Quantitative Determination of Quantum Fluctuations in the Spin-½ Planar Antiferromagnet

Frequency moments of the light-scattering spectrum from spin-pair excitations are calculated for the spin-\textonehalf{} 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\ifmmode\pm\else\textpm\fi{}50 ${\mathrm{cm}}^{\ensuremath{-}1}$. 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.