Resonant X-Ray Scattering from CeB$_{6}$

TL;DR

This paper models resonant x-ray scattering in CeB$_6$, explaining experimental spectra and dependencies through a microscopic approach that considers electronic states and Coulomb interactions without lattice distortions.

Contribution

It provides a detailed microscopic calculation of RXS spectra in CeB$_6$, incorporating electronic interactions and reproducing experimental observations without assuming lattice distortions.

Findings

RXS intensities are explained by modulation of 5d states via 5d-4f Coulomb interaction.

Spectral shape, temperature, and magnetic field dependences match experiments.

A small pre-edge peak appears in the magnetic ground state.

Abstract

We calculate the resonant x-ray scattering (RXS) spectra near the Ce $L_{\rm III}$ absorption edge in CeB$_6$, on the basis of a microscopic model that the $4f$ states of Ce are atomic while the $5d$ states form an energy band with a reasonable density of states. In the initial state, we employ an effective Hamiltonian of Shiina {\it et al}. in the antiferro-quadrupole (AFQ) ordering phase, while we construct the wave function consistent with the neutron scattering experiment in the magnetic ground state. In the intermediate state, we take full account of the intra-atomic Coulomb interaction. Without assuming any lattice distortion, we obtain sufficient RXS intensities on the AFQ superlattice spot. We obtain the spectral shape, the temperature and magnetic field dependences in good agreement with the experiment, thus demonstrating the mechanism that the intensity is brought about by the modulation of $5d$ states through the anisotropic term of the $5d$-$4f$ Coulomb interaction. In the magnetic ground state, a small pre-edge peak is found by the $E_2$ process. On the magnetic superlattice spot, we get a finite but considerably small intensity. The magnetic form factor is briefly discussed.