Raman scattering in a two-layer antiferromagnet

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 ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$. 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 ${\mathit{J}}_2$ for the Raman spectra in ${\mathit{A}}_{1\mathit{g}}$ and ${\mathit{B}}_{1\mathit{g}}$ scattering geometries both in the nonresonant regime (when the Loudon-Fleury model is valid) and at resonance. We show that within the Loudon-Fleury approximation, a nonzero ${\mathit{J}}_2$ gives rise to a finite signal in ${\mathit{A}}_{1\mathit{g}}$ scattering geometry. Both in this approximation and at resonance the intensity in the ${\mathit{A}}_{1\mathit{g}}$ channel has a peak at small transferred frequency equal to twice the gap in the spin-wave spectrum. We compare our results with experiments in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.1}$ and ${\mathrm{Sr}}_2$ ${\mathrm{CuO}}_2$ ${\mathrm{Cl}}_2$ compounds and argue that the large value of ${\mathit{J}}_2$ suggested in a number of recent studies is incompatible with Raman experiments in ${\mathit{A}}_{1\mathit{g}}$ geometry. © 1996 The American Physical Society.