  In a tight binding model of charged spin-1/2 electrons on a square lattice, a
fully polarized ferromagnetic spin configuration generates an apparent U(1)
flux given by $2\pi$ times the skyrmion charge density of the ferromagnetic
order parameter. We show here that for an antiferromagnet, there are two
``fictitious'' magnetic fields, one staggered and one unstaggered. The
staggered topological flux per unit cell can be varied between
$-\pi\le\Phi\le\pi$ with a negligible change in the value of the effective
nearest neighbor coupling constant whereas the magnitude of the unstaggered
flux is strongly coupled to the magnitude of the second neighbor effective
coupling.
