Kinetic Energy Driven Ferromagnetic Insulator

We construct a minimal model of interacting fermions establishing a ferromagnetic insulating phase. It is based on the Hubbard model on a trimerized triangular lattice in the regime of t≫|t^{'}|>0 with t and t^{'} the intra- and intertrimer hopping amplitudes, respectively. At the 1/3-filling, each trimer becomes a triplet spin-1 moment, and the intertrimer superexchange is ferromagnetic with J=-2/27(t^{'2}/t) in the limit of U/t=+∞. As U/t becomes finite, the antiferromagnetic superexchange competes with the ferromagnetic one. The system enters into a frustrated antiferromagnetic insulator when λ>U/t≫1 where λ is a constant at the order of 10. In contrast, a similar analysis to the trimerized Kagome lattice shows that only the antiferromagnetic superexchange exists at 1/3-filling.