Spin Dynamics and Magnetic Correlation Length in Two-Dimensional Quantum Heisenberg Antiferromagnets

The correlated spin dynamics and temperature dependence of the correlation length $\xi \left(T\right)$ in two-dimensional quantum $(S=1\mathrm{}/2)$ Heisenberg antiferromagnets (2DQHAF) on a square lattice are discussed in light of experimental results of proton spin lattice relaxation in copper formiate tetradeuterate. In this compound the exchange constant is much smaller than the one in recently studied 2DQHAF, such as ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{Sr}}_2{\mathrm{CuO}}_2{\mathrm{Cl}}_2$. Thus the spin dynamics can be probed in detail over a wider temperature range. The NMR relaxation rates turn out to be in excellent agreement with a theoretical mode-coupling calculation. The deduced temperature behavior of $\xi \left(T\right)$ is in agreement with high-temperature expansions, quantum Monte Carlo simulations, and the pure quantum self-consistent harmonic approximation. Contrary to the predictions of the theories based on the nonlinear $\sigma$ model, no evidence of crossover between different quantum regimes is observed.