Crossover to non-Fermi-liquid spin dynamics in cuprates

The antiferromagnetic spin correlation function $S_{\mathbf{Q}}$, the staggered spin susceptibility ${\chi }_{\mathbf{Q}}$ 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 $c_h<c_h^{\ast }\sim 0.16$, while it shows a steep increase in the overdoped regime. A quantitative analysis of NMR spin-spin relaxation-rate $1\mathrm{/}{T}_{2G}$ 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.