Heavy-Fermion Superconductivity in URANIUM-PLATINUM(3)

A phenomenological spin fluctuation model for superconductivity in the heavy-fermion metal UPt _3 is presented. The wavevector dependence of the interaction is assumed to be the same as the wavevector dependent magnetic susceptibility extracted from the neutron scattering experiments of Aeppli, et al. The other input for the calculation is the Fermi surface of UPt _3. Single particle band calculations done for UPt_3 give a Fermi surface which is very anisotropic. Despite the presence of strong correlations in UPt_3 the Fermi surface derived from band calculations is confirmed by the de Haas-van Alphen measurements of Taillefer, et al. However, the calculated band masses are smaller than the observed masses by a factor of 20. UPt_3 can thus be described at low temperatures in its normal state as a Fermi liquid, with very massive quasiparticles. The model considered here for the superconducting state is the pairing of the heavy quasiparticles by means of the spin fluctuation mediated interaction. A phase diagram is derived in terms of two dimensionless parameters giving the relative strength of the local repulsive part of the interaction and the in plane ferromagnetic interaction compared to the nearest neighbor antiferromagnetic interaction. s -, p- and d-wave phases are possible. The symmetry of the gap function favored by this model is the E_ {1g} representation of D_ {rm 6h}. To determine the symmetry of the gap function for this two dimensional representation the fourth order terms in the Ginzburg-Landau free energy are considered. The resulting gap function has a line of nodes in the basal plane and point nodes along the c -axis. A qualitative comparison of calculated properties for UPt_3 with this d-wave gap function to measured properties is given. Emphasis is on the observed power law temperature dependences for many low temperature properties and the difficulties in identifying the nodal structure due to impurity scattering. A discussion of the limitations of the model and future improvements and extensions of the model is also given.