Zero-Field Splitting ofS-State Ions. II. Overlap and Covalency Model

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Abstract
A general formulation including both overlap and charge-transfer covalency effects is developed for the parameters D and E in the spin Hamiltonian HS=D(3Sz2−S(S+1))+E(Sx2−Sz2) for a S6 ion surrounded by six singly charged negative closed-shell ions. The contributions to D and E arise in second order from the spin-orbit interaction and in first order from the spin-spin interaction. These contributions can be broken down into three categories: local, nonlocal, and distant, depending on whether the ligand orbitals are involved not at all, once, or twice. Specific application is made to the case of a Mn2+ ion surrounded by six F− ions (Mn2+:ZnF2). The calculations are performed for the recent crystal-structure parameters given by Baur. We find, on the one hand, that for the spin-spin interaction, the nonlocal terms predominate over the local and distant terms, and are of the same sign. On the other hand, for the spin-orbit interaction, the local and distant terms predominate over the nonlocal terms, and are of opposite sign, though similar in magnitude. The total (overlap only) contribution to D is found to be -10.94×10−4 cm−1, which is comparable and of opposite sign to the point-charge contribution 24.01×10−4 cm−1 calculated in our earlier publication on this problem. The sum of the two contributions (point charge and overlap) is found to be 13.07×10−4 cm−1, very close to the experimental value of +10.5×10−4 cm−1. The overlap contribution to E is found to be -19.77×10−4 cm−1, which is rather smaller than the point-charge contribution of -102.32×10−4 cm−1. The combined result,