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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 fm 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.

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Table S1. Anisotropic displacement parameters for Gd3Fe5O12

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