Theoretical study of elastic and inelastic resonant x-ray scattering

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We have studied the elastic and inelastic resonant x-ray scattering from the microscopic viewpoint, and have clarified their mechanism. Elastic scattering (RXS)Inelastic scattering (RIXS)1. We have analyzed the spectra at the superlattice spots of the Cr spin density wave in Cr K edge resonance on the basis of the ab initio band structure calculation. It has been clarified that the intensities arise from the orbital polarization of the 4p bands induced by the orbital polarization of the 3d states at neighboring Cr sites through the p-d hybridization. We have also analysed the spectra at the superlattice spots of Cr charge density wave in Cr L edge resonance. It has been predicted that strong intensities come out from the modulation in 3d states due to the SDW exchange potential.2. On the basis of the localized electron picture, we have derived general expressions relating the spectra to the multipole ordering for the dipole and quadrupole transitions. These formulas have been applied to analyze the actinide M_<4,5> Edge spectra in NpO_2 and Ce_<1-x>La_xB_6, having clarified the relation of the spectra and the octupole ordering.Inelastic scattering (RIXS)1. We have obtained a general formula of the inelastic scattering on the basis of the Keldysh Green function formalism. We have examined the validity of the Born approximation by analyzing the multiple scattering by the core-hole potential. We have applied this formula to the RIXS from La_2CuO_4, SrCuO_2, CuGeO_3, NiO. The calculated spectra have reproduced well the spectral shapes as a function of energy loss and their momentum dependence, having clarified the relation of the charge excitation and the spectra.2. We have formulated the two-magnon spectra in Heisenberg antiferromagnets. Having employed the 1/S-expansion (S is the magnitude of spin), we have analyzed the two-magnon RIXS spectra. This study has clarified the difference from the light scattering.