Existence of ferromagnetism in a two-dimensional two species bosonic Hubbard model with the presence of confinement

With recent experimental advances on cold atoms in atomic traps, the realization of exotic magnetic phases in the presence of confinement is an area of renewed interest. We investigate a two-dimensional bosonic Hubbard
model with two species in the presence of a harmonic trapping potential. In particular, we focus on the appearance of a novel high entropy ferromagnetic phase at finite doping and polarization. We find that in the presence of confinement, this ferromagnetic phase appears in both hard-core and soft-core bosonic models. In the hard-core limit, we observe phase separation where the heavy species is localized in the center
of the trap, and it is surrounded by the light species. In the soft-core limit, we observe that the light species gets trapped in the center of the lattice, and it is surrounded by the heavy species. We link our results with experimental observables relevant for magnetic phases of trapped cold atoms.