This research work focuses on the theoretical investigation of the possible coexistence of superconductivity and ferromagnetism in ErRh 4 B 4 . By developing a model Hamiltonian for the given system and by using the double time temperature-dependent Green's function formalism, we obtained expressions for superconducting transition temperature ( ), magnetic ordering temperature (T m ), superconducting and magnetic ordering parameters ( ) and ( ) respectively. By using the experimental and

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... ical values and by considering plausible approximations of the parameters in the obtained expressions, the phase diagrams of superconducting transition temperature versus magnetic ordering parameter and magnetic ordering temperature versus magnetic ordering parameter are plotted. Finally, by combining the two phase diagrams, we showed the possible coexistence of superconductivity and ferromagnetism in ErRh 4 B 4 .