QUADRUPOLAR PHASES IN UPD3

UPd3 is a hexagonal crystal that exhibits quadrupolar ordering at low temperatures. The order parameter has three components corresponding t o modulations in three directions in the basal plane of the hexagonal crystal. For the case that no symmetry-breaking fields are present the ordered phase has been identified as a trigonal triple-Q phase. Using group theory, we show that under the influence of symmetry-breaking f ields up to eight distinct quadrupolar ordered phases are realized in the crystal. We deduce the phase diagram from a Landau free energy tha t includes magnetic fields and stress and find lines of tetracritical points and one point at which eight phases coexist, an ''octacritical' ' point. By reviewing renormalization-group results we address the eff ect of critical fluctuations on the phase diagram. Finally, we discuss experimental tests of our model for the quadrupolar phases of UPd3.