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Probing the susceptibility $χ'(q)$ in cuprates using Ni impurities

Recent NMR experiments on $YBa_2(Cu_{1-x}Ni_x)_3O_{6+δ}$ (Bobroff et al. Phys. Rev. Lett. 79, 2117 (1997)) have shown that Ni impurities provide an important probe for the momentum dependence of the static spin susceptibility $χ'(q)$. Combining the measurements of the $^{17}$O line width $Δν$ with those of the Gaussian relaxation time $T_{2G}$, we find that the magnetic correlation length $ξ$ must have a substantial temperature dependence. Using numerical simulations we present a detailed analysis of $Δν$ as a function of temperature and impurity concentration. For a Lorentzian shape of $χ'(q)$ $Δν$ strongly depends on $ξ$, in contrast to the Gaussian form. This result together with the experimental finding that $ξ$ is temperature dependent rules out the Gaussian form of $χ'(q)$.