We report a neutron scattering study of the long-wavelength dynamic spin correlations in the model two-dimensional $S=1/2\mathrm{}$ square lattice Heisenberg antiferromagnets ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$ and ${\mathrm{Sr}}_2{\mathrm{Cu}}_3{\mathrm{O}}_4{\mathrm{Cl}}_2$. The characteristic energy scale, ${\omega }_0(T/J)$, is determined by measuring the quasielastic peak width in the paramagnetic phase over a wide range of temperature ( $0.2\lesssim T/J\lesssim 0.7$). The obtained values for ${\omega }_0(T/J)$ agree quantitatively between the two compounds and also with values deduced from quantum Monte Carlo simulations. The combined data show scaling behavior, $\omega \sim {\xi }^{-z}$, over the entire temperature range with $z=1.0\mathrm{}\left(1\right)$, in agreement with dynamic scaling theory.

• Received 21 November 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.3144