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

Recent NMR experiments on $YBa_2(Cu_{1-x}Ni_x)_3O_{6+\delta}$ (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 $\chi'(q)$. Combining the measurements of the $^{17}$O line width $\Delta \nu$ with those of the Gaussian relaxation time $T_{2G}$, we find that the magnetic correlation length $\xi$ must have a substantial temperature dependence. Using numerical simulations we present a detailed analysis of $\Delta \nu$ as a function of temperature and impurity concentration. For a Lorentzian shape of $\chi'(q)$ $\Delta \nu$ strongly depends on $\xi$, in contrast to the Gaussian form. This result together with the experimental finding that $\xi$ is temperature dependent rules out the Gaussian form of $\chi'(q)$.