Magnetism in the Itinerant Electron Model
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(this chapter deals with fundamentals, and may be skimmed over during a first reading)
In chapter 7, we showed under what circumstances a magnetic moment can exist onan isolated atom, and then in a solid made up of these atoms (or ions) under the assumption that the electrons remain localized on the atoms. In some metals, however, electrons can propagate throughout the solid. How can such a system be magnetic? This is the basic question we address in this chapter.
1. GENERALITIES W e have seen in chapter 3 that many elements, in the free atom state, possess a magnetic moment (tab. 3.1). However, in the solid state, the majority of them are diamagnetic: only the metals of the third row, from chromium to nickel, and most of the rare earth elements and actinides carry magnetic moments (tab. 3.2). This means that the formation of a chemical bond significantly alters the electronic orbits that are responsible for magnetism. The transition metals (3d series) are in fact far more sensitive to these effects, and the magnetic moments observed in these elements, their compounds, and alloys, generally differ markedly from those of the free atoms or isolated ions. We have already treated, in the preceding chapter, the materials in which the electrons responsible for the magnetism are localized. In other situations, most importantly in the metals and alloys of the 3d transition series, the magnetic moment carried by a magnetic atom is rarely the same as that of the isolated atom because the valence electrons now propagate throughout the material, and their wavefunctions are very different from those in the isolated atom. In this case we cannot say anything a priori about the magnetism of a given material. Understanding the magnetism of metals and alloys is therefore more subtle than for the compounds and oxides described in the previous chapter. The rare earth elements are a special case, as their magnet moment arises from the f electrons, while the valence electrons responsible
284
MAGNETISM - FUNDAMENTALS
for conduction are of s and d character. Localized magnetic moments are then observed in metallic environments, and we will return to this situation later. In this chapter, we will show how the electrons responsible for the electronic conductivity can at the same time give rise to magnetism. We will establish that this magnetism arises from the interplay of Coulomb repulsion between electrons with the Pauli exclusion principle, and that in a metallic system the existence of the magnetic moment on an atom depends very strongly on its local environment. Before we explain why some materials are magnetic, we must remember why the majority are not. According to the Pauli principle, in a system of atoms the electronic states which extend over all the atoms can be occupied by jus1t two electrons with opposed spins. In most solids, all these states are doubly occupied, and correspondingly the substance remains diamagnetic.
2.
SPECIAL PROPERTIES OF MAGNETIC METALS
Some experimental properties of magnetic metals cannot be exp
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