We have seen in the previous chapter that chemical bonds are the glue for condensed matter. If the temperature is low enough so that thermal fluctuations do not break the bonds, it is no surprise that atoms and molecules condense, i.e. stick together, so that there are large pieces of matter.

However, the precise structure of condensed matter is often quite surprising. For example, we might guess that the typical result of attractive chemical bonds would be a disorderly mass of molecules. This does occur; such materials are called glasses. However, very commonly something else happens: at low enough temperatures the atoms or molecules form a remarkable ordered structure, a crystal. A crystal is an ordered, periodic array of atoms or molecules. In the next chapter we will give a precise definition of this concept. For our purposes, it is enough to understand that crystals are made up of identical building blocks that are repeated many times. See Figure 2.1 for an example, the face-centered cubic (fcc) crystal structure.

Chemistry tells us that atoms or ions can have a magnetic moment, either from orbital currents or unpaired spins. However, you might expect that when large numbers of such ions are stuck together that the orientation of the moments would be random. This is not always the case. For some elements, e.g. Fe, Ni, Co, and many compounds the moments line up in regular arrays of various kinds due to the exchange interaction, discussed above.