L'Étude de la Structure Électronique des Métaux des Terres Rares

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Abstract
In rare earth metals, one can neglect interactions between 4f shells centred on neighbouring sites. The conduction band is occupied by three sd electrons (eventually two in europium and ytterbium). These sd electrons are coupled to the f electrons through an interaction of the form where s e is the spin of a conduction electron and Sf i the spin of the ith f electron of a given ion. It is therefore possible to consider two groups of properties: 1. The ones, related to the nature of the conduction electrons, change very little through the series: this is the case of the crystalline structure, of the atomic volume. 2. The others, such as the magnetic properties, are related to the internal shells and vary with the filling of the 4f shell. Experiment shows a correlation between those two groups of properties. De Gennes formalism, essentially valid in the hypothesis of tightly bound 4f electrons, gives a satisfactory picture of the properties of the metals in the second half of the series, but it does not give as good a picture for the first rare earth metals, especially for cerium. In the cerium free atom, the 4f, 5d, 6s states have comparable energies and one might think that, in the trivalent metal, the 4f states are broadened in energy by resonances with the extended sd states, but still do not overlap from one atom to the other. They would then occupy virtual bound states analogous to the virtual bound states described by Blandin and Friedel for the transition impurities in noble metals. An identical situation seems to occur in ytterbium under pressure: one observes a huge increase of the electrical resistivity which goes back to low values at very high pressures. This might also be the case of the actinide metals, especially of Plutonium, in which the 5f states begin to stabilize. So we have to consider two cases: 1. The 4f electrons occupy bound states. 2. The 4f electrons occupy virtual bound states. In the first part (§ 2), we use de Gennes formalism for 4f bound states. The energy related to magnetic interactions is computed making the assumption of a spherical Fermi surface. A correlation between the crystalline structure and the magnetic properties shows up. In the second half of the series, one can neglect the crystalline field effects and the total energy is the sum of the magnetic term and of the elastic term due to the contribution of the conduction electrons. For every state of magnetic order, the crystalline structure is well defined, corresponding to the minimum of the total energy, and conversely. It is possible to explain in this manner: 1. The b.c.c. structure of europium, which is unusual for a divalent transition metal. 2. The variation of the c/a ratio of the h.c.p. structure both through the series and with temperature. 3. The anomalies in the thermal expansion coefficient observed below the magnetic order-disorder transitions. 4. The helix pitch of the magnetic configurations of this type. The anomalies of the thermoelectric power observed at the transition points are related to the different dependences of the spin correlations above and below the transition temperatures. The agreement between theory and experiment is satisfactory. Some discrepancy can be attributed to the rather crude approximation of a spherical Fermi surface. In the second part (§ 3), we deal with a situation where the 4f electrons occupy virtual bound states. These levels are very narrow, about 10−2 ev wide, and separated in energy by the correlations between electrons. Using Blandin's formalism we calculate the electrical and magnetic properties associated with such a situation. Calculations lead to very strong magnetic coupling; the indirect interaction between magnetic ions is antiferromagnetic for first nearest neighbours, whereas in the case of 4f bound states it is ferromagnetic. Finally, it is possible to explain the properties of cerium and ytterbium. 1. In Cerium, the two first levels overlap at the Fermi level, in such a way that the f electron be almost entirely distributed in the first level. 2. In ytterbium, under pressure, the fourteenth level comes across and above the Fermi level. The maximum resistivity is obtained for a half filling of this level. In the third part (§ 4), we attempt to apply this model of virtual bound states to plutonium, although in this metal, the 5f shells have a larger spatial extension than the 4f orbitals in rare earths. Anomalies in several physical properties of plutonium seem to indicate a magnetic transition at about 65° K, but no anomaly shows up in the magnetic susceptibility. Using a virtual bound state model associated with a very small polarization of the 5f states, it is possible to explain all the physical properties of plutonium. This model leads to a very small magnetic moment, that cannot be detected by experiment.