Competitions in Layered Ruthenates: Ferromagnetism versus Antiferromagnetism and Triplet versus Singlet Pairing

Involvement of O in magnetism leads to ferromagnetic fluctuations in Sr₂RuO₄, while Ca₂RuO₄ is antiferromagnetic, suggesting a possibility of antiferromagnetic fluctuations in Sr₂RuO₄ as well. Our calculations show that the ferro- and antiferromagnetic fluctuations coexist, leading to an instability in Ca₂RuO₄ and to a competition between p- and d-wave superconductivities in Sr₂RuO₄. The antiferromagnetism is due to the nesting, with Q≈(2π/3a,2π/3a,0). The p-wave state is more stable than the d-wave one except in close vicinity of the magnetic instability. The d-wave state has a vanishing gap in one out of three bands; in the p channel it is comparable in all three bands.