Gyromagnetic Factors and Spin—Orbit Coupling in Ligand Field Theory

It has been customary to compute the effect of spin—orbit coupling on the magnetic properties of transition metal ions in crystals with the expression taken over from atomic spectroscopy, although this expression is valid only in a spherically symmetric field. In the present work, we show how the use of a spin—orbit interaction Hamiltonian derived from the Bethe—Salpeter approximation to the relativistic Breit equation for a partly covalent complex leads to a dependence of the gyromagnetic factor on the spin—orbit coupling parameter of the ligand atoms. We develop an expression of g for a d8-ion in a cubic field and apply it to the case of KNiF3. The calculated g values agree very well with experimental results. Other differences between our expression and those found by other authors are discussed.