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We show how off-resonant light scattering can provide quantitativeinformation on antiferromagnetic ordering of a two-species fermionic atomic gasin a tightly-confined two-dimensional optical lattice. We analyze the emergingmagnetic ordering of atoms in the mean-field and in random phase approximationsand show how the many-body static and dynamic correlations, evaluated in thestandard Feynman-Dyson perturbation series, can be detected in the scatteredlight signal. The staggered magnetization reveals itself in the magnetic Braggpeaks of the individual spin components. These magnetic peaks, however, can beconsiderably suppressed in the absence of a true long-range antiferromagneticorder. The light scattered outside the diffraction orders can be collected by alens a with highly improved signal-to-shot-noise ratio when the diffractionmaxima are blocked. The collective and single-particle excitations areidentified in the spectrum of the scattered light. We find that thespin-conserving and spin-exchanging atomic transitions convey information ondensity, longitudinal spin, and transverse spin correlations. The differentcorrelations and scattering processes exhibit characteristic angulardistribution profiles for the scattered light and, e.g., the diagnostic signalof transverse spin correlations could be separated from the signal by thescattering direction, frequency, or polarization. We also analyze the detectionaccuracy by estimating the number of required measurements, constrained by theheating rate that is determined by inelastic light scattering events. Theimaging technique could be extended to the two-species fermionic states inother regions of the phase diagram where the ground state properties are stillnot fully understood.

Optical signatures of antiferromagnetic ordering of fermionic atoms in an optical lattice