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

Phase diagram of the Hubbard-Kondo lattice model from variational cluster approximation