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To understand effects of orbital degeneracy on magnetism, in particulareffects of Hund's rule coupling, we study the two-orbital Hubbard model on asquare lattice by a variational Monte Carlo method. As a variational wavefunction, we consider a Gutzwiller projected wave function for a staggered spinand/or orbital ordered state. We find a ferromagnetic phase with staggeredorbital order around quarter-filling, i.e., electron number n=1 per site, andan antiferromagnetic phase without orbital order around half-filling n=2. Inaddition, we find that another ferromagnetic phase without orbital orderrealizes in a wide filling region for large Hund's rule coupling. These twoferromagnetic states are metallic except for quarter filling. We show thatorbital degeneracy and strong correlation effects stabilize the ferromagneticstates.

Variational Monte Carlo study of ferromagnetism in the two-orbital Hubbard model on a square lattice