Atomic-scale observation of $d$-$\pi$-$d$ spin coupling in coordination structures

Spin coupling between magnetic metal atoms and organic radicals plays a pivotal role in high-performance magnetic materials. The complex interaction involving multi-spin centers in bulk materials makes it challenging to study spin coupling at the atomic scale. Here, we investigate the $d$-$\pi$-$d$ spin interaction in well-defined metal-organic coordinated structures composed of two iron (Fe) atoms and four all-trans retinoic acid (ReA) molecules, using low-temperature scanning tunneling microscopy and atomic force microscopy. The ReA molecule is turned into a spin-$1/2$ radical state by dehydrogenation, facilitating strong magnetic coupling with the coordinated Fe atoms. Comprehensive theoretical analysis, based on density functional theory and valence bond theory, further elucidates the intrinsic mechanism of ferrimagnetic spin coupling in the coordination structure. Specifically, simultaneous antiferromagnetic coupling of Fe dimer to ReA radicals parallelizes the dimer spin orientation. This work contributes to the fundamental understanding of spin interaction in metal-organic coordination structures and provides microscopic insights for designing advanced magnetic materials.