| Abstract: | We study two-dimensional antiferromagnets and ask whether it is possible for the lattice to melt without destroying the antiferromagnetic order. We address this question on a system of hard spheres confined between parallel plates, in which spin is represented by the height of the sphere. We find a partially molten, tetratic, phase in which the antiferromagnetism survives. The antiferromagnetism is strong enough to make the tetratic phase topologically ordered, with free dislocations of Burgers vector |b|=\sqrt{2}, while dislocations with |b|=1 remain bound. |