Theoretical derivation of the higher order electron-nuclear interaction terms in the spin Hamiltonian for d3ions in cubic symmetry

A theoretical expression for the coefficient U of the higher order electron-nuclear interaction term U(S 3 x S 3 y I y +S 3 z I z - 1 / 5 (S.I)(3S(S+1)-1)) in the spin Hamiltonian is derived for V 2+ in MgO. Racah formalism is used in order to include in the calculation the effects of interactions between the ground 4 F state and the low lying excited 2 G and 4 P states. The calculated value of U is then compared with the experimental value obtained from ENDOR data. It is found that the discrepancy between theoretical and experiment values of U is removed. The contribution of the 2 G state to U is found to be an order of magnitude larger than that of the ground 4 F state, but the effect of the 4 P state is insignificant in comparison. The same expression can be applied to Cr 3+ in MgO and to Co 2+ in CaF 2 , and it is shown that the contribution of the 2 G state is also important for these ions.