Itinerant Ferromagnetism in an Atom Trap

We propose an experiment to explore the magnetic phase transition in interacting fermionic systems, and establish signatures of ferromagnetic correlations in the observed ground states. We find, that for large trap radii (R> 4, in units of coherence length), ground states are topological in nature, a "skyrmion" in 2D, and a "hedgehog" in 3D. Finally, we describe how to obtain the ferromagnetic phase diagram of itinerant electron systems from these experiments.