Resonant and non-resonant magnetic scatterings with circularly polarized X-rays: magnetic scattering factor and electron density of gadolinium iron garnet

Theoretical and experimental studies on resonant magnetic scattering have been carried out using circularly polarized X-rays. Polarization dependence of the asymmetric ratio between right- and left-handed polarized scattering amplitudes has revealed that resonant and non-resonant magnetic scatterings can be observed simultaneously. In this study, synchrotron X-ray intensity experiments were conducted on Gd iron garnet (GdIG) at the pre-edge of the Fe K absorption edge. The asymmetric ratio between circular polarizations exhibited three peaks due to the resonant magnetic responses of Fe³⁺ in the Fe2 (24d) site. These magnetic responses are antiparallel and have apparently higher resolution than dispersive X-ray magnetic circular dichroism at the pre-edge region; this can be mainly attributed to electric dipole transitions from 1s to t₂ energy levels of the 3d orbitals in the tetrahedral symmetry in an unstable state quenched at higher temperature. Resonant magnetic scattering factors f′_m were estimated from the asymmetric ratios. Fourier analysis was conducted using the intensity differences among circularly polarized X-rays at an energy of E = 7.1085 keV. At this energy level, the characteristic distribution of magnetic electron density was clearly observed. This distribution was interpreted as a spin arrangement of Gd and Fe ions in GdIG. Also observed was the presence of hybridization of the magnetic electron orbitals as well as of the resonant magnetic Fe³⁺. The proposed method has the potential to be widely used in crystal structure analysis.