Actinides, 433 --- spin

Lanthanide and actinide compounds are difficult to model due to the very large number of electrons. However, they are somewhat easier to model than transition metals because the unpaired / electrons are closer to the nucleus than the outermost d shell. Thus, all possible spin combinations do not always have a significant effect on chemical bonding. 

As the actinides are a Second f series it is natural to expect similarities with the lanthanides in their magnetic and spectroscopic properties. However, while previous treatments of the lanthanides (p. 1242) provide a useful starting point in discussing the actinides, important differences are to be noted. Spin-orbit coupling is again strong (2000-4000 cm ) but, because of the greater exposure of the 5f... 

Apart from d- and 4f-based magnetic systems, the physical properties of actinides can be classified to be intermediate between the lanthanides and d-electron metals. 5f-electron states form bands whose width lies in between those of d- and 4f-electron states. On the other hand, the spin-orbit interaction increases as a function of atomic number and is the largest for actinides. Therefore, one can see direct similarity between the light actinides, up to plutonium, and the transition metals on one side, and the heavy actinides and 4f elements on the other side. In general, the presence or absence of magnetic order in actinides depends on the shortest distance between 5f atoms (Hill limit). 

Concerning induced orbital moments of U-based intermetallic compounds, many PND experiments have been performed and have shown that the ratio iL/ -is can be used as a measure of the hybridisation [42-44] (in the light actinides, orbital and spin moments are oppositely directed and the neutron magnetic form factors are highly sensitive to the ratio uL/us). Indeed, this ratio is reduced as compared to the free ion expectations (Figure 4). 

Lebech, B., Wulff, M. and Lander G.H. (1991) Spin and orbital moments in actinide compounds (invited), J. Appl. Phys., 69, 5891-5896. 

In their subsequent analysis Baker and Bleaney (ibidem) decided to ignore the last term on the assumption that gdl 3b hv. Although this is a reasonable approximation for lanthanide and actinide integer-spin ions doped in single crystals, it is not usually an acceptable assumption for the broad-line spectra from metalloproteins. Furthermore, the assumption of a A-distribution around zero (i.e., D 0 but all other zero-field interaction parameters are zero) is equally untenable for biomolecules. Therefore, we go for a later extension of the theory, based on a full Equation 12.9 and on (A) 0, for application to metalloproteins (Hagen 1982b). 

One of the prime reasons to consider (early) actinides for the development of SMMs with stable magnetizations at high temperatures is that they can potentially display much stronger interactions to neighbouring spin carriers due... 

Unlike the lanthanides, the actinides U, Np, Pu, and Am have a tendency to form linear actinyl dioxo cations with formula MeO and/or Me02. All these ions are paramagnetic except UO and they all have a non-spherical distribution of their unpaired electronic spins. Hence their electronic relaxation rates are expected to be very fast and their relaxivities, quite low. However, two ions, namely NpO and PuOl", stand out because of their unusual relaxation properties. This chapter will be essentially devoted to these ions that are both 5/. Some comments will be included later about UOi (5/°) and NpOi (5/ ). One should note here that there is some confusion in the literature about the nomenclature of the actinyl cations. The yl ending of plutonyl is often used indiscriminately for PuO and PuOl and the name neptunyl is applied to both NpO and NpOi. For instance, SciFinder Scholar" makes no difference between yl compounds in different oxidation states. Here, the names neptunyl and plutonyl designate two ions of the same 5f electronic structure but of different electric charge and... 

A better description of the energy level structure of the actinide atoms is obtained by adding to (3) terms of relativistic origin, which, in fact, represent the magnetic interaction of orbital and spin momenta of the electrons. (They are of particular importance for actinides since they depend on the fourth power of the atomic number Z) ... 

Hi H2 this is the so-called intermediate couphng. When the electrostatic and spin orbit interactions are of the same order of magnitude - and this is the case of the actinides - both should be included in first-order perturbation theory. 

In Sect. 4 and 5, the consequences of spin polarization in unsaturated 5f shells are analysed, and the Stoner and Mott-Hubbard theories briefly reviewed. In this way, concepts which are central for actinides, and which the reader may find only when perusing many textbooks (references of which are duly given) are adequately concentrated. 

It is known that an atom containing an unsaturated inner shell displays a net magnetic moment. This is the reason of magnetism being found in transition metal atoms (unfilled d shell), in lanthanides (unfilled 4 f" shell) and in actinides (unfilled 5 P shell). The magnetic moment is caused by the fact that the electrons fill the shell in such a way as to have the maximum alignment of their spins a set of rules, Hund s rules, give a very precise prescription ... 

A last remark the LDA approach disregards spin-polarization phenomena. Taking into account this effect (already indicated by Koelling as the future direction of development for band calculations) has turned out to be of paramoimt importance at the centre of the actinide series. We shall examine it in the next section. 

For solids in which IN([Xf) is very near to 1, often, although no magnetic order occurs, long-range fluctuations of coupled spins may take place, giving particular form to properties such as the (Stoner enhanced) magnetic susceptibility x, the electrical resistivity, and the specific heat of the solid. Spin fluctuations have been observed in actinides, and will be discussed in more detail in Chap. D. 

Brooks and Johansson , by calculating I and AE have been able to show that these curves are very much affected by the spin-polarization energy AE, which, in fact, appears as the most important contribution in cohesion for actinide elements in which the beginning of localization of 5 f orbitals occurs (at the half-filling of the 5 f" shell) and for which spin-polarization plays a major role (see Chaps. C and F). 

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