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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 (2D) spin-1/2 Heisenberg antiferromagnet by exact diagonalization and quantum Monte Carlo techniques on clusters of up to 144 sites and, on a 16-site cluster, by considering the phonon-magnon interaction which leads to random fluctuations of the exchange integral. Results are in good agreement with experiments on various high-T_c precursors, such as La_2CuO_4 and YBa_2Cu_3O_{6.2}. In particular, our calculations reproduce the broad lineshape 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.