Theoretical study of elastic and inelastic resonant x-ray scattering

我们从微观的角度研究了弹性和非弹性共振X射线散射，并阐明了它们的机制。弹性散射(RXS)非弹性散射(RIXS)1.在从头算能带结构计算的基础上，分析了CrK边共振中Cr自旋密度波超晶格点的能谱。通过p-d杂化，阐明了这些强度是由相邻铬位上3d态的轨道极化引起的4p带的轨道极化引起的。我们还分析了铬L边共振中铬电荷密度波的超晶格点的光谱。已经预言，由于SDW交换势，3D态的调制会产生很强的强度。在局域电子图像的基础上，我们导出了与偶极和四极跃迁的多极有序有关的谱的一般表达式。用这些公式分析了NpO_2和Ce_&lt；1-x&gt；La_xB_6中的鳗系元素M_&lt；4，5&gt；边谱，阐明了谱线与八极序的关系。通过分析核孔势的多次散射，验证了玻恩近似的有效性。我们将该公式应用于La_2CuO_4、SrCuO_2、CuGeO_3、NiO的RIXS。计算的光谱很好地再现了作为能量损失及其动量依赖关系的光谱形状，阐明了电荷激发与光谱的关系。我们推导了海森堡反铁磁体的双磁振子谱。利用1/S展开(S是自旋的量级)，我们分析了双磁振子的RIXS谱。这项研究澄清了与光散射的区别。

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.