Theory of Interplay of Nuclear Magnetism and Superconductivity in AuIn2

The recently reported coexistence of a magnetic order, with the critical temperature T_M=35 \mu*K, and superconductivity, with the critical temperature T_S=207 m*K, in AuIn_2 is studied theoretically. It is shown that superconducting (S) electrons and localized nuclear magnetic moments (LM's) interact dominantly via the contact hyperfine (EX) interaction, giving rise to a spiral (or domain-like) magnetic order in superconducting phase. The electromagnetic interaction between LM's and S electrons is small compared to the EX one giving minor contribution to the formation of the oscillatory magnetic order. In clean samples (l>\xi_0) of AuIn$_2$ the oscillatory magnetic order should produce a line of nodes in the quasiparticle spectrum of S electrons giving rise to the power law behavior. The critical field H_c(T=0) in the coexistence phase is reduced by factor two with respect to its bare value.