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Ru based perovskites demonstrate an amazing richness in their magneticproperties, including 3D and quasi-2D ferromagnetism, antiferromagnetism, andunconventional superconductivity. Tendency to ferromagnetism, stemming from theunusually large involvement of O in magnetism in ruthenates, leads toferromagnetic spin fluctuations in Sr2RuO4 and eventually to p-wavesuperconductivity. A related compound Ca2RuO4 was measured to beantiferromagnetic, suggesting a possibility of antiferromagnetic fluctuationsin Sr2RuO4 as well. Here we report first principles calculations thatdemonstrate that in both compounds the ferro- and antiferromagneticfluctuations coexist, leading to an actual instability in Ca2RuO4 and to aclose competition between p-wave and d-wave superconducting symmetries inSr2RuO4. The antiferromagnetism in this system appears to be mostly relatedwith the nesting, which is the strongest at Q=(2pi/3,2pi/3,0). Surprisingly,for the Fermiology of Sr2RuO4 the p-wave state wins over the d-wave oneeverywhere except in close vicinity of the antiferromagnetic instability. Themost stable state within the d-wave channel has vanishing order parameter atone out of three Fermi surfaces in Sr2RuO4, while in the p channel itsamplitude is comparable at all three of them.Comment: 4 Revtex pages with 4 embedded postscript figure. Some figures are  color, but should look OK in B&W as wel

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