Theoretical study of elastic and inelastic resonant x-ray scattering

我们从微观角度研究了弹性和非弹性x射线共振散射，并阐明了它们的机理。非弹性散射（RIXS）在从头算带结构计算的基础上，分析了Cr K边缘共振中Cr自旋密度波的超点位光谱。通过p-d杂化，已经澄清了这些强度是由相邻Cr位的3d态轨道极化引起的4p波段的轨道极化引起的。我们还分析了Cr - L边共振中Cr电荷密度波超晶格点处的光谱。据预测，由于SDW交换电位的作用，在三维状态下调制会产生较强的强度。在局域电子图的基础上，我们导出了偶极子和四极子跃迁的谱与多极序的一般表达式。应用这些公式分析了NpO_2和Ce_<1-x>La_xB_6中锕系元素M_<4,5>的边缘光谱，明确了光谱与八极序的关系。非弹性散射（RIXS）在Keldysh - Green函数形式的基础上，得到了非弹性散射的一般公式。我们通过分析核孔势的多重散射，检验了玻恩近似的有效性。我们将此公式应用于La_2CuO_4， SrCuO_2, CuGeO_3， NiO的RIXS。计算得到的光谱很好地再现了能量损失及其动量依赖的光谱形状，阐明了电荷激发与光谱的关系。我们建立了海森堡反铁磁体的双磁振子谱。采用1/S展开（S为自旋大小），我们分析了双磁振子RIXS光谱。本研究澄清了光散射与光散射的区别。

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.