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

The low-temperature ordered state of neptunium dioxide (NpO2) 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 3-bar m (D3d), because corresponding magnetic groups 3-bar m', 3-bar 'm' and 3-bar '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 M2,3 and L2,3 resonant scattering via E2-E2 events. The Lorentzian-squared lineshape observed at the M4 resonance is shown to be the result of the anisotropy of the 3p3/2 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 |ε( 1/2 )|=0.7 6(2) eV. (paper)