Vl. Libero et Dl. Cox, SIMPLE-MODEL FOR COUPLED MAGNETIC AND QUADRUPOLAR INSTABILITIES IN URANIUM HEAVY-FERMION MATERIALS, Physical review. B, Condensed matter, 48(6), 1993, pp. 3783-3791
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.