In this chapter we continue our survey of magnetic phenomena with a look at magnetism in magnetic semiconductors and insulators. A large practical motivation for the study of magnetic semiconductors is their potential for combining semiconducting and magnetic behavior in a single material system. Such a combination will facilitate the integration of magnetic components into existing semiconducting processing methods, and also provide compatible semiconductor–ferromagnet interfaces. As a result, diluted magnetic semiconductors are viewed as enabling materials for the emerging field of magnetoelectronic devices and technology. Because such devices exploit the fact that the electron has spin as well as charge, they have become known as spintronic devices, and their study is known as spintronics. In addition to their potential technological interest, the study of magnetic semiconductors is revealing a wealth of new and fascinating physical phenomena, including persistent spin coherence, novel ferromagnetism, and spin-polarized photoluminescence.

We will focus on the so-called diluted magnetic semiconductors (DMSs), in which some of the cations, which are non-magnetic in conventional semiconductors (Fig. 17.1 left panel), are replaced by magnetic transition-metal ions (Fig. 17.1 center panel). We will survey three classes of DMSs. First are the II–VI diluted magnetic semiconductors, of which the prototype is (Zn, Mn)Se, which have been studied quite extensively over the last decade or so.

In the previous chapter we discussed the diamagnetic effect, which is observed in all materials, even those in which the constituent atoms or molecules have no permanent magnetic moment. Next we are going to discuss the phenomenon of paramagnetism, which occurs in materials that have net magnetic moments. In paramagnetic materials these magnetic moments are only weakly coupled to each other, and so thermal energy causes random alignment of the magnetic moments, as shown in Fig. 5.1(a). When a magnetic field is applied, the moments start to align, but only a small fraction of them are deflected into the field direction for all practical field strengths. This is illustrated in Fig. 5.1(b).

Many salts of transition elements are paramagnetic. In transition-metal salts, each transition-metal cation has a magnetic moment resulting from its partially filled d shell, and the anions ensure spatial separation between cations. Therefore the interactions between the magnetic moments on neighboring cations are weak. The rare-earth salts also tend to be paramagnetic. In this case the magnetic moment is caused by highly localized f electrons, which do not overlap with f electrons on adjacent ions. There are also some paramagnetic metals, such as aluminum, and some paramagnetic gases, such as oxygen, O2.

Ferromagnetic domains are small regions in ferromagnetic materials within which all the magnetic dipoles are aligned parallel to each other. When a ferromagnetic material is in its demagnetized state, the magnetization vectors in different domains have different orientations, and the total magnetization averages to zero. The process of magnetization causes all the domains to orient in the same direction. The purpose of this chapter is to explain why domains occur, to describe their structure and the structure of their boundaries, and to discuss how they affect the properties of materials. As a preliminary, we will describe some experiments which allow us to observe domains directly with rather simple equipment.

Observing domains

Domains are usually too small to be seen using the naked eye. Fortunately there are a number of rather straightforward methods for observing them. The first method was developed by Francis Bitter in 1931. In the Bitter method, the surface of the sample is covered with an aqueous solution of very small colloidal particles of magnetite, Fe3O4. The magnetite deposits as a band along the domain boundaries, at their intersection with the sample surface. The outlines of the domains can then be seen using a microscope.

We've now worked our way through all of the most important types of magnetic ordering, and discussed the microscopic arrangements of the magnetic moments and the physics and chemistry that determine them. We've also described the resulting macroscopic behavior in each case. Before we move on, let's summarize the basics that we have learned so far.

Review of types of magnetic ordering

Remember that we have covered four main classes of magnetic materials: the para-, antiferro-, ferro-, and ferrimagnets. In Fig. 10.1 we reproduce the local ordering and magnetization curves, which we first introduced in Chapter 2, for each of the classes. Let's summarize their properties:

Finally we have reached the last chapter in our survey of the most important types of magnetic ordering. In this chapter we will discuss ferrimagnets. Ferrimagnets behave similarly to ferromagnets, in that they exhibit a spontaneous magnetization below some critical temperature, Tc, even in the absence of an applied field. However, as we see in Fig. 9.1, the form of a typical ferrimagnetic magnetization curve is distinctly different from the ferromagnetic curve.

In fact ferrimagnets are also related to antiferromagnets, in that the exchange coupling between adjacent magnetic ions leads to antiparallel alignment of the localized moments. The overall magnetization occurs because the magnetization of one sublattice is greater than that of the oppositely oriented sublattice. A schematic of the ordering of magnetic moments in a ferrimagnet is shown in Fig. 9.2. We will see in the next section that the observed susceptibility and magnetization of ferrimagnets can be reproduced using the Weiss molecular field theory. In fact the localized-moment model applies rather well to ferrimagnetic materials, since most are ionic solids with largely localized electrons.

The fact that ferrimagnets are ionic solids means that they are electrically insulating, whereas most ferromagnets are metals.

Before we can begin our discussion of magnetic materials we need to understand some of the basic concepts of magnetism, such as what causes magnetic fields, and what effects magnetic fields have on their surroundings. These fundamental issues are the subject of this first chapter. Unfortunately, we are going to immediately run into a complication. There are two complementary ways of developing the theory and definitions of magnetism. The “physicist's way” is in terms of circulating currents, and the “engineer's way” is in terms of magnetic poles (such as we find at the ends of a bar magnet). The two developments lead to different views of which interactions are more fundamental, to slightly different-looking equations, and (to really confuse things) to two different sets of units. Most books that you'll read choose one convention or the other and stick with it. Instead, throughout this book we are going to follow what happens in “real life” (or at least at scientific conferences on magnetism) and use whichever convention is most appropriate to the particular problem. We'll see that it makes most sense to use Système International d'Unités (SI) units when we talk in terms of circulating currents, and centimeter–gram–second (cgs) units for describing interactions between magnetic poles.

Magnetic properties of small particles

The magnetic properties of small particles are dominated by the fact that below a certain critical size a particle contains only one domain. Remember from Chapter 7 that the width of a domain wall depends on the balance between the exchange energy (which prefers a wide wall) and the magnetocrystalline anisotropy energy (which prefers a narrow wall). The balance results in typical domain-wall widths of around 1000 Å. So, qualitatively, we might guess that if a particle is smaller than around 1000 Å a domain wall won't be able to fit inside it, and a single-domain particle will result!

We can make a better estimate of the size of single-domain particles by looking at the balance between the magnetostatic energy and the domain-wall energy (Fig. 12.1). A single-domain particle (Fig. 12.1(a)) has high magnetostatic energy but no domain-wall energy, whereas a multi-domain particle (Fig. 12.1(b)) has lower magnetostatic energy but higher domain-wall energy. It turns out that the reduction in magnetostatic energy is proportional to the volume of the particle (i.e. r3, where r is the particle radius), and the increase in the domain-wall energy is proportional to the area of the wall, r2. The magnetostatic and exchange energies depend on particle radius as shown in Fig. 12.2. Below some critical radius, rc, it is energetically unfavorable to form domain walls, and a single-domain particle is formed.

Now that we have studied the phenomenon of cooperative ordering in ferromagnetic materials, it is time to study the properties of antiferromagnets. In antiferromagnetic materials, the interaction between the magnetic moments tends to align adjacent moments antiparallel to each other. We can think of antiferromagnets as containing two interpenetrating and identical sublattices of magnetic ions, as illustrated in Fig. 8.1. Although one set of magnetic ions is spontaneously magnetized below some critical temperature (called the Néel temperature, TN), the second set is spontaneously magnetized by the same amount in the opposite direction. As a result, antiferromagnets have no net spontaneous magnetization, and their response to external fields at a fixed temperature is similar to that of paramagnetic materials – the magnetization is linear in the applied field, and the susceptibility is small and positive. The temperature dependence of the susceptibility above the Néel temperature is also similar to that of a paramagnet, but below TN it decreases with decreasing temperature, as shown in Fig. 8.2.

The first direct imaging of the magnetic structure of antiferromagnets was provided by neutron diffraction experiments. We will begin this chapter by reviewing the physics of neutron diffraction, and showing some examples of its successes.