Combined ligand field and density functional theory analysis of the magnetic anisotropy in oligonuclear complexes based on Fe(III)-CN-M(II) exchange-coupled pairs

Magnetic anisotropy in cyanide-bridged single-molecule magnets (SMMs) with Fe(III)-CN-M(II) (M = Cu, Ni) exchange-coupled pairs was analyzed using a density functional theory (DFT)-based ligand field model. A pronounced magnetic anisotropy due to exchange was found for linear Fe(III)-CN-M(II) units with fourfold symmetry. This results from spin-orbit coupling of the Fe(III)(CN)6](3-) unit and was found to be enhanced by a tetragonal field, leading to a (2)E g ground state for Fe(III). In contrast, a trigonal field (e.g., due to tau 2g Jahn-Teller angular distortions) led to a reduction of the magnetic anisotropy. A large enhancement of the anisotropy was found for the Fe(III)-CN-Ni(II) exchange pair if anisotropic exchange combined with a negative zero-field splitting energy of the S = 1 ground state of Ni(II) in tetragonally compressed octahedra, while cancellation of the two anisotropic contributions was predicted for tetragonal elongations. A recently developed DFT approach to Jahn-Teller activity in low-spin hexacyanometalates was used to address the influence of dynamic Jahn-Teller coupling on the magnetic anisotropy. Spin Hamiltonian parameters derived for linear Fe-M subunits were combined using a vector-coupling scheme to yield the spin Hamiltonian for the entire spin cluster. The magnetic properties of published oligonuclear transition-metal complexes with ferromagnetic ground states are discussed qualitatively, and predictive concepts for a systematic search of cyanide-based SMM materials are presented.