Recent NMR experiments on ${\mathrm{YBa}}_2({\mathrm{Cu}}_{1-x}{\mathrm{Ni}}_x{)}_3{\mathrm{O}}_{6+\delta }$ [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 ${\chi }^{\prime }\left(\mathbf{q}\right).\mathrm{}$ Combining the measurements of the ${}^{17}\mathrm{O}$ line width $\Delta \nu$ with those of the Gaussian relaxation time $T_{2\mathrm{G}},$ 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 ${\chi }^{\prime }\left(\mathbf{q}\right)\hspace{0.5em}\Delta \nu$ 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 ${\chi }^{\prime }\left(\mathbf{q}\right).\mathrm{}$

• Received 26 January 1998

DOI:https://doi.org/10.1103/PhysRevB.58.11193