Scaffolding, Ladders, Chains, and Rare Ferrimagnetism in Intermetallic Borides: Electronic Structure Calculations and Magnetic Ordering

The electronic structures of "Ti9-nFe2+nRu18B8" (n = 0, 0.5, 1, 2, 3), in connection to the recently synthesized Ti9-nFe2+nRu18B8 = 1, 2), have been investigated and analyzed using LSDA tight-binding calculations to elucidate the distribution of Fe and Ti, to determine the maximum Fe content, and to explore possible magnetic structures to interpret experimental magnetization results. Through a combination of calculations on specific models and using the rigid band approximation, which is validated by the DOS curves for "Ti9-nFe2+nRu18B8" (n = 0, 0.5, 1, 2, 3), mixing of Fe and Ti is anticipated at both the 2b- and 4h-chain sites. The model "Ti8.5Fe2.5Ru18B8" (n = 0.5) revealed that both Brewer-type Ti-Ru interactions as well as ligand field splitting of the Fe 3d orbitals regulated the observed valence electron counts between 220 and 228 electrons/formula unit. Finally, models of magnetic structures were created using "Ti6Fe5Ru18B8" (n = 3). A rigid band analysis of the LSDA DOS curves concluded preferred ferromagnetic ordering at low Fe content (n <= 0.75) and ferrimagnetic ordering at higher Fe content (n > 0.75). Ferrimagnetism arises from antiferromagnetic exchange coupling in the scaffold of Fel-ladder and 4h-chain sites.