Magnetic Raman Scattering in Two-Dimensional Spin-1/2 Heisenberg Antiferromagnets: Spectral Shape Anomaly and Magnetostrictive Effects

We calculate the Raman spectrum of the two-dimensional spin-1/2 Heisenberg antiferromagnet by exact diagonalization and quantum Monte Carlo techniques on clusters of up to 144 sites. On a 16-site cluster, we consider the phonon-magnon interaction which leads to random fluctuations of the exchange integral. Results are in good agreement with Raman scattering experiments on various high- $T_c$ precursors, such as ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.2}$. In particular, our calculations reproduce the broad line shape of the two-magnon peak, the asymmetry about its maximum, the existence of spectral weight at high energies, and the observation of nominally forbidden $A_{1g}$ scattering.