In Chapters 2 and 3, we discussed the magnetism of isolated single atoms. Let’s now consider an aggregate of atoms to form a solid. Nature ‘‘prefers’’ to place atoms in a highly ordered manner to form solids. We will not enumerate all the possible ordered crystal structures solids can have. The most common crystal structures encountered in ordered magnetic materials are that of cubic and hexagonal crystal structures. We will henceforth assume only one or the other crystal structure. We will also assume that at each site where an atom or magnetic ion is located in the solid, it can be represented by a set of values for~L,~S, and gJ . In essence, we are assuming a localized picture for the existence of magnetism in a solid. The other picture is the so-called electron itinerant model in which the electrons giving rise to magnetism are not bound to any given site in the solid. They are free to roam in the solid. A description of this picture is beyond the scope of this book. However, even for the itinerant model, one could represent a local site by an effective ~L,~S, and gJ in which the quantization rules are no longer expressed in terms of integers or half integers. It becomes a problem of determining the percentage of time an electron spends near a given site. The reader is referred to the ‘‘References’’ section at the end of last chapter for more information about the itinerant model of magnetism. However, once the exchange parameter and other magnetic parameters are specified for magnetic metals, our semiclassical approach is appropriate for most practical magnetic metals. The basic interaction energies between spins in a solid are Zeeman,

exchange, dipole-dipole, and spin-spin interaction energies. We will discuss briefly the nature of each interaction before introducing the concept of the magnetic free energy.