Theoretical investigation of superconductivity in itinerant ferromagnets

Abstract

The interplay between itinerant ferromagnetism and superconductivity in a model single-band homogeneous system has been studied by using a mean-field approximation. The solutions to the coupled equations of superconducting gap $\Delta$ and magnetization $m$ are given, and the associated free energies are calculated. It is shown that there generally exists a coexistent ($\Delta \ne 0$ and $m\ne 0$) solution to the coupled equations of order parameters in the temperature range $0<T<\mathrm{}min(T_S,T_F)$, where $T_S$ and $T_F$ are, respectively, the superconducting and ferromagnetic transition temperatures. The free energy of this solution, however, is always higher than those of the superconducting and ferromagnetic states. The comparison between free energies of different solutions reveals that it is possible to become superconducting via a first-order transition if the system, on cooling, first shows ferromagnetism. On the other hand, the present model predicts that itinerant ferromagnetism never appears when superconductivity is already present.