Gyromagnetic Factors and Covalency in Iron-Series Complexes

Abstract

The gyromagnetic factor appropriate to a transition-metal salt such as KNi${\mathrm{F}}_3$, is inspected in detail, with emphasis on extracting information concerning $3d$-electron covalent mixing from experiment. The necessary spin-orbit and orbital Zeeman matrix elements are evaluated within the framework of Hund—Mulliken—Van Vleck molecular-orbital theory and, contrary to frequent usage, the "orbital reduction effects" appropriate to the two types of matrix elements are very different. [The two-center terms, originally considered by Stevens and Tinkham, are important to the orbital matrix element (as they anticipated) but not to spin-orbit operator.] Taking $s$ and $\sigma$ bonding estimates from transferred hyperfine experiments, the observed $g$ shift for ${\mathrm{Ni}}^{2+}$ in KMg${\mathrm{F}}_3$ is used to deduce the $\pi$ bonding. The result is suprisingly large (${\gamma }_{\pi }=0.24\mathrm{}$) and is extraordinarily sensitive to computational details. For example, a simple perturbation-theory treatment, linear in spin-orbit coupling, is inadequate. The result is very likely too high because of a suspected understimate in the $\sigma$ bonding. It and the parameters obtained from transferred hyperfine measurements appear to supply an adequate and internally consistent set for understanding the various experimental quantities affected by covalency. Some difficulty arises when one attempts to relate the results to recent $a$ priori estimates of covalency, and the implications of this for the model (underlying both the results and those estimates) are discussed.