  We study lattice melting in two dimensional antiferromagnets. We argue that,
for strong enough magnetic interactions, single lattice dislocations are
prohibitive due to magnetic frustration. This leads to a melting scenario in
which a tetratic phase, composed of free dislocation pairs and bound
disclinations, separates the solid from the liquid phases. We demonstrate this
phase numerically in a system of hard spheres confined between parallel plates,
where spins are represented by the the heights of the spheres. We find that, in
the tetratic phase, the spins are as antiferromagnetically ordered as allowed
by their spatial configuration.
