Antiferromagnetic Order of Repulsively Interacting Fermions on Optical lattices

The N\'eel state in fermionic mixtures of two pseudospin species in an optical lattice is analyzed at low temperatures. Experimentally it remains a challenge to demonstrate antiferromagnetic correlations in ultracold fermionic quantum gases. We find that, while in balanced systems the N\'eel order parameter can point in any spatial direction, in imbalanced mixtures antiferromagnetism is strictly perpendicular to the quantization axis (i.e., the z-axis). Since, experimentally, one always has to assume some minimal imbalance this should have important consequences for ongoing experiments.