Lanthanides paramagnetic moments

As we know, this paramagnetic moment originates in the spins and orbital motions of the unpaired electrons in the substance. There are three possible modes of coupling between these components spin-spin, orbital-orbital, and spin-orbital. For some complexes, particularly those of the lanthanides, we must consider all three types of coupling. The theoretical paramagnetic moment for such a complex is given by... 

In Table 1, we show the quantum numbers for the bivalent lanthanide ions, the Lande g-factor, and the high-temperature paramagnetic moment given as ... 

It is notable that the spin and orbital contributions of the localized states are nearly the same as for the ionic case. This shows that in the light lanthanides, the f-states are as localized as for the heavy lanthanides. For the paramagnetic moments, the agreement between theory and experiment is very satisfactory (Table 9) and much better than using a band description of adding the contributions of the localized and delocalized states (Table 8). Sm and Eu are less well described by this procedure and it could be that the assumption of pure trivalent Sm and pure divalent Eu are not fully applicable and some divalent Sm and some trivalent Eu might be mixed into the groimd state. 

T-atomic magnetic moment (Mt effective paramagnetic moment (p r), numbers of nearest neighbours of R and T atoms in a number of the lanthanide-transition metal series. Values of An deduced from the ordering temperature (Tj) for the 3d sublattice in Gd-T compounds are also listed (see eq. (36) in the... 

The broadly successful application of these formulas to the paramagnetism of lanthanide complexes was due to the wide multiplet widths in the/block metals (large spin—orbit coupling coefficients X) and to the small effect of the ligand field on the deep-lying / orbitals. No comparably useful formula for the magnetic moments of d block complexes exists, except perhaps for the spin-only formula ... 

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