Praseodymium crystal fields

The first published work on the pressure dependence of optical spectra of solids seems to be of Paetzold (1940), who has studied the effect of pressure on absorption spectra of praseodymium nitrate, ruby, and other minerals between 1938 and 1939. To generate a maximum pressure of 0.1 GPa the samples were subjected to pressurised nitrogen. Using the same high pressure apparatus, Hellwege and Schrock-Vietor (1955) studied the pressure dependence of the absorption spectra of EuZn-nitrate. These authors, for the first time, applied the crystal-field Hamiltonian formalism for the analysis of the high pressure spectroscopic results. 

By far, the most studied quantum cutting system to date is for praseodymium, where the 4f2 1 So state lies below the lowest 5d state for many fluorides and some oxides. For most Pr3+ doped systems, the nephelauxetic effect and the 5d crystal field splitting are large enough to push the lowest 5d level below the 1 So state. However, for those systems in which the So... 

It can be seen from the comparison of the known Neel temperatures between R2C3 and RC2 (Atoji 1978) that in the light rare earth compounds the crystal field effect is often predominant, as exemplified by the fact that praseodymium carbides have exceptionally low values of and strongly suppressed ordered moments (1.14/1b in PrC2). In the heavy lanthanide compounds, the exchange interaction and anisotropy energy become the major factors in the magnetization. 

Whilst there have been several theoretical investigations of the effect of hybridisation on the crystal-field excitations within the ground multiplet (Maekawa et al. 1985, Lopes and Coqblin 1986), there have been relatively few in which the spin-orbit level is explicitly included. Cox et al. (1986) have shown, in the context of the Anderson impurity model, that when is comparable to the spin-orbit splitting, the inelastic peak is broadened and shifted to lower energies. Given that the cross-section is weak, at about half the intensity of the praseodymium spin-orbit cross-section, they concluded that the transition was unlikely to be seen except in heavy-fermion compounds with low values of This appears to be confirmed by the failure to observe such a transition in CePdj in recent measurements on HET (Osborn, unpublished). On the other hand, the... 

Fig. 6.17. Experimental results for the temperature dependence of the reciprocal susceptibility of praseodymium (Johansson et al. 1971). The solid lines indicate the behaviour calculated by Rainford (1972) using the crystal field energy level scheme shown on the right.

Fig. 6.19. The high field magnetization of praseodymium, as a function of internal field along [0001]. Arrows represent results for increasing and decreasing fields. The schematic field dependence of the low-lying crystal field levels for the hexagoncd sites is also indicated (after McEwen et al. 1973, Cock 1976).

The problem of the nature of the electronic multipole ordering is especially interesting for some praseodymium hexagonrd compounds with the doublet ground state E of the Pr + ion in the crystal field of Csh symmetry (chlorides, bromides, hydroxides, trifluoromethane sulfonates, ethylsulfates). In the effective S=j formalism, neglecting hyperfine interactions, the single-ion Hamiltonian can be written as follows ... 

As an example we present in fig. 10 the results obtained for praseodymium by McEwen (1978). The curvature in is due to the increasing population of the crystal-field levels with increasing temperature. In the case of antiferromagnetic lanthanide metals an anomalous behaviour has been observed, since below gaps are opened in the conduction band as a result of distortions of the Fermi surface, which modify the transport properties of the metals. Figure 11 displays a comparison... 

The mean deviation resulting from experimental/calculated fits is usually satisfactory. The accuracy does not depend only on the number of levels (for instance 91 versus 364 for trivalent praseodymium and neodymium, respectively), but also on the strength of the crystal field. While the deviation is 6cm and 10cm for Pr " and Nd doped in LaCls respectively, it rises up to 31 and 15cm in Y2O3. 

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