Fig. 4: Electron-electron exchange interaction of magnetic IAEs.
a Periodic polyhedral cavities trapping IAEs in the 2D interlayer space between cationic [YGdC]2+ layers. Two possible configurations (type 1 and type 2) of mixed-cations in the periodic polyhedral cavities are shown. Exchange interactions of Je–e and Je–Gd are represented by red and green zigzag lines, respectively. There is a negligible magnetic exchange interaction between Y cations and IAEs due to the non-magnetic character. b–d ELFs and MDMs for [YGdC]2+·2e− (b, c) and [Gd2C]2+·2e− (d). Black circles denote the maximum points in ELFs. Colored lines in b–d are the distances between black circles. Color of the MDM for each IAE determines the spin direction. Detailed electronic structures are shown in Supplementary Fig. 11. e Spin dynamics of the magnetic IAEs. Two regions divide the ferrimagnetic (sky-blue) and FM (pink) orderings of IAEs. The distance of IAE (O)–IAE (T) is plotted as a function of the cationic ratio in the tetrahedral cavities. The spin direction of IAE (T) strongly depends on the inter-distance of magnetic IAEs.
