Resonant Raman scattering in antiferromagnets

Two-magnon Raman scattering provides important information about electronic correlations in the insulating parent compounds of high-(Formula presented) materials. Recent experiments have shown a strong dependence of the Raman signal in (Formula presented) geometry on the frequency of the incoming photon. We present an analytical and numerical study of the Raman intensity in the resonant regime. It has been previously argued by Chubukov and Frenkel that the most relevant contribution to the Raman vertex at resonance is given by the triple resonance diagram. We derive an expression for the Raman intensity in which we simultaneously include the enhancement due to the triple resonance and a final-state interaction. We compute the two-magnon peak height (TMPH) as a function of incident frequency and find two maxima at (Formula presented) and (Formula presented) We argue that the high-frequency maximum is cut only by a quasiparticle damping, while the low-frequency maximum has a finite amplitude even in the absence of damping. We also obtain an evolution of the Raman profile from an asymmetric form around (Formula presented) to a symmetric form around (Formula presented) We further show that the TMPH depends on the fermionic quasiparticle damping, the next-nearest-neighbor hopping term (Formula presented) and the corrections to the interaction vertex between light and the fermionic current. We discuss our results in the context of recent experiments by Blumberg et al. on (Formula presented) and (Formula presented) and Rübhausen et al. on (Formula presented) and show that the triple resonance theory yields a qualitative and to some extent also quantitative understanding of the experimental data.