Itinerant 4/ electrons

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. 

The problem could be stated from another point of view. In an isostructural series the uranium and neptunium compounds tend to be itinerant electron magnets or band magnets (like iron) and their orbital contribution is at least partially quenched. For much heavier actinides we know that the compounds will make local moment magnets with orbital contributions. It is quite possible that in between these two clear cut forms of magnetism that the intermediate case could be dominated by fluctuations, and no recognizable form of magnetism would occur. To state that the... 

Zener appears to have been the first to consider this problem to some depth in his theoretical work on ferromagnetic crystals of the type l.a. Ca.MnO, (Zener 1951). For x = 0 one has LainMnin03 but for x > 0 some of the Mn will be 4+, and so we have the structure I. a " / a " Mn "(Mn CL in which some Mn-Mn pairs will be mixed valence, that is, MiF Mnj) or MnJ) Mn . Mnm is 3d4 (S = 2) and MnIV is 3d3 (S = 3/2), and Zener proposed that the excess electron (also called itinerant electron or Zener electron) on Mn111 can travel to the MnIV via a doubly-occupied p-orbital of... 

The 29Si relaxation rate 7j"1 at 1.6 K vs donor concentration nD shows a sharp decrease between nD = 2.5 x 1018 cm 3 and nu = 6 x 1018 cm 3. This reflects the fact that in the semiconducting regime (lower donor concentrations), the unionized donors are paramagnetic point sources of relaxation for the 29Si nuclei. Their localized electron spins are more effective in inducing relaxation than the itinerant electrons found in a conduction band at the higher donor concentrations [18]. 

The reduced orbital overlap between the radicals reduces the bandwidth and the electronic structures could be better considered as those of a localised rather than itinerant electron system. This poor overlap results in very small antiferromagnetic interactions being observed, and the compounds behave as nearly perfect Curie-Weiss paramagnets. In the cases when improved lateral interactions between the stacks are achieved by change of the substituents85 the compounds behave as weak ID ferromagnets due to the effective orthogonality of the S C interactions. 

Fig. 2 Representation of the ferromagnetic alignment of d localized spins resulting from the interaction with itinerant electrons through short intermolecular contacts...

J. K. Kiibler, Theory of Itinerant Electron Magnetism, Oxford University Press, Oxford,... 

In passing, it would be worth mentioning the corresponding situation in condensed matter physics. Magnetism and superconductivity (SC) have been two major concepts in condensed matter physics and their interplay has been repeatedly discussed [14], Very recently some materials have been observed to exhibit the coexistence phase of FM and SC, which properties have not been fully understood yet itinerant electrons are responsible to both phenomena in these materials and one of the important features is both phases cease at the same critical pressure [15]. In our case we shall see somewhat different features, but the similar aspects as well. 

The Stoner model, which we discuss in its simplest form, describes the formation of a net magnetic moment for itinerant electrons in a narrow band by adding to the basic Hamiltonian (11) of band theory a perturbing term accounting for total energy increase in case the itinerant electrons spins are not polarized (as in an atom for states not maximizing the spin). 

A somewhat different interpretation has been given by Johansson who applied the Mott-Hubbard theory of localized versus itinerant electron behaviour also to compounds. This interpretation differs from the above one mainly in that it assumes complete localization for magnetic compounds, and that at a certain critical inter-atomic distance we have to switch our description from a metallic state to an insulating one for the 5 f electrons (see Eq. (42)). In Eq. (42), an is substituted by a convenient measure of the spatial extension of the 5 f orbital, the expectation values (analogous to (of Fig. 10) and Xmoh is calculated from the R j radii of actinide metals (Fig. 3). The result is given in Table 6. 

The total electronic pressure Peiectrons can be expressed in terms of partial pressures due to the different electronic waves forming the itinerant electrons cloud (partial waves analysis) ... 

This approxiination assumes Koopmans theorem (which has been discussed in Chap. A) to be vahd. It is recalled that this theorem is valid for broad bands in solids, where electrons have a fully itinerant character. In this case, Eb as given by (6 a) is simply the one-electron energy E(fc) of an itinerant electron in the E(fe) band. 

The cross-sections for itinerant electrons, as, e.g., electrons in broad bands, are evaluated by taking into account that the electrons in the initial as well as in the final state may be represented by Bloch-wavefunctions P = u,t(/ ) exp(i R) (see Chap. A). In these wavefunctions atomic information is contained in the amplitude factor Uj (i ), whereas the wave part exp (i R) is characterized by the wavenumber k of the propagating wave (proportional to the momentum of the electron). 

A somewhat simplified form of the intensity of itinerant electron emission is ... 

The mixed-valence iron oxides provide an experimental test-bed for studying the evolution of charge-transfer processes from the localized-electron to the itinerant-electron regimes. Moreover, it is possible to monitor the influence of the charge transfer on the interatomic magnetic coupling since the iron ions in oxides carry localized magnetic moments. 

The condition for localized electrons with spontaneous atomic moments is U > w that for itinerant electrons with no spontaneous moment is Un < w. The intermediate case Un = w is of considerable theoretical interest. In the case of iron oxides, a U5 = 3 eV ensures a localized 3 d majority-spin configuration at both Fe " and Fe " ions since the cubic-field splitting Ag < Ag, is small enough to leave the ions in the high-spin state. However, localization of the minority-spin electron, particularly in the mixed Fe / Fe " state, does not necessarily follow. Similarly, a much smaller U4 will be seen to make U4 = w for Fe " in the perovskites A Fe03. 

With mixed-valence compounds, charge transfer does not require creation of a polar state, and a criterion for localized versus itinerant electrons depends not on the intraatomic energy defined by U , but on the ability of the structure to trap a mobile charge carrier with a local lattice deformation. The two limiting descriptions for mobile charge carriers in mixed-valence compounds are therefore small-polaron theory and itinerant-electron theory. We shall find below that we must also distinguish mobile charge carriers of intennediate character. 

Itinerant electrons occupy band states, which are molecular orbitals for an entire crystal they therefore belong equally to all like atoms on energetically equivalent sites and are described by band theory. 

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