SIMPLE-MODEL FOR COUPLED MAGNETIC AND QUADRUPOLAR INSTABILITIES IN URANIUM HEAVY-FERMION MATERIALS

We present a mean-field calculation of the phase diagram of a simple m odel of localized moments, in the hexagonal uranium heavy-fermion comp ounds. The model considers a non-Kramers quadrupolar doublet ground st ate magnetically coupled with a singlet excited state, favoring in-pla ne van Vleck magnetism, as has been conjectured for UPt3. The Hamilton ian that defines the model is Heisenberg-like in both magnetic and qua drupolar moments. No Kondo-effect physics is included in the calculati ons. Among our main results are (i) for zero intersite quadrupolar cou pling, the magnetic order is achieved by a first-order transition abov e a critical intersite magnetic coupling value, which becomes second o rder at higher coupling strengths (ii) for finite intersite quadrupola r coupling, at temperatures below a second-order quadrupolar ordering transition, the minimal magnetic coupling value is increased, but (a) the magnetic ordering temperature is enhanced above this value, and (b ) the ordering of first- and second-order transitions in the phase dia gram is reversed. By considering the general structure of the Ginsburg -Landau free energy, we argue that the Kondo effect will not modify th e shape of the phase diagram, but will modify the quantitative values at which transitions occur.