  To understand effects of orbital degeneracy on magnetism, in particular
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
realizes 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.
