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Spectral analysis of resonant x-ray scattering in CeB6 under an external magnetic field

We study the resonant x-ray scattering (RXS) spectra of CeB_{6} in an antiferroquadrupole (AFQ) ordering phase, near the Ce L_3 edge under the applied magnetic field H // (-1,1,0). 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 (E1) and quadrupole (E2) 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.