Hidden Order and Low-Energy Excitations in ${\mathrm{NpO}}_2$

We investigate the nature of the hidden order parameter in the ordered phase of ${\mathrm{NpO}}_2$, which had been identified with a staggered arrangement of ${\Gamma }_5$ magnetic multipoles. By analyzing the existing experimental data, we show that the most likely driving order parameter is not provided by octupoles, as usually assumed, but rather by the rank-5 triakontadipoles. Calculations of the coupled dynamics of spins, ${\Gamma }_5$ quadrupoles, and ${\Gamma }_5$ triakontadipoles in the ordered phase enable us to analyze the resulting structure of low-energy excitations. We show that the powder inelastic neutron scattering cross section should contain, in addition to the already-observed peak at 6.5 meV, a second weaker peak at about 14 meV.

Figure 1

Calculated cubic CF levels and mean-field splitting of the ground ${\Gamma }_8$ quartet in the ordered phase. The ($x=-0.48$, $W=-4.8$) CF set and the rank-5 ${\Gamma }_5$ MM OP have been used. Numbers in parentheses are degeneracies. The image represents the arrangement of the ${\Gamma }_5$ MMs (cones) and of the induced ${\Gamma }_5$ quadrupoles (ellipsoids) in the 4-sublattices triple-$\mathbf{q}$ ground state.

Figure 2

(a) $T$ dependence of the square of the secondary quadrupolar OP $Q^2$ normalized to its value at 10 K, calculated for the three different models of ${\Gamma }_5$ MM order discussed in the text (the MF transition temperature has been set to $T_0$). Inset: The same quantity measured by x-ray scattering [3]. (b) CF reduction factor for the ${\Gamma }_8$ ground quartet, ${\mu }_{\mathrm{CF}}^2/{\mu }_0^2$, as a function of the CF parameter $x$ ($W<0$). The arrow indicates the most likely value of $x$.

Figure 3

(a) Intensity plot showing the calculated $T=0$ momentum-transfer and energy dependence of the scattering function $S$ along $⟨001⟩$. (b) Measured powder INS spectrum for $Q=1.9{\AA }^{-1}$ [12] (black squares: spin flip; gray circles: non-spin flip). Line: Present calculation convoluted with the 3 meV Gaussian resolution function. The left-hand peak involves excited states where typically 1 Np ion (indicated by an arrow) has its quadrupole reverted and vanishing ${\Gamma }_5$ MM moment (i.e., the ${\Gamma }_4$ MF excited state in Fig. 1). The right-hand peak involves excited states where typically 1 Np ion has its ${\Gamma }_5$ MM moment reverted (i.e., the ${\Gamma }_6$ MF excited state in Fig. 1).