Analysis of f-p model for octupole ordering in NpO2

In order to examine the origin of octupole ordering in NpO2, we propose a microscopic model constituted of neptunium 5f and oxygen 2p orbitals. To study multipole ordering, we derive effective multipole interactions from the f-p model by using the fourth-order perturbation theory in terms of p-f hopping integrals. Analyzing the effective model numerically, we find a tendency toward \Gamma_{5u} antiferro-octupole ordering.Comment: 4 pages, 3 figure

Resonant x-ray scattering spectra from multipole orderings: Np M_{4,5} edges in NpO2

We study resonant x-ray scattering (RXS) at Np M_{4,5} edges in the triple-\textbf{k} multipole ordering phase in NpO_{2}, on the basis of a localized electron model. We derive an expression for RXS amplitudes to characterize the spectra under the assumption that a rotational invariance is preserved in the intermediate state of scattering process. This assumption is justified by the fact that energies of the crystal electric field and the intersite interaction is smaller than the energy of multiplet structures. This expression is found useful to calculate energy profiles with taking account of the intra-Coulomb and spin-orbit interactions. Assuming the \Gamma_{8}-quartet ground state, we construct the triple-\textbf{k} ground state, and analyze the RXS spectra. The energy profiles are calculated in good agreement with the experiment, providing a sound basis to previous phenomenological analyses.Comment: 10 pages, 7 figure

Microscopic theory of multipole ordering in NpO2

In order to examine the mysterious ordered phase of NpO2 from a microscopic viewpoint, we investigate an f-electron model on an fcc lattice constructed based on a j-j coupling scheme. First, an effective model with multipole interactions is derived in the strong-coupling limit. Numerical analysis of the model clearly indicates that the interactions for \Gamma_{4u} and \Gamma_{5u} moments are relevant to the ground state. Then, by applying mean-field theory to the simplified model including only such interactions, we conclude that longitudinal triple-q \Gamma_{5u} octupole order is realized in NpO2 through the combined effects of multipole interactions and anisotropy of the \Gamma_{5u} moment.Comment: 5 pages, 2 figure

Triple-q octupolar ordering in NpO_2

We report the results of resonant X-ray scattering experiments performed at the Np M_4,5 edges in NpO_2. Below T_0 = 25 K, the development of long-range order of Np electric quadrupoles is revealed by the growth of superlattice Bragg peaks. The electronic transition is not accompanied by any measurable crystallographic distortion, either internal or external, so the symmetry of the system remains cubic. The polarization and azimuthal dependence of the intensity of the resonant peaks is well reproduced assuming Templeton scattering from a triple-q longitudinal antiferroquadrupolar structure. Electric quadrupole order in NpO_2 could be driven by the ordering at T_0 of magnetic octupoles of Gamma_5 symmetry, splitting the Np ground state quartet and leading to a singlet ground state with zero dipole magnetic moment.Comment: 4 Pages, 3 Figures, submitted to Phys. Rev. Lett. v2: resubmitted after referee report