Ground state of a three-band Hubbard model with Hund's coupling: Janus-faced behavior in presence of magnetic order

We study the ground state of the three-band degenerate Hubbard model on a square lattice at integer fillings using the variational slave-spin mean field method. At half-filling, the method reproduces the well known result that the ground state is antiferromagnetic (AF) insulating at smaller values of Hubbard onsite repulsion U, while it becomes Mott insulating with Neel AF order at higher U. Away from half-filling, for two particles per site, we show that the model supports a ferromagnetic (FM) metallic state with fully polarized spins at sufficiently large U. The FM state occurs irrespective of the value of Hund's coupling J. The ferromagnetism at J = 0 can be explained by the Stoner mechanism while that for J > 0 is shown to arise from the superexchange process. At this band filling, the Hund's coupling J is known to have the Janus-faced effect on electronic correlations where it enhances correlations at smaller U while reducing it at higher U. We show that these two effects are separated by the paramagnetic (PM) to FM transition point. The former effect is obtained at the PM state while the latter occurs in the FM state. The FM phase also occurs for one particle per site but here Hund's coupling J reduces the effect of electronic correlations at all U.