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

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Abstract
A theoretical expression for the coefficient U of the higher order electron-nuclear interaction term U(S3xS3yIy+S3zIz-1/5 (S.I)(3S(S+1)-1)) in the spin Hamiltonian is derived for V2+ in MgO. Racah formalism is used in order to include in the calculation the effects of interactions between the ground 4F state and the low lying excited 2G and 4P 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 2G state to U is found to be an order of magnitude larger than that of the ground 4F state, but the effect of the 4P state is insignificant in comparison. The same expression can be applied to Cr3+ in MgO and to Co2+ in CaF2, and it is shown that the contribution of the 2G state is also important for these ions.
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