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 (Formula presented)(Formula presented)(Formula presented). 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 (Formula presented) for the Raman spectra in (Formula presented) and (Formula presented) 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 (Formula presented) gives rise to a finite signal in (Formula presented) scattering geometry. Both in this approximation and at resonance the intensity in the (Formula presented) 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 (Formula presented)(Formula presented)(Formula presented) and (Formula presented)(Formula presented)(Formula presented) compounds and argue that the large value of (Formula presented) suggested in a number of recent studies is incompatible with Raman experiments in (Formula presented) geometry.