Phonon Effects on Two-Magnon Raman Spectra in Layered Cuprate Systems

We have analyzed the anomalous line shapes of the two-magnon Raman spectra of undoped high T_c cuprates, using the spin wave theory in a two-dimensional Heisenberg antiferromagnet. In order to describe a shoulder peak structure near 4J, which is primarily associated with magnetic excitations of B_1g symmetry, we have explored the phonon contribution to the Raman spectra. Incorporating the magnon-phonon Hamiltonian due to the modulated exchange interaction by phonons, we have evaluated the two-magnon Raman spectral function coming from the lowest order magnon-phonon-magnon scattering. It is found that the magnon-phonon-magnon scattering gives rise to a phonon-induced shoulder peak near 4J besides the dominant two-magnon peak near 3J, in good agreement with experiments.