Theoretical analysis of magnetic Raman scattering in La2CuO4: two-magnon intensity with the inclusion of ring exchange

We evaluate the Raman light scattering intensity for the square lattice Heisenberg antiferromagnet with plaquette ring exchange J_\Box. With the exchange couplings as fixed before from an accurate fit to the spin-wave dispersion in La2CuO4, leading in particular to J_\Box=0.24J, we demonstrate in a parameter free calculation that the inclusion of the plaquette exchange contribution to the dispersion and the magnon-magnon interaction vertex gives a peak position in $B_{1g}$ scattering geometry E_max = 2.71J which is in excellent agreement with the experimental data. Yet, the intrinsic width and the lineshape of the two-magnon remain beyond a descriptions in terms of a spin-only Hamiltonian.