Neptunium multipoles and resonant x-ray Bragg diffraction by neptunium dioxide (NpO2)

The low-temperature ordered state of neptunium dioxide (NpO(2)) remains enigmatic. After decades of experimental and theoretical efforts, long-range order of a time-odd (magnetic) high-order atomic multipole moment is now generally considered to be the fundamental order parameter, the most likely candidate being a magnetic triakontadipole (rank 5). To date, however, direct experimental observation of the primary order parameter remains outstanding. In the light of new experimental findings, we re-examine the effect of crystal symmetry on the atomic multipoles and the resulting x-ray resonant scattering signature. Our simulations use the crystallographic point group ̅3m (D(3d)), because corresponding magnetic groups ̅3m', ̅3'm', and ̅3'm are shown by us to be at odds with a wealth of experimental results. In addition to the previously observed (secondary) quadrupole order, we derive expressions for higher-order multipoles that might be observed in future experiments. In particular, magnetic octupole moments are predicted to contribute to Np M(2,3) and L(2,3) resonant scattering via E2–E2 events. The Lorentzian-squared lineshape observed at the M(4) resonance is shown to be the result of the anisotropy of the 3p(3/2) core levels. Quantitative comparison of our calculations to the measured data yields a core–hole width Γ = 2.60(7) eV and a core-state exchange energy [absolute value]ε(1/2)[absolute value] = 0.76(2) eV.