Exchange coupling and contribution of induced orbital angular momentum of low-spin Fe3+ ions to magnetic anisotropy in cyanide-bridged Fe2M2 molecular magnets: Spin-polarized density-functional calculations

Electronic structure and intramolecular exchange constants are calculated for three cyanide-bridged molecular magnets, Tp(star)Fe(III)(CN)(3)M-II(DMF)(4)(OTf)(2)center dot 2DMF (M-II=Mn,Co,Ni) (abbreviated as Fe2Mn2, Fe2Co2, and Fe2Ni2) that have been recently synthesized, within a generalized-gradient approximation in spin-polarized density-functional theory (DFT). Here Tp(star)=C-3(CH3)(2)HN2BH, OTf=O3SCF3, and DMF=HCON(CH3)(2). Due to strong ligand fields present in the Tp(star)Fe(III)(CN)(3) units, the Fe3+ ions exhibit a low ground-state spin of S=1/2. Our calculations show that the metal ions in the Fe2Mn2 molecule interact antiferromagnetically via cyanide ligands, while those in the Fe2Co2 and Fe2Ni2 molecule interact ferromagnetically. The calculations also suggest that the smallest gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for Fe2Mn2, Fe2Co2, and Fe2Ni2 are 0.12, 0.03, and 0.33 eV. Based on the calculated electronic structures, the second-order magnetic anisotropy is computed including single-electron spin-orbit coupling within a DFT formalism. In comparison to a prototype single-molecule magnet Mn-12, the three cyanide-bridged molecular magnets are found to bear substantial transverse magnetic anisotropy that becomes 15%-36% of molecular longitudinal anisotropy. Spin-orbit coupling arising from the low-spin Fe3+ and high-spin Co2+ ions induces significant orbital angular momentum that contributes to the total magnetic anisotropy of the three cyanide-bridged molecular magnets. The induced orbital angular momentum is 4-8 times those calculated for Mn-12. The total magnetic anisotropy present in the three molecular magnets is due to competition between the magnetic anisotropy of the Fe3+ and of the M2+ ions. In the Fe2Mn2 and Fe2Ni2 molecules, the anisotropy is primarily due to the Fe3+ ions, while in the Fe2Co2 molecule, the single-ion anisotropy of the Co2+ ions counters the Fe3+ contributions. These results are supported by previously reported magnetic measurements.