Abstract
Within the framework of the $t\ensuremath{-}J$ model, the evolution, with hole doping, of the antiferromagnetic (AF) correlation length and the spin correlation function in high-${T}_{c}$ superconductors are studied. The dynamic spin susceptibility has been calculated by using a two-time Green's function method that allows one to take into account both electron and AF spin correlation. A comparison of our results with NMR and neutron scattering data shows that the model is able to reproduce the main features of the temperature and doping dependences of the AF correlation length in both the pure Heisenberg antiferromagnet (e.g., ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4})$ and doped compounds (e.g., ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}).$
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