  The interplay between the Kondo effect and magnetic ordering driven by the
Ruderman-Kittel-Kasuya-Yosida interaction is studied within the two-dimensional
Hubbard-Kondo lattice model. In addition to the antiferromagnetic exchange
interaction, $J_\perp$, between the localized and the conduction electrons,
this model also contains the local repulsion, $U$, between the conduction
electrons. We use variational cluster approximation to investigate the
competition between the antiferromagnetic phase, the Kondo singlet phase, and a
ferrimagnetic phase on square lattice. At half-filling, the N\'eel
antiferromagnetic phase dominates from small to moderate $J_\perp$ and
$UJ_\perp$, and the Kondo singlet elsewhere. Sufficiently away from
half-filling, the antiferromagnetic phase first gives way to a ferrimagnetic
phase (in which the localized spins order ferromagnetically, and the conduction
electrons do likewise, but the two mutually align antiferromagnetically), and
then to the Kondo singlet phase.
