Impurity-induced spin polarization and NMR line broadening in underdoped cuprates

We present a theory of magnetic $\mathrm{}(S=1\mathrm{})\mathrm{}$ Ni and nonmagnetic Zn impurities in underdoped cuprates. Both types of impurities are shown to induce $S=\frac{1}{2}$ moments on Cu sites in the proximity of the impurity, a process which is intimately related to the spin gap phenomenon in cuprates. Below a characteristic Kondo temperature, the Ni spin is partially screened by the Cu moments, resulting in an effective impurity spin $S=\frac{1}{2}.$ We further analyze the Ruderman-Kittel-Kasiya-Yosida–type response of planar Cu spins to a polarization of the effective impurity moments and derive expressions for the corresponding ${}^{17}\mathrm{O}$ NMR line broadening. The peculiar aspects of recent experimental NMR data can be traced back to different spatial characteristics of Ni and Zn moments, as well as to an inherent temperature dependence of local antiferromagnetic correlations.