Neutron scattering study of the two-dimensional spin S=1/2 square-lattice Heisenberg antiferromagnet Sr₂CuO₂Cl₂

We have carried out a neutron scattering investigation of the static structure factor S(q_{2 D}) (q_{2 D} is the in-plane wave vector) in the two-dimensional spin S=1/2 square-lattice Heisenberg antiferromagnet Sr₂CuO₂Cl₂. For the spin correlation length ξ we find quantitative agreement with Monte Carlo results over a wide range of temperature. The combined Sr₂CuO₂Cl₂-Monte Carlo data, which cover the length scale from ≈1 to 200 lattice constants, are predicted without adjustable parameteres by renormalized classical theory for the quantum nonlinear sigma model. For the structure factor peak S(0), on the other hand, we find S(0)∼ξ² for the reduced temperature range 0.16<T/2 πρ_s<0.36, whereas current theories predict that at low temperatures S(0)∼T²ξ². This discrepancy has important implications for the interpretation of many derivative quantities such as NMR relaxation rates. In the ordered phase, we have measured the temperature dependence of the out-of-plane spin-wave gap. Its low-temperature value of 5.0 meV corresponds to an XY anisotropy J_XY/J=1.4×10^-4. From measurements of the sublattice mangetization we obtain β=0.22±0.01 for the order parameter exponent. This may either reflect tricricality as in La₂CuO₄, or it may indicate finite-size two-dimensional XY behavior as suggested by Bramwell and Holdsworth. As in the S=1 system K₂NiF₄, the gap energy in Sr₂CuO₂Cl₂ scales linearly with the order parameter up to the Néel temperature. We also reanalyze static structure factor data for K₂NiF₄ using the exact low temperature result for the correlation length of Hasenfratz and Niedermayer and including the Ising anisotropy explicitly. Excellent agreement between experiment and theory is obtained for the correlation length, albeit with the spin-stiffness ρ_s reduced by ≈20% from the spin-wave value. As in Sr₂CuO₂Cl₂ we find that S(0)∼ξ² for the reduced temperature range 0.22<T/2 πρ_s<0.47.