  We present accurate results based on Quantum Monte Carlo simulations of
two-component bosonic systems on a square lattice and in the presence of an
external harmonic confinement. Starting from hopping parameters and interaction
strengths which stabilize the Ising antiferromagnetic phase in the homogeneous
case and at half integer filling factor, we study how the presence of the
harmonic confinement challenge the realization of such phase. We consider
realistic trapping frequencies and number of particles, and establish under
which conditions, i.e. total number of particles and population imbalance, the
antiferromagnetic phase can be observed in the trap.
