Coexistence of superconductivity and ferromagnetism in hybrid rutheno-cuprate superconductors RuSr2RCu2O8

I consider the extended two-band s–f model with additional terms, describing inter-site Cooper pairs interaction between two-subsystems s and f, respectively. Following Green’s function technique and equation of motion method self-consistent equations for superconducting order parameter (Δ) and magnetic order parameter (m_f) are derived. The expressions for specific heat, density of states, and free energy are also derived. The theory has been applied to explain the coexistence of superconductivity and ferromagnetism in hybrid rutheno-cuprate superconductors RuSr₂RECu₂O₈ (RE = Gd, Eu). The theory shows that it is possible to become superconducting via a second order phase transition if the system is already ferromagnetic. The agreement between theory and experimental observations is quite satisfactory.