Electronic and Magnetic Properties of the Lanthanides

The spins of the individual electrons(s) are coupled together (added vectorially) to give the spin quantum number for the ion (S). The orbital angular momenta (/) of the individual electrons are coupled similarly. 

For an f electron, Z = 3, so that the magnetic quantum number mi can have any one of the seven integral values between - -3 and -3. Vectorial addition of the m/-vaiues for the f electrons for the multi-electron ion affords L, the total orbital angular momentum quantum number  

There is a weaker coupling, spin-orbit coupling, between S and L. 

Lanthanide and Actinide Chemistry 2006 John Wiley Sons, Ltd. 

Vector addition of L and S affords the resulting quantum number, J. J can have values of 

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The outline of the present chapter is as follows. Section 2 deals with the relevant physical, electronic, and magnetic properties of the lanthanides. Section 3 reviews briefly the above-mentioned theoretical methods, with the focus on the SIC-LSDA method, and, in particular, the full implementation of SIC, involving repeated transformations between Bloch and Wannier representations (Temmerman et al., 1998). This is then compared with the local-SIC, implemented in the multiple scattering theory (Liiders et al., 2005). Section 4 deals with the valence (Strange et al., 1999) and valence transitions of the lanthanides. Section 5 discusses the local magnetic moments of the lanthanides. Section 6 discusses two spectroscopies applied to lanthanides and some of their compoimds. Section 7 outlines a methodology of calculating the finite temperature (T) properties of the lanthanides and their... 

Table 2.1 Electronic and magnetic properties of the trivalent lanthanide ions Ln +...

Relation between electronic structure and magnetic properties of the lanthanide metals... 

The decrease in radius in moving from La3+ to Lu3+ is 117.2 to 100.1 pm which is less than 114-88 pm for elements Ca2+ to Zn2+. In the case of Sc3+ to Ga3+, the radius decreases from 88.5 to 76 pm. This comparison shows that the percent contraction is greater in the case of Sc3+ to Ga3+ and Ca2+ to Zn2+ series than lanthanides series. The fact is that the magnitude of the lanthanide contraction is small and the usual interpretation of magnetic and spectroscopic properties of the lanthanides are inconsistent with the idea of considerable shielding of 4/ electrons from the chemical environment of the ion by the 5s25p6 configuration. Thus the implication that the size of lanthanide atoms or ions is determined by the 4 fn subshell must be incorrect. 

Since some properties of each sublattice, ei ecially the anisotropy of the lanthanide sublattice, as experimentally established, govern the behavior of the whole crystal of the magnet, the magnetic properties of the lanthanide sublattice will affect the sublattice of the transition metals, i.e., interactions between sublattices exist. The 4f electrons, however, have almost no direct bonds with the 3d electrons of the transition-metal sublattice, so the anisotropy of the 4f electrons initially transfers to the outer orbitals of 6s, 5d and/or 6p electrons of the lanthanide atoms, and these in turn interact with 4s and/or 4d electrons of the transition-metal sublattice, which is composed of and/or spd bands with the transition metal s 3d electrons. The interactions between the 4f and 3d electrons, therefore, are indirect. Figure la schematically shows the band structure in the lanthanide-transition-metal compounds. 

The opening chapter describes the dual character of the 4f core electrons that may either be part of the valence states or be inert and form part of the core using first principles theory. Here, W. M. Temmerman and coauthors begin with a review of the relevant physical, electronic, and magnetic properties of lanthanide materials. 

The magnetic properties of the lanthanide metals follow from the basic property that there is an unfilled shell of 4f electrons which is well separated from the conduction band electrons and which is also well localized on the ion sites, so that direct f-shell overlap or exchange effects are negligible. The ion containing the f-shell is tripositive, the three outer electrons going into the conduction band. The conduction electrons interact with the f-electrons and... 

Some magnetic properties of the lanthanides are presented in section 3 in comparison with the actinides. Table 33 and fig. 27 should be consulted for specific electronic configurations and magnetic moments in each series. 

To a large extent the opulent diversity of electronic and magnetic properties manifested by lanthanide materials arises from the existence of an open shell of atomic-like 4f electrons. A number of challenging theoretical problems accompanies the panoply of physical phenomena, not only for the exotic mixed valence systems but for comparitively simpler materials such as the metals as well. In this chapter we treat one of these issues, the calculation of 4f electron excitation energies in the lanthanide metals. Measurement of the excitation energies is one of the principal achievements of the high-energy spectroscopies which form the subject of the present volume. 

The interpretation of the electronic and especially of the magnetic properties of the actinides is much more complicated than in the lanthanides for the following reasons ... 

Low temperature processes are desirable in material sciences. Lanthanide nitrides which possess intrinsic electronic and magnetic properties are typically synthesized by ammonolysis of the metals at temperatures near 1000 °C. Inorganic amides of type Ln(NH2)s(x = 2,3) are intermediates in this process (Sect. 2.1). A versatile method starting from molten Ln(btsa)3 precursors was reported by LaDuca and Wolczanski [286]. The formation of low crystalline LnNj x according to Scheme 15 was observed at about 210 °C after 3 h. 

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