Local magnetic moments around a nonmagnetic impurity in the two-dimensional t-J model

Local magnetic moments around a nonmagnetic impurity in the two-dimensional t-J model are studied within Gutzwiller approximations and the Bogoliubov-de Gennes theory. We show that the resonance peak in the local density of states expected around the impurity splits into two when local magnetic moments are induced near the impurity. Therefore, in the recent scanning tunneling spectroscopy data on Bi₂Sr₂Ca(Cu_1-xZn_x)₂O _8+δ [Pan et al., Nature (London) 403, 746 (2000)] which show the sharp resonance peak, there is no evidence of the existence of local moments around the Zn impurities. It is shown that the absence of local moments is caused by the tendency of electrons to avoid the impurity.