Electronic structure and magnetic mechanism of pairing in HTSC transition metal oxides

Starting from the multiband p-d model of strongly correlated electrons, we derive the effective Hamiltonian in the form of the generalized singlet-triplet t-t'-J model which transforms to the usual t-t'-J model in the low-energy limit. Both n- and p-type copper oxides are considered in the mean field approximation for Gorkov type Green functions in the X-operator representation. Different signs of the t'/t ratio result in different normal state properties and T c values conserving the d x 2 -y 2 gap symmetry both for n- and p-oxides. Comparison with ruthenates and the coexistence of superconductivity and magnetism in RuSr 2 GdCu 2 O 8 are studied in the extended t-J-I model with ferromagnetic coupling between Ru ions.