The correlated spin dynamics and the temperature dependence of the correlation length $xi(T)$ in two-dimensional quantum ($S=1/2$) Heisenberg antiferromagnets (2DQHAF) on square lattice are discussed in the light of experimental results of proton spin lattice relaxation in copper formiate tetradeuterate (CFTD). In this compound the exchange constant is much smaller than the one in recently studied 2DQHAF, such as La$_2$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$. Thus the spin dynamics can be probed in detail over a wider temperature range. The NMR relaxation rates turn out in excellent agreement with a theoretical mode-coupling calculation. The deduced temperature behavior of $xi(T)$ 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 Non-Linear $sigma$ Model, no evidence of crossover between different quantum regimes is observed.
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