor instantaneous interaction with interaction energy $\ensuremath{-}J$. Application of this approach to the intermediate-$U$ regime, which is of relevance for cuprate antiferromagnets, is also discussed. Incorporating the zero-temperature magnon damping, which is estimated in terms of quantum spin fluctuations, the two-magnon Raman scattering intensity is evaluated and compared with experiments on ${\mathrm{La}}_{2}$Cu${\mathrm{O}}_{4}$.

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