A Simple Model for Coupled Magnetic and Quadrupolar Instabilities in Uranium Heavy-Fermion Materials

TL;DR

This paper models coupled magnetic and quadrupolar instabilities in uranium heavy-fermion materials, revealing how intersite couplings influence the order and transition types of magnetic and quadrupolar phases.

Contribution

It introduces a mean-field model capturing the interplay of magnetic and quadrupolar moments, elucidating phase transition behaviors in uranium heavy-fermion compounds.

Findings

Magnetic order can be first or second order depending on intersite magnetic coupling.

Finite quadrupolar coupling raises the minimal magnetic coupling needed for order.

The phase diagram shows reversed order of transitions with quadrupolar interactions.

Abstract

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 UPt$_3$. The Hamiltonian which defines the model is Heisenberg like in both, magnetic and quadrupolar moments. 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.