On magnon mediated Cooper pair formation in ferromagnetic superconductors

Abstract

Identification of pairing mechanism leading to ferromagnetic superconductivity is one of the most challenging issues in condensed matter physics. Although different models have been proposed to explain this phenomenon, a quantitative understanding about this pairing is yet to be achieved. Using the localized-itinerant model, we find that in ferromagnetic superconducting materials both triplet pairing and singlet pairing of electrons are possible through magnon exchange depending upon whether the Debye cut off frequency of magnons is greater or lesser than the Hund's coupling (J) multiplied by average spin (S) per site. Taking into account the repulsive interaction due to the existence of paramagnons, we also find an expression for effective interaction potential between a pair of electrons with opposite spins. We apply the developed formalism in case of UGe2 and URhGe. The condition of singlet pairing is found to be fulfilled in these cases, as was previously envisaged by Suhl [Suhl, Phys. Rev. Lett. 87, 167007 (2001)]. We compute the critical temperatures of URhGe at ambient pressure and of UGe2 under different pressures for the first time through BCS equation. Thus, this work outlines a very simple way to evaluate critical temperature in case of a superconducting system. A close match with the available experimental results strongly supports our theoretical treatment.