Spectral analysis of resonant x-ray scattering inCeB6under an external magnetic field

Abstract

We study the resonant x-ray scattering ͑RXS͒ spectra of CeB 6 in an antiferroquadrupole ͑AFQ͒ ordering phase, near the Ce L 3 edge under the applied magnetic field H ʈ ͑1 ,1,0͒. On the basis of a localized electron model equipped with a mechanism that the RXS signal is brought about by the intra-atomic Coulomb interaction in Ce, we calculate the RXS spectra. The obtained spectra exhibit two contributions around the electric dipole ͑E1͒ and quadrupole ͑E2͒ positions, and differ drastically when the orientation of H is reversed. The difference is brought about by the cross terms between the even-rank AFQ and magnetic-induced odd-rank contributions. At the E1 region, the relevant cross term is the one within the E1 process, while at the E2 region, they are ones within the E2 process and between the E1 and E2 processes. These findings capture the characteristic features the recent experimental data show, and provide a strong support and information of the field-induced multipole orderings. We also evaluate the RXS spectra near the L 2 edge. Though the results show no E2 contribution, we find that the intensity around the E1 transition, which is as large as that at the L 3 edge, can be detected experimentally.

Antiferroquadrupole order and magnetic field induced octupole in CeB6

“…As pointed out in Ref. 34, the difference term can arise at the E1 energy, which is explicitly shown in Eq. (A7).…”

“…Here, we analyze the experimental spectra using the spectral functions of α (ν) E1 (ω) and α (ν) E2 (ω) used in Ref. 34, regarding Z (ν)…”

“…This situation is explained in Ref. 34 in detail. The authors have made a spectral analysis based on a more solid theory and gave an explanation to the field reversal effect of the resonance spectrum.…”

“…The purpose of the present paper is to analyze the energy spectrum and its field reversal effect using the theory and spectral functions given in Ref. 34. We extract the field dependencies of the AFQ and AFO moments for the field along [1 1 0] in the same way as before, but the data treatments are now theoretically more justified.…”

Resonant X-ray Scattering Experiments on the Ordering of Electronic Degrees of Freedom

“…In such cases, it is essential to consider that the energy profile depends on the rank of the scattering process. 63,64) Finally, we remark that the multipole operators in the RXS theory should not be confused with the real multipole moments of the relevant shell. The real multipole moments, as defined in Ref.…”