We present a mean-field calculation of the phase diagram of a simple model of localized moments, in the hexagonal uranium heavy-fermion compounds. The model considers a non-Kramers quadrupolar doublet ground state magnetically coupled with a singlet excited state, favoring in-plane van Vleck magnetism, as has been conjectured for ${\mathrm{UPt}}_3$. The Hamiltonian that defines the model is Heisenberg-like in both magnetic and quadrupolar moments. No Kondo-effect physics is included in the calculations. Among our main results are (i) for zero intersite quadrupolar coupling, the magnetic order is achieved by a first-order transition above a critical intersite magnetic coupling value, which becomes second order at higher coupling strengths (ii) for finite intersite quadrupolar 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 diagram is reversed. By considering the general structure of the Ginsburg-Landau free energy, we argue that the Kondo effect will not modify the shape of the phase diagram, but will modify the quantitative values at which transitions occur.

• Received 19 March 1993

DOI:https://doi.org/10.1103/PhysRevB.48.3783