  Motivated by the recent experiment realizing bidirectional spin-orbit-coupled
Bose-Einstein condensates (BEC), we theoretically explore the properties of
repulsive fermions in the two-dimensional (2D) optical lattice with such
non-Abelian gauge fields. Within the mean-field level, we find a novel phase of
topological antiferromagnetic (TAFM) order which incorporates both the
non-trivial topology due to spin-flip hopping and spontaneous symmetry breaking
(SSB) for the in-plane spin order. We argue that the appearance of such a phase
is generic for repulsive fermions in Chern bands achieved through spin-orbit
coupling. Our work paves the way for further studies of fermionic
generalization of 2D non-Abelian spin-orbit-coupled quantum gases.
