Exceedingly Large Cubic Zeeman Terms for a High Spin Cobalt(II) Complex Originated from the Substantial Unquenched Orbital Angular Momentum.

The spin Hamiltonian (SH) has been widely used to model magnetic properties of transition metal complexes. In the case of parametrization of the electronic Zeeman splitting, it has been shown that the linear Zeeman term is adequate for S = 1/2 and 1 transition metal complexes, and for S ≥ 3/2 systems higher-order Zeeman terms typically can be neglected. However, it has been reported that CoTp2 (Tp = tris(pyrazolyl)borate), a high-spin S = 3/2 cobalt(II) complex possessing an orbitally almost doubly degenerate 4E ground level, features a non-negligible cubic Zeeman term that is even on a par with the corresponding linear term. Here we describe the physical origin of the exceptionally large cubic Zeeman term of CoTp2. Based on highly correlated wave function-based ab initio calculations, our effective Hamiltonian analysis successfully reproduces the zero-field splitting and effective g-factors of the ground Kramers doublet determined experimentally. It further discloses that substantial first-order orbital angular momentum that is introduced to the ground quartet by the efficient spin-orbit coupling within the 4E manifold is disproportionate to the spin angular momentum for a given magnetic substate. As a consequence, the total magnetic moment derived from both spin and orbital angular momenta does not scale proportionally to the linear combination of pseudospin operators, which necessitates incorporation of cubic Zeeman terms in the SH to accurately model the magnetic moment. More importantly, our in-depth dissection reveals that when the energy gap of the two orbital components of 4E is less than 2ζ (ζ is the effective one-electron spin-orbit coupling constant), the magnitude of the cubic Zeeman terms becomes comparable to those of the linear counterparts. Thus, higher-order Zeeman terms become essential for S ≥ 3/2 systems featuring orbital near-degeneracies.