Nontrivial interplay of superconductivity and spin-orbit coupling in noncentrosymmetric ferromagnets

Motivated by the recent discoveries of ferromagnetic and noncentrosymmetric superconductors, we present a mean-field theory for a superconductor that both lacks inversion symmetry and displays ferromagnetism, a scenario which is believed to be realized in UIr. We study the interplay between the order parameters to clarify how superconductivity is affected by the presence of ferromagnetism and spin-orbit coupling. One of our key findings is that the spin-orbit coupling seems to enhance both ferromagnetism and superconductivity in all spin channels. We discuss our results in the context of the heavy fermion superconductor UIr and analyze possible symmetries of the order parameter by the group theory method.

Figure 1

(Color online) Self-consistent solution of the order parameters [(a)–(d)] as a function of the FM exchange parameter $\tilde{I}$, the ratio between the singlet and triplet gaps (e) $R_{\Delta }={\Delta }_{\uparrow \downarrow }/\left({\Delta }_{\uparrow }+{\Delta }_{\downarrow }\right)$, and the maximal critical temperature (f) $T_{c,\text{max}}$ as a function of the FM exchange parameter $\tilde{I}$.