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

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