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An orbitally degenerate two-band Hubbard model is analyzed with inclusion ofthe Hund's rule induced spin-triplet paired states and their coexistence withmagnetic ordering. The so-called statistically consistent Gutzwillerapproximation (SGA) has been applied to the case of a square lattice. Thesuperconducting gaps, the magnetic moment, and the free energy are analyzed asa function of the Hund's rule coupling strength and the band filling. Also, theinfluence of the intersite hybridization on the stability of paired phases isdiscussed. In order to examine the effect of correlations the results arecompared 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-spacepairing) appear in the stability regions of the considered phases. Our resultssupplement the analysis of this canonical model used widely in the discussionsof pure magnetic phases with the detailed elaboration of the stability of thespin-triplet superconducting states and the coexistent magnetic-superconductingstates. At the end, we briefly discuss qualitatively the factors that need tobe included for a detailed quantitative comparison with the correspondingexperimental results.

new journal of physics

Coexistence of spin-triplet superconductivity with magnetism within a  single mechanism for orbitally degenerate correlated electrons:  Statistically-consistent Gutzwiller approximation