Raman scattering in a two-layer antiferromagnet

TL;DR

This paper develops a theoretical framework for two-magnon Raman scattering in a two-layer antiferromagnet, analyzing the effects of interlayer exchange coupling on spectra and comparing results with experiments in cuprate compounds.

Contribution

It provides a detailed diagrammatic theory for Raman scattering in two-layer antiferromagnets, including the effects of interlayer exchange and resonance, and challenges recent claims of large interlayer coupling based on experimental data.

Findings

Nonzero interlayer exchange coupling $J_2$ affects Raman spectra in $A_{1g}$ geometry.

The $A_{1g}$ signal peaks at small transferred frequency related to the spin-wave gap.

Large $J_2$ values are inconsistent with experimental Raman data in certain compounds.

Abstract

Two--magnon Raman scattering is a useful tool to verify recent suggestions concerning the value of the interplanar exchange constant in antiferromagnetic two--layer systems, such as $YBa_2Cu_3O_{6+x}$. We present a theory for Raman scattering in a two--layer antiferromagnet. We study the spectra for the electronic and magnetic excitations across the charge transfer gap within the one--band Hubbard model and derive the matrix elements for the Raman scattering cross section in a diagrammatic formalism. We analyze the effect of the interlayer exchange coupling $J_2$ for the Raman spectra in $A_{1g}$ and $B_{1g}$ scattering geometries both in the non--resonant regime (when the Loudon--Fleury model is valid), and at resonance. We show that within the Loudon--Fleury approximation, a nonzero $J_2$ gives rise to a finite signal in $A_{1g}$ scattering geometry. Both, in this approximation and at resonance, the intensity in the $A_{1g}$ channel has a peak at {\it small} transferred frequency equal to twice the gap in the spin--wave spectrum. We compare our results with experiments in $YBa_2Cu_3O_{6.1}$ and $Sr_2CuO_2Cl_2$ compounds and argue that the large value of $J_2$ suggested in a number of recent studies is incompatible with Raman experiments in $A_{1g}$ geometry.