Resonant Raman Scattering in Antiferromagnets

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 ${\omega }_{res}^{(1)}\approx 2\Delta +3J$ and ${\omega }_{res}^{(2)}\approx 2\Delta +8J$. 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 ${\omega }_{res}^{(1)}$ to a symmetric form around ${\omega }_{res}^{(2)}$. 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 $S{r}_{2}Cu{O}_{2}C{l}_2$ and $YB{a}_{2}C{u}_3{O}_{6.1}$ and Rübhausen et al. on $PrB{a}_{2}C{u}_3{O}_7$ and show that the triple resonance theory yields a qualitative and to some extent also quantitative understanding of the experimental data.

19 pages, RevTeX, 16 figures embedded in the text, ps-file is also available at http://lifshitz.physics.wisc.edu/www/morr/morr_homepage.html

References in corpus (6)

• Correlated Electrons in High Temperature Superconductors
• Quasiparticle Dispersion of the 2D Hubbard Model: From an Insulator to a Metal
• Resonant two-magnon Raman scattering in antiferromagnetic insulators
• Influence of next-nearest-neighbor electron hopping on the static and dynamical properties of the 2D Hubbard model
• Magnetic Raman Scattering in Two-Dimensional Spin-1/2 Heisenberg Antiferromagnets: Spectral Shape Anomaly and Magnetostrictive Effects
• Systematic 1/S study of the 2D Hubbard model at half-filling

Cited by in corpus (12)

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• Inelastic Light Scattering From Correlated Electrons
• Electronic Raman scattering in correlated materials: exact treatment of nonresonant, mixed, and resonant scattering with dynamical mean field theory
• Raman Response of Magnetic Excitations in Cuprate Ladders and Planes
• Higgs Mode and Magnon Interactions in 2D Quantum Antiferromagnets from Raman Scattering
• Two-magnon Raman scattering in insulating cuprates: Modifications of the effective Raman operator
• Resonant Enhancement of Inelastic Light Scattering in Strongly Correlated Materials
• Magnetic excitations and amplitude fluctuations in insulating cuprates
• Electron-phonon coupling in undoped cuprate $YB{a}_{2}C{u}_3{O}_6$ estimated from Raman and optical conductivity spectra
• Magnon and Hole Excitations in the Two-Dimensional Half-filled Hubbard Model
• Resonant Enhancement of Electronic Raman Scattering
• Elementary excitations in undoped layered cuprates