  An orbitally degenerate two-band Hubbard model is analyzed with inclusion of
the Hund's rule induced spin-triplet paired states and their coexistence with
magnetic ordering. The so-called statistically consistent Gutzwiller
approximation (SGA) has been applied to the case of a square lattice. The
superconducting gaps, the magnetic moment, and the free energy are analyzed as
a function of the Hund's rule coupling strength and the band filling. Also, the
influence of the intersite hybridization on the stability of paired phases is
discussed. In order to examine the effect of correlations the results are
compared with those calculated earlier within the Hartree-Fock (HF)
approximation combined with the Bardeen-Cooper-Schrieffer (BCS) approach.
Significant differences between the two used methods (HF+BCS vs. SGA+real-space
pairing) appear in the stability regions of the considered phases. Our results
supplement the analysis of this canonical model used widely in the discussions
of pure magnetic phases with the detailed elaboration of the stability of the
spin-triplet superconducting states and the coexistent magnetic-superconducting
states. At the end, we briefly discuss qualitatively the factors that need to
be included for a detailed quantitative comparison with the corresponding
experimental results.
