SuperconductingUPt3in a magnetic field

We use earlier calculations of the possible phases of ${\mathrm{UPt}}_3$ in a magnetic field and recent measurements to identify all the anisotropic superconducting phases of ${\mathrm{UPt}}_3$. We also determine more precisely the structure of the high-field phases and demonstrate their stability by an exact solution of the Ginzburg-Landau equations at the normal-superconducting phase boundary. The upper critical field as a function of temperature shows upward curvature. This is identified as arising from coupling of superconductivity and antiferromagnetism.