Magnetic pairing in a lattice of Kondo ions: Application toUPt3

Recently, several groups have calculated possible superconducting solutions for ${\mathrm{UPt}}_3$ from magnetic fluctuation pairing, by utilizing the band-structure Fermi surface and experimental dynamic susceptibility as input. The resulting solutions do not have proper periodicity in reciprocal-lattice space, though. In this paper, a more fundamental derivation of the pairing interaction is given by treating a lattice of interacting Kondo ions. Proper inclusion of umklapp processes leads to odd-parity solutions for ${\mathrm{UPt}}_3$, with order parameters of $A_{1u}$ or $E_{1u}$ symmetry preferred.