Spin dynamics in a two-dimensional disordered S= Heisenberg paramagnetfrom ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ NQR relaxation in Zn-doped ${\mathrm{La}}_2$${\mathrm{CuO}}_4$

${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ NQR ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ relaxation measurements in ${\mathrm{La}}_2$${\mathrm{Cu}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Zn}}_{\mathrm{x}}$${\mathrm{O}}_4$, for 0⩽x⩽0.11 and in the temperature range ${\mathrm{T}}_{\mathrm{N}}$⩽T⩽900 K, are presented. The results are used to derive insights into the ${\mathrm{Cu}}^{2+}$ correlated spin dynamics in the paramagnetic phase of the S= two-dimensional (2D) Heisenberg (H) antiferromagnets (AF), and into the disorder effects associated with the spin vacancy due to ${\mathrm{Zn}}^{2+}$ (S=0) for ${\mathrm{Cu}}^{2+}$ substitution. In particular, by using scaling arguments for the static generalized susceptibility, χ(q-→,0), and for the decay rate, ${\mathrm{\Gamma }}_{\mathrm{q}-\to }$, of the normal excitations, ${\mathrm{T}}_2$ and ${\mathrm{T}}_1$ are related to the in-plane correlation length ${\xi }_{2\mathrm{D}}$(x,T) and its dependence on temperature and Zn doping, x, is extracted. The experimental findings are analyzed in light of the quantum critical and renormalized classical behaviors for ${\xi }_{2\mathrm{D}}$ predicted by recent theories for S=1/2 HAF on square lattices. It is shown that up to T≃900 K, ${\xi }_{2\mathrm{D}}$ is consistent with the assumption of a renormalized classical regime, in agreement with recent neutron scattering results and at variance with previous interpretations of the NQR data. It is discussed how Zn affects ${\xi }_{2\mathrm{D}}$ through the modification in the spin stiffness and comparison with the disorder induced by itinerant extra holes is made.