Raman Scattering in Layered Cuprate Materials

Raman scattering has provided valuable information on High-T_{c} materials, both in the insulating and doped case. Here we are concerned with the question of explaining the lineshape of inelastic light scattering in the undoped phase, which is believed to be due to magnetic excitations. This lineshape is very peculiar, because of its broad line width and long tail at high frequencies. The model that we use is a spin S = 1/2 Heisenberg antiferromagnet, which has been shown to explain very well the long wavelength properties of the undoped cuprates. The coupling between the light and the magnetic system is described by an effective spin-pair perturbation. The technique used is spin-wave theory beyond the linear approximation. We have carried out a careful analysis of spin-wave interactions, which has allowed us to obtain precise estimates for the spin-wave velocity, staggered magnetization, and the dispersion of interacting spin-waves in the whole Brillouin Zone. The main result is that the elementary excitations of this model, at long and short wavelengths, are ordinary, weakly interacting, spin-waves. For the Raman scattering we have carried out a systematic evaluation of the two spin-wave and four-spin -wave contribution. The overall lineshape obtained is in good agreement with moments computed by other techniques, but is still far from the experimental lineshape. This suggests that the standard model used fails to capture some of the essential physics in these unusual materials.