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Studies on X-ray Thomson Scattering from Antiferroquadrupolar Order in TmTe

We study Thomson scattering from the antiferroquadrupole ordering phase in TmTe. On the basis of the group theoretical treatment, we classify the selection rules of the scattering intensity governed by the orientation of the scattering vector G. Then, numerical verification is performed by invoking the ground states which are deduced from a J=7/2 multiplet model. The obtained intensity varies drastically depending on the magnitude and direction of G. We also calculate the scattering intensities under the applied field for H//(001) and (110). Their results behave differently when the orientation of G is changed, which is ascribed to the difference of their primary order parameters; O_{2}^{0} and O_{2}^{2} for H // (001) and (110), respectively. We make critical comparisons between our results for TmTe and the experimental ones for CeB_6. First, we assert that the intensities expected from TmTe at several forbidden Bragg spots are sufficient enough to be experimentally detected. Second, their intensities at (7/2,1/2,1/2) differ significantly and may be attributed to the difference of the order parametersbetween the Γ_3-type (O_{2}^{2} and O_{2}^{0}) and Γ_5-type (O_{yz}, O_{zx}, and O_{xy}) components, respectively.