Introduction to Nanoscience and Nanotechnology. Chris Binns

source of magnetism in materials is their constituent atoms, which consist of tiny permanent dipolar magnets whose strength is given by the magnetic moment¹ of the atom (see Advanced Reading Box 1.1). In a material such as Fe, there is a strong interaction (the exchange interaction) between the atoms that line up the atomic magnets to produce a macroscopic magnetization. Note that the exchange interaction is a quantum mechanical effect and is not the normal interaction that you would see between two bar magnets, for example. For one thing, the interaction between bar magnets aligns them in opposite directions and for another, the exchange interaction is thousands of times stronger than the direct magnetic interaction.

Figure 1.4 Simple experiment to demonstrate magnetic domains. (a) Soft Fe does not attract the ball bearing. (b) A conventional magnet does; however, (c) when the soft Fe is magnetized by being in the presence of the magnet, it becomes more magnetic than the magnet and the ball bearing stays with the soft Fe in preference to the magnet. (d) The situation persists until the magnet is far enough away that the soft Fe reverts to its domain structure and externally generates no magnetic field.

Advanced Reading Box 1.1 Atomic Magnetic Moments and the Exchange Interaction

      The individual atoms of most elements have a permanent magnetic moment, so they generate a dipolar magnetic field similar to a simple bar magnet. The source of the atomic magnetic moment is twofold. It arises from the orbital motion of the electrons around the nucleus, which can be considered to constitute a simple current loop and also from the intrinsic angular momentum (spin) of the electrons. These two contributions generate an orbital and a spin magnetic moment and, for the elements Fe, Co, and Ni, the two contributions are simply added to obtain the total magnetic moment. The exchange interaction that acts between neighboring atoms arises from the Pauli exclusion principle. This tends to keep electrons apart if they have the same spins so that the Coulomb repulsion energy between the outermost electrons of neighboring atoms is reduced if the electrons align their spins in the same direction. This appears as a very strong magnetic interaction trying to align the spin magnetic moments, but it is an electrostatic effect produced by the quantum nature of the electrons. It is typically 3–4 orders of magnitude stronger than the direct magnetic interaction of the atomic magnetic moments assuming they are simple bar magnets.

So in a magnetic material, the powerful exchange interaction tries to line up all the microscopic atomic magnets to lie in the same direction. This, however, is not necessarily the preferred configuration because the uniformly magnetized state generates a magnetic field that passes through the material and the magnetization finds itself pointing the wrong way in its own magnetic field, that is, it has the maximum magnetostatic energy.² Of course, reversing the magnetization is of no use because the generated field reverses and again the sample magnetization and the generated field are aligned in the least favorable direction to minimize energy. The exchange interaction and the magnetostatic energy are thus competing, which at first glance does not appear to be much of a competition considering that the exchange energy per atom between nearest neighbors is 3–4 orders of magnitude stronger than the magnetostatic one. The magnetostatic interaction, however, is long‐range while the exchange interaction only operates between atomic neighbors. There is thus a compromise that will minimize the energy relative to the totally magnetized state by organizing the magnetization into so‐called domains with opposite alignment (Figure 1.5a). If these domains have the right size, the reduction in magnetostatic energy is greater than the increased exchange energy from the atoms along the boundaries that are neighbors and have their magnetization pointing in opposite directions. In the minimum energy state, the material does whatever is necessary to produce no external magnetic field and this is what has happened in Figure 1.4a. The magnetization of the soft Fe has organized itself into domains and externally it is as magnetically dead as a piece of copper. The actual magnet has been treated to prevent the domains forming so that it stays magnetized (Figure 1.4b). When we bring the piece of soft Fe into the field of the magnet, its domains are all aligned in the same direction and it has a greater magnetization than the magnet so that when we pull the two apart the ball bearing stays stuck firmly to the soft Fe. This continues until the soft Fe is far enough away from the magnet to revert to its domain structure and become magnetically dead externally.

The phrase “If these domains have the right size” in the previous paragraph encapsulates the essential point. If we do the Democritus experiment and start chopping the piece of soft Fe into smaller and smaller pieces, the number of domains within the material reduces (Figure 1.5b). There must come a size, below which the energy balance that forms domains simply does not work anymore and the particle maintains a uniform magnetization in which all the atomic magnets are pointing in the same direction (Figure 1.5c). So what size is this? It turns out to be about 100 nm, that is, the upper edge of the nanoworld. Any Fe particle that is smaller than this is a single domain and is fully magnetized. This may seem like a subtle size effect but it has profound consequences. Fully magnetized Fe is a much more powerful magnet than any actual magnet as shown in Figure 1.4. The reason is that a permanent magnet must contain some nonmagnetic material to prevent the process of domain formation so that its magnetization is diluted compared to the pure material. A world in which every piece of Fe or steel was fully magnetized would be very different from our familiar one. Every steel object would attract or repel every other one with enormous force. Cars with their magnetization in opposite directions would be very difficult to separate if they came into contact.

Figure 1.5 Single‐domain particles. Domain formation in Fe to minimize energy. Below a critical size (approx. 100 nm), the energy balance favors just a single domain and the piece of Fe stays permanently and fully magnetized. Arrows show the direction of magnetization.

Nature makes good use of this magnetic size effect. Bacteria such as the one shown in Figure 1.6 have evolved, which use strings of magnetic nanoparticles to orient their body along the local magnetic field lines of the Earth. The strain shown in the figure, which is found in Northern Germany, lives in water and feeds off sediments at the bottom. For a tiny floating life‐form such as this knowing up and down is not trivial. If the local field lines have a large angle to the horizontal, as they do in Northern Europe, then the string of magnetic nanoparticles makes the body point downwards and all the bacterium has to do is to swim, knowing that it will eventually find the bottom.

      The intelligence of evolution is highlighted here. If the particles are single‐domain particles, then they will stay magnetized forever, so forming a string of these ensures that the navigation system will naturally work. If the bacterium formed a single piece of the material the same size as the chain of particles, a domain structure would form and it would become magnetically dead. The nanoparticles are composed of magnetite (Fe₃O₄) rather than pure Fe but the argument is the same. There is currently research devoted to persuading the bacteria to modify the composition of the nanoparticles by feeding them