  By solving self-consistently an effective Hamiltonian including interactions
for both antiferromagnetic spin-density wave (SDW) and d-wave superconducting
(DSC) orderings, a comparison study is made for the local magnetic structure
around superconducting vortices and unitary impurities. To represent the
optimally doped regime of cuprates, the parameter values are chosen such that
the DSC is dominant while the SDW is vanishingly small. We show that when
vortices are introduced into the superconductor, an oscillating SDW is induced
around them. The oscillation period of the SDW is microscopically found,
consistent with experiments, to be eight lattice constants ($8a_0$). The
associated charge-density wave (CDW) oscillates with a period of one half
($4a_0$) of the SDW. In the case of unitary impurities, we find a SDW
modulation with identical periodicity, however without an associated CDW. We
propose neutron scattering experiments to test this prediction.
