Itinerant states

Fig. 12a-c. Schematic representation of the effective potential Vejf and of different possibilities of localized and itinerant states for electrons of high 1 quantum number, a) The solid line d represents the periodic potential set-up by the cores R and R +i, which is a superimposition of central potential a dashed line). The dashed line b represents the centrifugal potential of kinetic origin 1(1 + l)/2 R in an atom, and c dashed line) the effective potential V f for an atom (compare Fig. 6) and full line) for a solid, b) Relative to two shapes of the effective potential Ve, two examples of localized state are given 1. resonant state 2. fully localized state. Notice that 1. is very near to Ep. h and t represent hopping and tunneling processes, c) A narrow band is formed (resonance band), pinning Ep 3. narrow band... 

The first part of the chapter is devoted to an analysis of these correlations, as well as to the presentation of the most important experimental results. In a second part the following stage of development is reviewed, i.e. the introduction of more quantitative theories mostly based on bond structure calculations. These theories are given a thermodynamic form (equation of states at zero temperature), and explain the typical behaviour of such ground state properties as cohesive energies, atomic volumes, and bulk moduli across the series. They employ in their simplest form the Friedel model extended from the d- to the 5f-itinerant state. The Mott transition (between plutonium and americium metals) finds a good justification within this frame. 

When the itinerant state is formed, a volume collapse AV/V is always encountered, as predicted by the theory of the preceding sections. In one of the lanthanides, cerium, this volume collapse is particularly accentuated for its isostructural transition from the y to the a form, possibly associated with a change in metallic valence from three to four (both oxidation numbers are stable in cerium chemistry) (see Fig. 1 of Chap. A),... 

There are, however, arguments, which contradict the partial localization interpretation. This interpretation must assume that the 5 f emission at Ep (itinerant state) and at the 2.5 eV satelhte have different photon energy dependence of the cross section at the resonance. As recently discussed this is difficult to explain since both structures are attributed to 5 f states. Furthermore, the main asymmetric 4 f core level should be accompanied by a shake-up satellite, induced by 6d screening of the localized hole, which has never been observed. 

Transitions from a localized to an itinerant state of an unfilled shell are not a special property of actinides they can, for instance, be induced by pressure as they rue in Ce and in other lanthanides or heavy actinides under pressure (see Chap. C). The uniqueness for the actinide metals series lies in the fact that the transition occurs naturally almost as a pure consequence of the increase of the magnetic moment due to unpaired spins, which is maximum at the half-filled shell. The concept has resulted in re-writing the Periodic Chart in such a way as to make the onset of an atomic magnetic moment the ordering rule (see Fig. 1 of Chap. E). Whether the spin-polarisation model is the only way to explain the transition remains an open question. In a very recent article by Harrison an Ander-... 

It is thus possible to emphasize the following points When the excited electron jumps in a wide conduction band, i.e. in itinerant states, the electronic speed in the band is sufficiently large for the electron to have a very small probability of returning to the inner hole. No resonance line is observed this is the general case in the solid. 

We have emphasised the distinction between localised and itinerant states. Under certain circumstances (governed by atomic properties) a given orbital is poised at the critical point where it can become either one or the other for small changes in the environment of the atom. In solid state physics, this gives rise to a first-order Mott transition. In the present context, such a situation is closely related to the problem of controlled orbital collapse (section 5.23) if a solid is built up from free atoms with a double well potential and the corresponding orbitals in the outer well, these may hybridise easily, the external part of the orbital going into itinerant states. If one forms a solid from atoms with collapsed orbitals, then they remain localised. 

Due to this repulsion and the expected weak quasiparticle dispersion, anisotropic superconducting phases and reduced coherence lengths seem probable, which is in accord with experiments. On the other hand, there does not really exist any conclusive correlation between an enhanced tendency towards magnetism and the occurrence of such superconductivity, see sect. 3. The conventional deformation-potential coupling mechanism, applied to the itinerant states alone, however, can apparantly not account for pairing between heavy fermions (Entel et al. 1985, Pickett et al. 1986, Fenton 1987, Normal 1988). 

One major advantage of the SIC-LSD energy fimctional is that it allows one to determine valencies of the constituent elements in the solid. This is accomplished by realizing different valence scenarios, consisting of atomic coidigurations with different total numbers of localized and itinerant states. The nominal valence is defined as the integer number of electrons available for band formation, namely... 

F or TmTe, a large y value is found if the f electrons are treated as itinerant states (Norman and Jansen 1988) and the predicted lattice constant is 4% too small (Monnier et al, 1985). Conversely, treating the f electrons as core states produces an insulating gap of 450 meV, consistent with experiment. 

This is especially puzzling for the superconducting materials, in which we would expect the spin susceptibility to disappear because of the formation of Cooper pairs. (A classic example of this is the paper on VjSi by Shull and Wedgwood (1966).) These results suggest that the susceptibility is well-described by localized U or Ce " f electrons. Two remarks are in order here. First, unlike the case of CeSn3 and CePdj, the bulk susceptibilities of the heavy-fermion materials show no anomalous increase at low temperature. Second, it must be remembered that the form factor is an elastic neutron measurement (i.e. long-time average). Differences between localized and itinerant states may depend on certain aspects of the temporal behavior of the electrons (Liu 1989) these are not addressed here, but under favorable conditions may be probed by neutron inelastic studies. 

---