Possible phase diagrams of superconductingUPt3

We enumerate and discuss several possibilities for the split transition in ${\mathrm{UPt}}_3$ and the phase diagrams that result. We find that the splitting may be due to weak basal-plane spin-orbit coupling or a near degeneracy of ${\mathit{E}}_1$ and ${\mathit{A}}_1$ representations of the hexagonal group. A further possibility is that only the ${\mathit{E}}_1$ representation is involved and is split by the coupling to antiferromagnetism, as suggested recently. However, as distinct from the previous results, we found that this coupling could lead to a superconducting glass phase if the antiferromagnetic domain size is small, as is observed. The implications of these ideas for the ${\mathit{H}}_{\mathit{c}2}$ curves are discussed, particularly the questions of the presence of the kink in the ${\mathit{H}}_{\mathit{c}2}$ curves and the isotropy of ${\mathit{H}}_{\mathit{c}2}$ in the basal plane.