Localized and itinerant

The physical description of strongly pressure dependent magnetic properties is the object of considerable study. Edwards and Bartel [74E01] have performed the more recent physical evaluation of strong pressure and composition dependence of magnetization in their work on cobalt and manganese substituted invars. Their work contrasts models based on a localized-electron model with a modified Zener model in which both localized- and itinerant-electron effects are incorporated in a unified model. Their work favors the latter model. 

Palacio F (1996) In Coronado E, Delhaes P, Gatteschi D, Miller JS (eds) Localized and itinerant molecular magnetism. From molecular assemblies to the devices. Kluwer Academic, NATO ASI Series C 321 5... 

For the elements highlighted by the diagonal strip there is an indication that the / and d electrons may be balanced between being localized and itinerant. According to Smith and Kmetko (1983), materials close to this localization-delocalization transition can have their properties modified appreciably by small... 

Veciana, J. In Localized and Itinerant Molecular Magnetism Coronado, E., Ed. Kluwer Academic Publishers Dordrecht, in press. 

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... 

Fig. 8. Enthalpy vs. pressure curves for localized and itinerant 5 f electrons in americium metal (from )...

A fundamental question is whether the transition between localized and itinerant electronic behavior is continuous or discontinuous. Mott (1949) was the first to point out that an on-site electrostatic energy Ua > Wr, is needed to account for the fact that NiO is an antiferromagnetic insulator rather than a metal. Hubbard (1963) subsequently introduced U formally as a parameter into the Hamiltonian for band electrons his model predicted a smooth transition from a Pauli paramagnetic metal to an antiferromagnetic insulator as the ratio W/U decreased to below a critical value of order unity. This metal-insulator transition is known as the Mott-Hubbard transition. 

E. Coronado, R. Georges, B.S. Tsukerblat, in Localized and Itinerant Molecular Magnetism From Molecular Assemblies to the Devices, NATO ASl Series, ed. by E. Coronado, P. Delhaes, D. Gatteschi, J. MiUer (Kluwer, Dordrecht, 1996), pp. 65-84... 

There is one overarching shortcoming of the standard model, which is slightly more philosophical. It treats the f-electrons as localized and the sd-electrons as itinerant, that is, it treats electrons within the same material on a completely different basis. This is aesthetically unsatisfactory and furthermore makes it impossible to define a reference energy. In principle, one has to know, a priori, which electrons to treat as band electrons and which to treat as core electrons. It would be infinitely better if the theory itself contained the possibility of both localized and itinerant behaviour and it chose for itself how to describe the electrons. 

While these methods provide some useful insight into Gd and Ce, they yield unrealistic results for any other lanthanide material as the f-bands bimch at the Fermi level leading to unphysically large densities of states at the Fermi energy and disagreement with the de Haas van Alphen measurements. It is clear that a satisfactory theory of lanthanide electronic structures requires a method that treats all electrons on an equal footing and from which both localized and itinerant behaviour of electrons may be derived. SIC to the LSDA provide one such theory. 

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... 

The similarity of the Fermi surface topologies for localized and itinerant Ce 4f states is a characteristic feature of the CeM2X2 systems with partially filled M d-bands. In addition, we mention that the topology of the Fermi surface for the heavy quasiparticles is qualitatively reproduced by standard band stracture calculations based on the LDA (Zwicknagl, 1988). 

In solids, one emphasizes the distinction between localized and itinerant states. In a localized state, the electron remains attached to an individual atomic centre, whereas, in an itinerant state, it may move throughout the lattice. Under circumstances governed by the nature and excitation state of the atom or ion a given orbital can be poised at the critical point where it will live in either the inner or the outer reaches for small changes in the environment. In solid-state physics, this gives rise to a first-order Mott transition. 

The Neel model was shown to be successful for obtaining insight into the order of magnitude of the various interactions in the R-3d compounds. The localization of the lanthanide moments is well established. However the 3d moments tend to show both localized and itinerant behaviour and therefore a pure localized picture as used in the original Neel model cannot be expected to describe the magnetic properties in detail. 

There are no direct Fermi surface studies of the transition metal Laves phases -which is unfortunate in light of the part they have played, and continue to play, in our understanding of f electron behavior. The Np Laves phases have played a special role because they appear to span the critical separation between localized and itinerant behavior (Aldred et al. 1974). The U and Ce transition metal Laves phases occur on the itinerant side of the Hill (1970) plots, but some do approach, and just cross, the critical separation. The transition to magnetic behavior can be very closely approached by considering NpRu Osz-x alloys (Aldred et al. 1975). Because their properties are consistent with the Hill correlation, it would initially appear that one has a nice simple picture based on a direct f-f overlap analysis. Certainly, a Hill plot analysis was part of the motivation for the extensive studies of the Np materials. However, it appears that these materials heavily involve interaction with the ligands. 

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. 

Sketch of the free energies F/and F/as a function of temperature, indicating transitions between localized and itinerant electronic states. For details, see text. 

P. Delhaes and L. Ducasse, in NATO ASI Series, Localized and Itinerant Molecular Magnetism, Kluwer, Dordrecht, 1996. 

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