Resonant Raman Scattering in Antiferromagnets

TL;DR

This paper analyzes the resonant Raman scattering in antiferromagnets, focusing on the two-magnon peak behavior near resonance, and compares theoretical predictions with recent experimental results in high-$T_c$ materials.

Contribution

It derives an expression for Raman intensity including triple resonance and final state interactions, explaining experimental observations in high-$T_c$ compounds.

Findings

Identifies two maxima in two-magnon peak height at specific incident frequencies.

Shows the evolution of Raman profile from asymmetric to symmetric around resonances.

Demonstrates the dependence of peak height on quasiparticle damping, hopping term, and interaction corrections.

Abstract

Two-magnon Raman scattering provides important information about electronic correlations in the insulating parent compounds of high-$T_c$ materials. Recent experiments have shown a strong dependence of the Raman signal in $B_{1g}$ 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 one of us (A.Ch) and D. 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 $\omega^{(1)}_{res} \approx 2\Delta + 3J$ and $\omega^{(2)}_{res} \approx 2\Delta + 8J$. 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 $\omega^{(1)}_{res}$ to a symmetric form around $\omega^{(2)}_{res}$. We further show that the TMPH depends on the fermionic quasiparticle damping, the next-nearest neighbor hopping term $t^{\prime}$ 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 $Sr_2CuO_2Cl_2$ and $YBa_2Cu_3O_{6.1}$ and R\"{u}bhausen et al. on $PrBa_2Cu_3O_7$ and show that the triple resonance theory yields a qualitative and to some extent also quantitative understanding of the experimental data.