Investigations into the Origin of the Crystalline Electric Field Effects on Rare Earth Ions: II. Contributions from the Rare Earth Orbitals

Abstract

Within the limitations of the ionic approximation, different contributions to the crystalline electric field parameters arising from the orbitals of the rare earth ions are calculated with particular reference to the Pr3+ ion in PrCl3. Contributions from the neighbouring point charges of both rare earth and ligand ions as well as those from the induced moments of the ligand ions have earlier been considered by Hutchings and Ray in 1963. Rare earth orbitals, on the other hand, affect the crystalline electric field in three different ways arising from (i) multipole electric moments of the f electrons in the externally impressed crystalline potential, (ii) induced moments on the closed s, p and d shells caused by the surrounding charges, and (iii) shielding of the external crystal field at the 4f electrons by the distorted orbitals. The first two factors are associated with the effect of rare earth orbitals of one ion on the crystalline electric field at another ion, whereas the last effect is concerned with the extra potential produced by the closed orbitals of the same ion for which the crystalline field parameters are being evaluated. The first factor is shown to contribute negligibly to the crystalline electric field parameters, whereas the effect of induced moments is of importance only for the A20 term. The general expression for the shielding of any crystal potential term has been derived and is shown to be independent of m. Numerical estimation of the shielding has been made for the A20 term and is found to reduce the external crystal field value by 52%, thus bringing the previously calculated value of A20 ⟨r2⟩ closer to the experimental one. The nuclear antishielding factor γ∞ is calculated for the Pr3+ ion, and on the basis of the point charge value of crystal potential, the expected quadrupolar frequency of nuclear magnetic resonance lines is evaluated for La3+ in LaCl3. This value is shown to be in excellent agreement with the one experimentally observed recently by Edmonds. Implications of the results are discussed and further improvements in the method of calculations have been suggested.