We study strongly interacting ultracold spin-1/2 fermions in a honeycomb lattice in the presence of a harmonic trap. Tuning the strength of the harmonic trap we show that it is possible to confine the fermions in artificial structures reminiscent of graphene nanoflakes in solid state. The confinement on small structures induces magnetic effects which are absent in a large graphene sheet. Increasing the strength of the harmonic potential we are able to induce different magnetic states, such as a Néel-like antiferromagnetic or ferromagnetic state, as well as mixtures of these basic states. The realization of different magnetic patterns is associated with the terminations of the artificial structures, in turn controlled by the confining potential.
