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X-ray magnetic circular dichroism analysis at the L and K edges reveals that the universal phenomenon of dichroic contribution to extended X-ray absorption fine structure and X-ray absorption near-edge structure correlates to the local magnetic structures of 4f and 3d elements. Systematic studies help understand the association of dichroic contribution in extended X-ray absorption fine structure with spin densities and magnetic moments of neighboring atoms. Band- and atomic structure pictures are reliable in elucidating the circular dichroism in the fine structure.