Frequency moments of the light-scattering spectrum from spin-pair excitations are calculated for the spin-½ planar Heisenberg antiferromagnet. The quantitative agreement with the experimental $B_{1g}$ spectrum in ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$ demonstrates that the observed linewidth is dominated by quantum fluctuations and yields a value for the exchange parameter $J$ of 1030±50 ${\mathrm{cm}}^{-1\mathrm{}}$. Quantum fluctuations also permit light scattering due to diagonal-next-neighbor spin-pair excitations. Observed spectral features in the $A_{1g}$ and $B_{2g}$ symmetries are consistent with those calculated for this process.

• Received 13 March 1989

DOI:https://doi.org/10.1103/PhysRevLett.62.2736