Neptunium octupole and hexadecapole motifs in NpO₂directly from electric dipole (E1) enhanced x-ray Bragg diffraction

Abstract

The phase transition in NpO2 at T0 ≈ 25.5 K is accompanied by the onset of superlattice reflections in the x-ray Bragg diffraction pattern, with intensity enhanced by an electric dipole (E1) event. Additional experiments using other techniques indicate no ordering at T0 of Np magnetic moments. Absence of long-range magnetic order below T0 fits with the outcome of a polarization analysis of superlattice intensities at 12 K; signals are observed in both the unrotated (σ'σ) and rotated (π'σ) channels of scattering while magnetic (dipole) moments would contribute only in the rotated channel. We demonstrate that these empirical findings, together with a narrow energy profile of the Bragg intensity at the Np M4 edge, are consistent with magnetic and charge contributions to the E1 Bragg amplitude described by Np 5f multipoles of ranks 3 (octupole) and 4 (hexadecapole). Key to our understanding of the x-ray diffraction data gathered in the vicinity of the Np M4 edge is recognition of an exchange field creating 3d3/2 core-level structure. The particular importance of the exchange field at the Np M4 edge is emphatically revealed in calculations of the corresponding x-ray absorption spectrum with and without the core–valence interaction. From the experimental information about NpO2 we can infer a ground-state wavefunction for the Np 5f3 valence shell and estimate saturation values for the octupole and hexadecapole. We are led to null values for Np multipoles of ranks 2 (quadrupole) and 5 (triakontadipole).