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Magnetism is a phenomenon by which materials assert an attractive or repulsive force on other materials. Some well known materials that exhibit magnetic properties are iron, some steels, and the naturally occurring mineral lodestone. In reality all materials are influenced to one degree or another by the presence of a magnetic field, although in some cases the influence is too small to detect without special equipment.

Magnetic forces are fundamental forces that arise due to the movement of electrically charged particles. The origin and behavior of these forces are described by Maxwell's equations.

For the case of electric current moving through a wire, the resulting force is directed according to the "right hand rule". If the thumb of the right hand points along the wire from positive towards the negative side, the magnetic forces will wrap around the wire in the direction indicated by the fingers of the right hand. If a loop is formed, such that the charged particles are traveling in a circle then all of the forces in the center of the loop are directed in the same direction. The result is called a magnetic dipole. When placed in a magnetic field, a magnetic dipole will tend to align itself with that field. For the case of a loop, if the fingers of the right hand are directed in the direction of current flow, the thumb will point in the direction corresponding to the North pole of the dipole. In the earth's magnetic field the North pole of the dipole will tend to point north.

Magnetic dipoles or magnetic moments can often result on the atomic scale due to the movements of electrons. Each electron has magnetic moments that originate from two sources. The first is the orbital motion of the electron around the nucleus. In a sense this motion can be considered as a current loop, resulting in a magnetic moment along its axis of rotation. The second source of electronic magnetic moment is due to a quantum mechanical property called spin.

In an atom the orbital magnetic moments of some electron pairs cancel each other. The same is true for the spin magnetic moments. The overall magnetic moment of the atom is thus the sum of all of the magnetic moments of the individual electrons, accounting for moment cancellation between properly paired electrons. For the case of a completely filled electron shell or subshell, the magnetic moments completely cancel each other out. Thus only atoms with partially filled electron shells have a magnetic moment. The magnetic properties of materials are in large part determined by the nature and magnitude of the atomic magnetic moments.

Several forms of magnetic behavior have been observed including:

• Diamagnetism
• Paramagnetism
• Ferromagnetism
• Antiferromagnetism
• Ferrimagnetism
• Superparamagnetism

## Diamagnetism

Diamagnetism is a very weak form of magnetism that is only exhibited in the presence of an external magnetic field. It is the result of changes in the orbital motion of electrons due to the external magnetic field. The induced magnetic moment is very small and in a direction opposite to that of the applied field. When placed between the poles of a strong electromagnet, diamagnetic materials are attracted towards regions where the magnetic field is weak. Diamagnetism is found in all materials, however because it is so weak it can only be observed in materials that do not exhibit other forms of magnetism.

An exception to the "weak" nature of diamagnetism occurs with the rather large number of materials that become superconducting, something that usually happens at lowered temperatures. Superconductors are perfect diamagnets and when placed in an external magnetic field expel the field lines from their interiors (depending on field intensity and temperature). Superconductors also have zero electrical resistance, a consequence of their diamagnetism. Superconducting structures have been known to tear themselves apart with astonishing force in their attempt to escape an external field. Superconducting magnets are the major component of most MRI systems, perhaps the only important application of diamagnetism.

A thin slice of pyrolitic graphite, which is an unusually strongly diamagnetic material, can be stably floated on a magnetic field, such as that from rare earth permanent magnets. This can be done with all components at room temperature, making a visually effective demonstration of diamagnetism.

## Paramagnetism

Paramagnetism refers to the tendency of the atomic magnetic dipoles in a material that is otherwise non-magnetic to align with an external magnetic field. The alignment of the atomic dipoles with the magnetic field tends to strengthen it, resulting in a relative magnetic permeability greater than one and a small positive magnetic susceptibility.

In paramagnetism the field acts on each atomic dipole independently and there are no interactions between individual atomic dipoles. Paramagnetic behavior can also be observed in magnetic materials that are above their Curie or Neel temperature.

## Ferromagnetism

Ferromagnetism is one of the strongest forms of magnetism. It is responsible for most of the magnetic behavior encountered in everyday life. Most permanent magnets are ferromagnetic, as are the metals that are attracted to them. Some examples of ferromagnetic materials include iron, cobalt, nickel, and gadolinium.

The strong magnetic forces in ferromagnetic materials arise due to a combination of the properties of the individual atoms and the properties of the crystal structure of the solid material. At the atomic level, magnetic forces arise due to the movements of electrons. Each electron has magnetic moments that originate from two sources. The first is the orbital motion of the electron around the nucleus. In a sense this motion can be considered as a current loop, which like a tiny electromagnet results in a magnetic moment along its axis of rotation. The second source of the electronic magnetic moment is due to a Quantum Mechanical property called "spin", this property is in some ways analogous to the picture of an electron spinning about an axis and is related to the electron's angular momentum. However, it should be remembered that the Quantum Mechanical "spin" is actually a unique phenomenon from spinning in a macroscopic sense, so the analogy doesn't always hold. The spin magnetic moments may be in one of two directions, either the "up" direction or the "down" direction.

In an atom the orbital magnetic moments of electron pairs point in opposite directions canceling each other. The same is true for the spin magnetic moments. The overall magnetic moment of the atom is thus the sum of all of the magnetic moments of the individual electrons, accounting for moment cancellation between properly paired electrons. For the case of a completely filled electron shell or subshell, the magnetic moments completely cancel each other out. Thus only atoms with partially filled electron shells have a magnetic moment. All ferromagnetic materials have partially filled electron shells and thus posses an atomic magnetic moment.

Although atomic magnetic moments are present in both Paramagnetic and Ferromagnetic materials, magnetic forces are much stronger in ferromagnetic materials. This is not due to differences in the atomic magnetic moments, but due to the crystal structure of ferromagnetic materials. In a ferromagnet coupling interactions cause the magnetic moments of adjacent atoms to align with one another. This contrasts sharply with paramagnets, in which the magnetic moments are randomly distributed in many directions, essentially canceling each other out, except in the presence of a strong magnetic field. The alignment of the atomic magnetic moments in ferromagnetic materials results in a strong permanent internal magnetic field within the material. It is this strong internal magnetic field that causes iron or other ferromagnetic materials to be attracted by a magnet.

While coupling forces tend to cause adjacent moments to align, usually not all of the moments point in the same direction throughout the material. Instead the material consists of a number of regions called domains. Within each domain the atomic magnetic moments are aligned, however, the various domains may or may not be aligned with each other. For example, the domains in a metal paperclip are not usually aligned with each other. As a result the magnetic forces from the various domains cancel each other and two paper clips are not magnetically attracted to each other. However, if the material is placed within a magnetic field (for example if a permanent magnet is brought near a paperclip), the magnetic forces will cause some of the domains to align. This alignment will then result in a magnetic force drawing the material to the magnet and causing the material to behave as if it too were a magnet.

If the magnetic field is removed, the domains will often shift back to their original alignment and the material will no longer act as a magnet. However, if the material is subjected to a strong magnetic field for a sufficient length of time the domains will permanently align and the material will become a permanent magnet.

## Superparamagnetism

Superparamagnetism is a phenomena by which magnetic materials may exhibit a behavior similar to paramagnetism at temperatures below the Curie or the Neel temperature.

Normally, coupling forces in magnetic materials cause the magnetic moments of neighboring atoms to align, resulting in very large internal magnetic fields. At temperatures above the Curie temperature (or the Neel temperature for antiferromagnetic materials), the thermal energy is sufficient to overcome the coupling forces, causing the atomic magnetic moments to fluctuate randomly. Because there is no longer any magnetic order, the internal magnetic field no longer exists and the material exhibits paramagnetic behavior.

Superparamagnetism occurs when the material is composed of very small crystallites (1-10 nm). In this case even though the temperature is below the Curie or Neel temperature and the thermal energy is not sufficient to overcome the coupling forces between neighboring atoms, the thermal energy is sufficient to change the direction of magnetization of the entire crystallite. The resulting fluctuations in the direction of magnetization cause the magnetic field to average to zero. The material behaves in a manner similar to paramagnetism, except that instead of each individual atom being independently influenced by an external magnetic field, the magnetic moment of the entire crystallite tends to align with the magnetic field.

The energy required to change the direction of magnetization of a crystallite is called the Crystalline anisotropy energy and depends both on the material properties and the crystallite size. As the crystallite size decreases, so does the Crystalline anisotropy energy, resulting in a decrease in the temperature at which the material becomes superparamagnetic.