## Friday, October 28, 2011

### Magnetism Explained: 2 The Mechanism of Magnetism

What is a Magnet?

A magnet is simply any material that produces a magnetic field around itself. Lodestones produce magnetic fields and so do the magnets below. They attract each other as well as various iron-containing steel items:

The Magnetic Dipole (And the Mystery of the Monopole)

Every magnet is a magnetic dipole. This means that all magnets have two opposing poles - a north pole and a south pole. Curiously, no magnetic monopole has ever been found. All magnets, no matter how small, must have two poles. Two opposite charges separated in space also create a dipole, an electric dipole in this case, with a positive end and a negative end. But electricity also has a monopole - a point charge, which can be either entirely positive or negative. No one is sure why electricity would have this basic unit but not magnetism, especially considering that both forces are part of one force, electromagnetism, as mentioned in the previous article, "An Introduction to Magnetism."

Magnetic Fields Don't Always Come From Magnets

Every magnet produces a magnetic field but magnetic fields are not all  produced by magnets. As we learned in the previous article, a moving electric charge or a changing electric field can also produce a magnetic field.  If you want to dissect magnetism down to its most fundamental units, you will discover that atoms, electrons and even atomic nuclei all possess magnetism. They, like all charged subatomic particles, have spin, and these tiny moving electric charges create tiny magnetic fields, and a force comes from this, which is called the magnetic moment. The magnetic moment is defined as the force that a magnet can exert on electric currents as well as the torque that a magnetic field can exert on a current. This torque is the force that tends to line up the magnetic moment with the magnetic field. Both magnetic moment and magnetic field are vector quantities and they are directly proportional to each other.

Charged subatomic particles are tiny magnetic dipoles. Magnetism in charged particles can arise in two ways: from the intrinsic (built-in) spin of a charged particle as well as from that particle's motion through space. An electron has a built-in spin of 1/2. All electrons have this spin - it is part of what makes an electron an electron. As a result, every electron has an intrinsic magnetic moment. It also moves around a nucleus, which creates an additional moving charge and an additional magnetic field. Every magnetic field exerts a force. It is the force that changing electric fields or moving charges exert on each other. The magnetic force of a magnet is technically the net sum of these forces. Because magnetic force is a vector force, it has strength and direction. Opposite-directed magnetic forces produced inside a magnet cancel each other out. That is why we say "net force."

The Magnetic Moment of Electrons: Why Isn't Wood Magnetic?

Generally, we talk about the spins of electrons when we talk about magnetism - these contribute by far the most magnetic force within materials. Let's explore why this is so.

Inside a block of wood, a material we don't think of as magnetic at all, magnetism exists. All of the wood's atoms, and in fact all atoms, have magnetic moments, and these moments are the net sum of various subatomic magnetic moments. However, this material displays zero magnetism. Why?

First of all, let's take a deeper look into the how the magnetic moments of electrons add up inside atoms. For each atom, individual electron spins are added to get a total spin. However, some rules must be followed when this is done. As I mentioned above, each electron acts like a tiny magnet, creating its own magnetic field. Only when these dipoles are aligned parallel to each other, can they be added together to create a larger magnetic field. And here's the hitch: electrons come in up/down pairs. Any filled valence shell of electrons has a zero net magnetic moment because all the oppositely spinning electrons cancel each other out. Some (electrically neutral!) atoms come with partially filled valence electron orbitals, as shown in this periodic table:

The number of unpaired electrons per atom is labeled in colour.

In these atoms, you get (usually) one or (occasionally) more unpaired electrons. And in these atoms, as a result, you get a net non-zero atomic magnetic moment. Because of Hund's rules, the first few electrons in a shell all tend to have the same spin (they don't get paired up right away) and atoms with this arrangement tend to have the largest atomic magnetic dipole moment. Notice where iron stands in the table above. It has four unpaired electrons, so iron atoms can exhibit a relatively large magnetic torque force. It is no surprise then that most magnets have a large iron component in them. These unpaired electron dipoles (we tend to just call these "spins" for simplicity) tend to line up with external magnetic fields, while paired electrons aren't so easily influenced. When a number of these atomic spins line up within a material, we say it is magnetized. And we can measure that with instruments.

Fine, you say, but how does this explain why wood isn't magnetic?

We've now covered the atomic contribution of electrons. What about the nucleus? The intrinsic spins of protons and neutrons inside the nucleus can also contribute to the magnetic moment of an atom, but they cancel each other out when both are in equal numbers. Most atoms, unless they are radioactive, exist in this balanced, or ground, state, and thus have zero net magnetic moment. Some elements, however, come in different (and sometimes stable) isotopes, however. Some of these isotopes can contain uneven numbers of neutrons and protons inside their nuclei. Therefore, one isotope of an element may have a nuclear magnetic moment while another isotope does not. Carbon-12 has 6 protons and 6 neutrons so it has a zero net nuclear magnetic moment. However, carbon-14 (yes it is radioactive - it's used in carbon dating), with 6 protons and 8 neutrons, does have one. You might find this idea intuitively weird - how can the number of electrically neutral particles in a nucleus have any effect on its overall magnetism? This question has a fairly complicated answer. It is because the magnetic moment of any particle is closely related to angular momentum. According to the nuclear shell model, the magnetic moment of a particle is a product of its orbital angular momentum and its spin. The angular momentum of a particle is a vector measurement of its inertia and its angular velocity. In subatomic particles such as neutrons and protons, this value is built-in and permanent; it's not related to their movement through space, like it is in larger systems. This value differs slightly between neutrons and protons, so it affects their arrangement within the nucleus - the nucleus isn't just a smeared positive charge in the center of an atom nor is it a single point of positive charge right in the center. The nucleus is a more complicated system that displays variance of charge across its radius. This leads to magnetic anisotropy in atomic nuclei with uneven numbers of protons and neutrons. This means that these isotopes have a directionally dependent magnetic moment. There is a lot of research going on right now to test various theories about how this magnetic moment arises in nuclei. Most nuclei with uneven numbers of protons and neutrons tend to be unstable, and they eventually decay into stable nuclei. For this reason most of the atoms in the materials we see everyday do not contribute any nuclear magnetic moment. Even when it is present, it is very small force that is difficult to detect and measure.

So, when we talk about the magnetism of atoms, we have the nuclear magnetic moment and the net magnetic moment of electrons to contend with. We can fairly confidently ignore the nuclear component for the reasons explained above. This still doesn't explain why wood isn't magnetic, does it?

All these magnetic moments add up to give a total magnetic moment for an atom, but as mentioned, we usually concern ourselves just with the net magnetic moment contributed by the spins of the atom's unpaired valence electrons. We are now ready to look back at our wood sample. The reason this material shows no magnetism is not that it is made up of atoms that don't have strong magnetic moments. Wood consists of about 50% carbon, 40% oxygen and 6% hydrogen, and traces of other elements. All three of these atoms have unpaired valence electrons. The catch is that they tend to be snugly bound up in covalent bonds. The unpaired electrons in wood tend to form stable pairs across atoms, so they now act as paired electrons. The molecular structures of various wood tissues also don't allow much electron motility. There aren't any unpaired motile electrons available for magnetism in this material, even though it consists of atoms that have unpaired electrons. Therefore, there are no electrons motile enough to line up with an external magnetic field and wood, as a result, exhibits no magnetism. Magnets, in contrast, have unpaired electrons that are freely available to line up their spins with each other and we can measure a net magnetic force very easily.

Magnetism is really all about the arrangements atoms find themselves in. These atomic arrangements determine how easily the spins of unpaired valence electrons can line up with each other. Atoms bond with each other into molecules to make matter. A number of atoms have measurable magnetic moments. But that does not mean that materials composed of these atoms display magnetism. The oxygen atoms in wood, for example, each have two unpaired electrons but they do not contribute to a magnetic moment in wood because the oxygen is chemically bound into various complex molecules, like cellulose. This is the case with almost all of the various kinds of molecules that make up our planet. Only very rarely do materials happen to have atomic arrangements that display magnetism. That is why we have so few natural magnets on Earth and it is why almost all magnetite is not lodestone.

Magnetism in Molecules Under Extreme Conditions

As the case with wood illustrates, atoms within most molecules do not contribute magnetism to materials. However, some molecules do display magnetic properties. Oxygen molecules (O2) display strong magnetism in response to an external magnetic field because they have unpaired spins that remain once two atoms bond with each other. Here, a trickle of transparent liquid molecular oxygen is deflected and attracted toward a magnet:

At very cold temperatures, molecular oxygen forms a highly magnetic solid. Solid oxygen is the only elementary molecular magnet known. Oxygen, nitrogen and hydrogen also become metallic at very low temperatures or under very high pressures. Hydrogen atoms, each with one unbound electron, metalize into a solid crystal lattice in which the unbound electrons act like conduction electrons in a metal. This structure also gives solid hydrogen, like solid oxygen, magnetic properties, and perhaps solid hydrogen, like solid oxygen is a magnet as well. Jupiter, Saturn, Uranus and Neptune all have mysteriously powerful magnetic fields. Most physicists link this magnetism to the flow of electric currents inside the planets, within metallic hydrogen in its liquid phase. This flow of current is in effect a dynamo, much like the one inside Earth but composed of different elements. It is this dynamo that generates the planet's magnetic field. Only Jupiter and Saturn are large enough to compress hydrogen into a metallic solid, however.  It is the solid phase of these elements that displays strong magnetism so it remains unknown whether hydrogen in this solid state also contributes to the magnetic fields of these two planets, which are exceptionally powerful. It is technically extremely challenging to make solid oxygen (freezing point is -219°C) and even more challenging to make solid hydrogen (freezing point is -259°C) but research is underway, testing the physical properties of these fascinating materials.

Magnetars Are The Most Powerful Magnets in The Universe

Magnetars are special neutron stars with magnetic fields hundreds of millions times stronger than any man-made magnet. Magnetic field strength is measured in units called Gauss. Magnetars have magnetic fields of around 1015 Gauss. To illustrate how strong that is, if we tried to make a magnet stronger than 4.5 x 105 Gauss, the physical stress of such a field would blow the magnet apart. Magnetars are held together only by unbelievably powerful gravitational forces. No one is entirely sure what mechanism is responsible for the magnetic field of a magnetar but physicists, using the latest in computer modelling, have an idea. They know that when a magnetar forms (after a very massive star blows up in a supernova), it consists of a boiling dense fluid, mostly made up of free neutrons. Free electrons affect this fluid's buoyancy and drive powerful convective currents. Free electrons and free protons set up powerful electric currents in the fluid. Young magnetars spin extremely fast and this spinning motion combined with convective motion drags magnetic field lines through the star. This process builds up the star's magnetic field, thus creating a dynamo effect, similar to the dynamos inside Earth and other planets. This dynamo acts to magnify the magnetic field. If you want to know more about magnetars, please see my article, "Stellar Objects Part 4: Magnetars."

New research suggests that the strongest theoretical magnetic field that could exist is between 1049 and 1053 Gauss. Any field stronger than this would break down the vacuum of space and spontaneously decay.

To sum up then, making a magnet is a bit like making a cake. Not only do you need the right ingredients (atoms with unpaired electrons), you also need to combine them in the right way to create a structure (atomic arrangement) that will display macroscopic magnetism. In the next article, "Ferromagnetism," we will explore the most common mechanism through which materials display magnetism, and what makes magnets magnets.