Electronic and Structural Factors Controlling the Spin Orientations of Magnetic Ions

Magnetic ions M in discrete molecules and extended solids form ML n complexes with their first-coordinate ligand atoms L. The spin moment of M in a complex ML n prefers a certain direction in coordinate space because of spin–orbit coupling (SOC). In this minireview, we examine the structural and electronic factors governing the preferred spin orientations. Elaborate experimental measurements and/or sophisticated computational efforts are required to find the preferred spin orientations of magnetic ions, largely because the energy scale of SOC is very small. The latter is also the very reason why one can readily predict the preferred spin orientation of M by analyzing the SOC-induced highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) interactions of the ML n complexes in terms of qualitative perturbation theory. The strength of this HOMO–LUMO interaction depends on the spin orientation, which is governed by the selection rules based on the minimum |ΔL z | value (i.e., the minimum difference in the magnetic quantum numbers) between the HOMO and LUMO. With the local z axis of ML n chosen as its n-fold rotational axis, the preferred spin orientation is parallel to the z axis (∥z) when |ΔL z | = 0 but perpendicular to the z axis (⊥z) when |ΔL z | = 1.