  A microscopic theory is presented for the local moment formation near a
non-magnetic impurity or a copper defect in high-T_c superconductors. We use a
renormalized meanfield theory of the t-J model for a doped Mott insulator and
study the fully self-consistent, spatially unrestricted solutions of the d-wave
superconducting (SC) state in both the spin S=0 and S=1/2 sectors. We find a
transition from the singlet d-wave SC state to a spin doublet SC state when the
renormalized exchange coupling exceeds a doping dependent critical value. The
induced S=1/2 moment is staggered and localized around the impurity. It arises
from the binding of an S=1/2 nodal quasiparticle excitation to the impurity.
The local density of states spectrum is calculated and connections to NMR and
STM experiments are discussed.
