The antiferromagnetic spin correlation function $S_{ \bf Q}$, the staggered spin susceptibility $\chi_{ \bf Q}$ and the energy scale $\omega_{ FL}=S_{ \bf Q}/\chi_{ \bf Q}$ are studied numerically within the t-J model and the Hubbard model, as relevant to cuprates. It is shown that $\omega_{ FL}$, related to the onset of the non-Fermi-liquid spin response at $T>\omega_{ FL}$, is very low in the regime below the 'optimum' hole doping $c_h < c_h^* \sim 0.16$, while it shows a steep increase in the overdoped regime. A quantitative analysis of NMR spin-spin relaxation-rate $1/T_{ 2G}$ for various cuprates reveals a similar behavior, indicating on a sharp, but continuous, crossover between a Fermi-liquid and a non-Fermi-liquid behavior as a function of doping.
Categories: cond-mat.str-el