Is [ReCl4(CN)2]2− a good Building Block for Single Molecule Magnets? A Theoretical Investigation.

Building blocks containing $5d$ spin centres are promising for constructing single molecule magnets due to their large spin-orbit interaction, but experimental and computational results obtained so far indicate that this might not be the case for Re$^\textrm{IV}$ centres in an octahedral environment. Density functional results obtained in this work for [ReCl$_4$(CN)$_2$]$^{2-}$ and trinuclear complexes formed by attaching Mn$^\textrm{II}$ centres to the cyano ligands indicate that zero field splitting in such complexes exhibits large rhombicity (which leads to fast relaxation of the magnetisation) even if there are only small distortions from an ideal geometry with a four-fold symmetry axis. This is already apparent if second-order spin-orbit perturbation theory is applied but even more pronounced if higher-order spin-orbit effects are included as well, as demonstrated by wavefunction based calculations. Computational results are cast into a ligand field model and these simulations show that especially a distortion which is not along the $C_4/C_2$ axeshas a large effect on the rhombicity. Quantum simulations on these complexes are difficult because the zero field splitting strongly depends on the energetic position of the low-lying doublets from the $t_{2g}^3$ configuration.

Atomic-scale insights into quantum-order parameters in bismuth-doped iron garnet

Bismuth and rare earth elements have been identified as effective substituent elements in the iron garnet structure, allowing an enhancement in magneto-optical response by several orders of magnitude in the visible and near-infrared region. Various mechanisms have been proposed to account for such enhancement, but testing of these ideas is hampered by a lack of suitable experimental data, where information is required not only regarding the lattice sites where substituent atoms are located but also how these atoms affect various order parameters. Here, we show for a Bi-substituted lutetium iron garnet how a suite of advanced electron microscopy techniques, combined with theoretical calculations, can be used to determine the interactions between a range of quantum-order parameters, including lattice, charge, spin, orbital, and crystal field splitting energy. In particular, we determine how the Bi distribution results in lattice distortions that are coupled with changes in electronic structure at certain lattice sites. These results reveal that these lattice distortions result in a decrease in the crystal-field splitting energies at Fe sites and in a lifted orbital degeneracy at octahedral sites, while the antiferromagnetic spin order remains preserved, thereby contributing to enhanced magneto-optical response in bismuth-substituted iron garnet. The combination of subangstrom imaging techniques and atomic-scale spectroscopy opens up possibilities for revealing insights into hidden coupling effects between multiple quantum-order parameters, thereby further guiding research and development for a wide range of complex functional materials.