Local moment and inhomogeneous hyperfine interaction in the CuO$_2$ plane of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) single crystal by ${}^{17}$O NMR

The ${}^{17}$O NMR spectra of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212) single crystals were measured in the magnetic field of 8 T from 4 K to 200 K. The linewidth of the oxygen in CuO$_2$ plane, O(1), was found to follow a Curie temperature dependence in the normal state, where the Curie coefficient decreases with the increase of $\delta$ oxygen in the crystal. In the superconductive state, it decreases with deceasing temperature, proportional to the decreasing Knight shift. This temperature dependence of the linewidth identifies the existence of local moment and inhomogeneous hyperfine interaction in the CuO$_2$ plane.