Strong-coupling theory of magnetic-exciton-mediated superconductivity inUPd2Al3

Abstract

There is compelling evidence from inelastic-neutron-scattering and tunneling experiments that the heavy-fermion superconductor ${\mathrm{UPd}}_{2}{\mathrm{Al}}_{3}$ can be understood as a dual system consisting of magnetic excitons, arising from crystal-field-split ${\mathrm{U}}^{4+}$ levels, coupled to delocalized $f$ electrons. We have computed the superconducting transition temperature and the mass renormalization arising from a dual model with maximal spin anisotropy using a strong-coupling approach. We find an instability to two possible opposite-spin-pairing states with even- or odd-parity gap functions. Each has a line node perpendicular to the $z$ direction, in agreement with NMR relaxation-rate, specific-heat and thermal-conductivity measurements. In addition, both have total spin component ${S}_{z}=0$, compatible with the observation of a pronounced Knight shift and ${H}_{c2}$ Pauli limiting. For parameter values appropriate to ${\mathrm{UPd}}_{2}{\mathrm{Al}}_{3}$, the calculated superconducting transition temperature and mass renormalization agree well with experiment for representative values of the coupling constant.