  The underdoped high-Tc materials are characterized by a competition between
Cooper pairing and antiferromagnetic (AF) order. Important differences between
the superconducting (SC) state of these materials and conventional
superconductors include the d-wave pairing symmetry and a remarkable magnetic
response to nonmagnetic perturbations, whereby droplets of spin-density wave
(SDW) order can form around impurities and the cores of vortices. In a simple
picture, whenever SC is suppressed locally, SDW order is nucleated. Within a
mean-field theory of d-wave SC in an applied magnetic field including disorder
and Hubbard correlations, we show in fact that the creation of SDW order is not
simply due to suppression of the SC order parameter, but rather due to a
correlation-induced splitting of the electronic bound state created by the
perturbation. Since the bound state exists because of the sign change of the
order parameter along quasiparticle trajectories, the induced SDW order is a
direct consequence of the d-wave symmetry. Furthermore the formation of
anti-phase domain walls is important for obtaining the correct temperature
dependence of the induced magnetism as measured by neutron diffraction.
