4f states

However, although f f transitions are, in principle, forbidden by the Laporte parity rule, most of the transitions in (RE) + ions occur at the electric dipole (ED) order. As we have already mentioned, this is an ED allowance due to the admixture of the 4f" states with opposite parity excited states 4f" 5d, as a result of the lack of inversion symmetry (ED forced transitions). The oscillator strength, /, for a / f absorption band can be estimated using expression (5.19). We now rewrite this expression as follows ... 

From the Judd-Ofelt theory, some general rules have been derived for ED transitions between 4f" states of (RE) + ions in crystals ... 

In light lanthanides (La, Ce, Pr, Nd) the pulled down 4f state is nearly localized and hybridizes only weakly with conduction states. The bandwidth W4f will be very narrow, U high and negative, and the occupation probabiUty by conduction electrons rather low. This results in the occurrence of shake-down satellites at a lower binding energy for lanthanides, accompanying a poorly screened main peak (Fig. 7 a). When proceeding to heavier lanthanides, the occupation probability and the intensity of the shake-down satellite are depressed the symmetric, poorly screened core level is left, i.e. the 4f states are completely localized. 

It was noted earlier that the charge density of a narrow resonance band lies within the atoms rather than in the interstitial regions of the crystal in contrast to the main conduction electron density. In this sense it is sometimes said to be localized. However, the charge density from each state in the band is divided among many atoms and it is only when all states up to the Fermi level have contributed that the correct average number of electrons per atom is produced. In a rare earth such as terbium the 8 4f electrons are essentially in atomic 4f states and the number of 4f electrons per atom is fixed without reference to the Fermi level. In this case the f-states are also said to be locaUzed but in a very different sense. Unfortunately the two senses are often confused in literature on the actinides and, in order not to do so here, we shall refer to resonant states and Mott-localized states specifically. 

In tetrahedral and cubic symmetry, the crystal-field levels are inverted, giving a single orbital state lowest. For dl in an octahedral field, the 4F state also has the single orbital state lowest, so we would expect the d1 configuration in a tetrahedral or cubic field to behave in a similar fashion and fit the spin Hamiltonian given in Eq. (158) solved for S=f. For most of the examples listed in Table XV, the tetrahedral symmetry is not distorted so that D = E=0 and no fine structure is reported. The 5=f character of the spin state is revealed in these cases by the fact that Eq. (80) must be added to the spin Hamiltonian to explain the ESR results on d1 in tetrahedral and cubic fields (131). For Co2+ in Cs3CoCl5, D= —4.5 cm-1 (222) and in CdS, D > 2 cm-1 (223). 

Figure 8.1. Splitting of the 4F state in weak and intermediate fields of cubic symmetry.

CeRii4P]2 is a narrow gap semiconductor with a gap of 0.075 eV estimated from electrical transport measurements on polycrystalline samples (Shirotani et al., 1996). XANES measurements indicate trivalent Ce with strong hybridization with ligand orbitals. The gap is presumably formed from the hybridization of the Ce 4f states with the Ru d and P-p orbitals... 

In general, due to the localized and screened nature of the 4f-electrons, their interaction with phonons is weak. However, this interaction affects the 4f states in many different ways and... 

U. Staub and L. Soderholm, Electronic 4f state splittings in cuprates 491 Author index 547... 

Similarly, peak Bi corresponds to transitions to the (4f5/2)(5d ,) configuration, while peak B2 corresponds to transitions to the (4f7/2)(5d ,) configuration. These results also indicate that the splitting between peak Bi and B2 originates from the spin-orbit splitting of Pr 4f levels. Compared with peaks A and B, the compositions of peaks C and E are complicated. Peak C corresponds to transitions to the mixed states of the (4f5/2)(5dc), (4f7/2)(5dc), (4f5/2)(5d ), and (4f7/2)(5drf) configurations which simply corresponds to the transitions from 4f states to... 

The peaks a. a2 arise from the transitions to (4f5 2)(5d ) configuration, <23 to (4f7,2)(5d ). 4 to transitions to the mixed states of (4fs 2)(5d/,) and (4f7 2)(5dj). Therefore, the difference between peaks a and a2 originates from the multiplet splitting within (4fs 2)(5dfl) configuration, i.e., the interaction between the 4fs 2 electron and 5da electron, while the difference between peaks a, a2 and peak 03 originates from the spin-orbit splitting of the Pr 4f state. Peak 04 arises from the transitions to Pr 5d/, levels. 

Neodymium systems have the potential for quantum cutting because Nd3+ has a high lying 4f" state, 2G(2)9/2, at about 47 000 cm-1, which has a 7000 cm-1 gap above the next lower level, 2F(2)7/2 (Camall et al., 1988). This energy gap is sufficient to prevent non-radiative relaxation between the two states, and emission from the 2G(2)y/2 state can be expected. Exciting the 2G(2)9/2 state directly is impractical, due to the very low transition probability from the ground state. However, if efficient absorption into the 5d band occurs, then the 2G(2)9/2 state may be populated via non-radiative phonon-assisted relaxation, resulting in 2G(2)9/2 emission. 

For the 4f7 configuration of Eu2+, the host sensitive energy levels of the 4f65d states are not far from the metastable 4f7 6P7/2 multiplet near 27 000 cm-1. The strength of crystal field interaction determines whether the lowest 4f65d state is above or below the excited 4f7 multiplet, which is insensitive to host lattice. Because there is no 4f state below 6P7/2, strong blue luminescence arises from the parity allowed 4f55d-4f7 transition. The intensity of the... 

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