We present a theory of magnetic (S = 1) Ni and nonmagnetic Zn impurities in
underdoped cuprates. Both types of impurities an shown to induce S = 1/2 m
oments on Cu sites in the proximity of the impurity, a process which is int
imately related to the spin gap phenomenon in cuprates, Below a characteris
tic Kondo temperature, the Ni spin is partially screened by the Cu moments,
resulting in an effective impurity spin S = 1/2. We further analyze the Ru
derman-Kittel-Kasiya-Yosida-type response of planar Cu spins to a polarizat
ion of the effective impurity moments and derive expressions for the corres
ponding O-17 NMR line broadening. The peculiar aspects of recent experiment
al NMR data can be traced back to different spatial characteristics of Ni a
nd Zn moments, as well as to an inherent temperature dependence of local an
tiferromagnetic correlations. [S0163-1829(99)15121-X].