Instantaneous spin correlations in ${\mathrm{La}}_2{\mathrm{CuO}}_4$

We have carried out a neutron-scattering study of the instantaneous spin-spin correlations in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ ${(T}_N=325\mathrm{}\mathrm{K})$ over the temperature range 337–824 K. Incident neutron energies varying from 14.7–115 meV have been employed in order to guarantee that the energy integration is carried out properly. The results so obtained for the spin-correlation length as a function of temperature when expressed in reduced units agree quantitatively both with previous results for the two-dimensional (2D) tetragonal material ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$ and with quantum Monte Carlo results for the nearest-neighbor square lattice $S=\frac{1}{2}$ Heisenberg model. All of the experimental and numerical results for the correlation length are well described without any adjustable parameters by the behavior predicted for the quantum nonlinear sigma model in the low-temperature renormalized classical regime. The amplitude, on the other hand, deviates subtly from the predicted low-temperature behavior. These results are discussed in the context of recent theory for the 2D quantum Heisenberg model.