  We examine antiferromagnetic and d-wave superfluid phases of cold fermionic
atoms with repulsive interactions in a two-dimensional optical lattice combined
with a harmonic trapping potential. For experimentally realistic parameters,
the trapping potential leads to the coexistence of magnetic and superfluid
ordered phases with the normal phase. We study the intriguing shell structures
arising from the competition between the magnetic and superfluid order as a
function of the filling fraction. In certain cases antiferromagnetism induce
superfluidity by charge redistributions. We furthermore demonstrate how these
shell structures can be detected as distinct anti-bunching dips and pairing
peaks in the density-density correlation function probed in expansion
experiments.
