Diamagnetism

Levitating pyrolytic carbon

Diamagnetism is the property of an object which causes it to create a magnetic field in opposition of an externally applied magnetic field, thus causing a repulsive effect. Specifically, an external magnetic field alters the orbital velocity of electrons around their nuclei, thus changing the magnetic dipole moment in the direction opposing the external field. Diamagnets are materials with a magnetic permeability less than $\mu _{0}$ (a relative permeability less than 1).

Consequently, diamagnetism is a form of magnetism that is only exhibited by a substance in the presence of an externally applied magnetic field. It is generally a quite weak effect in most materials, although superconductors exhibit a strong effect.

Diamagnetic materials cause lines of magnetic flux to curve away from the material, and superconductors can exclude them completely (except for a very thin layer at the surface).

Diamagnetic properties of materials

Notable diamagnetic materials

Material	χm=Km-1 x 10-5
Bismuth	-16.6
Carbon (diamond)	-2.1
Carbon (graphite)	-1.6
Copper	-1.0
Lead	-1.8
Mercury	-2.9
Silver	-2.6
Water	-0.91
Superconductor	-105

All materials show a diamagnetic response in an applied magnetic field. In fact, diamagnetism is a very general phenomenon, because all paired electrons, including the core electrons of an atom, will always make a weak diamagnetic contribution to the material's response. However, for materials that show some other form of magnetism (such as ferromagnetism or paramagnetism), the diamagnetism is completely overpowered. Substances that mostly display diamagnetic behaviour are termed diamagnetic materials, or diamagnets. Materials that are said to be diamagnetic are those that are usually considered by non-physicists to be "non-magnetic", and include water, wood, most organic compounds such as petroleum and some plastics, and many metals including copper, particularly the heavy ones with many core electrons, such as mercury, gold and bismuth.

Diamagnetic materials have a relative magnetic permeability that is less than 1, thus a magnetic susceptibility which is less than 0, and are therefore repelled by magnetic fields. However, since diamagnetism is such a weak property its effects are not observable in every-day life. For example, the magnetic susceptibility of diamagnets such as water is $\ \chi _{v}$ = −9.05×10⁻⁶. The most strongly diamagnetic material is bismuth, $\ \chi _{v}$ = −1.66×10⁻⁴ , although pyrolytic graphite may have a susceptibility of $\ \chi _{v}$ = −4.00×10⁻⁴ in one plane. Nevertheless these values are orders of magnitudes smaller than the magnetism exhibited by paramagnets and ferromagnets.

A superconductor acts as an essentially perfect diamagnetic material when placed in a magnetic field and it excludes the field, and the flux lines avoid the region

Superconductors may be considered to be perfect diamagnets ($\ \chi _{v}$ = −1), since they expel all fields from their interior due to the Meissner effect. However this effect is not due to eddy currents, as in ordinary diamagnetic materials, see the article on superconductivity.

Additionally, all conductors exhibit an effective diamagnetism when they experience a changing magnetic field. The Lorentz force on electrons causes them to circulate around forming eddy currents. The eddy currents then produce an induced magnetic field which opposes the applied field, resisting the conductor's motion.

History

In 1778 S. J. Bergman was the first person to observe that bismuth and antimony were repelled by magnetic fields. However, the term "diamagnetism" was coined by Michael Faraday in September 1845, when he realized that all materials in nature possessed some form of diamagnetic response to an applied magnetic field.

Demonstrations of diamagnetism

Curving water surfaces

If a thin (under 0.5 cm) layer of water is placed on top of a powerful magnet (such as a supermagnet) then the field of the magnet repels the water. This causes a slight dimple in the water's surface that may be seen by its reflection.

Diamagnetic levitation

A live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a magnetic field of about 16 teslas at the Nijmegen High Field Magnet Laboratory. Movie

Diamagnets may be levitated in stable equilibrium in a magnetic field, with no power consumption. Earnshaw's theorem seems to preclude the possibility of static magnetic levitation. However, Earnshaw's theorem only applies to objects with permanent moments m, such as ferromagnets, whose magnetic energy is given by m·B. Ferromagnets are attracted to field maxima, which do not exist in free space. Diamagnetism is an induced form of magnetism, thus the magnetic moment is proportional to the applied field B. This means that the magnetic energy of diamagnets is proportional to B², the intensity of the magnetic field. Diamagnets are also attracted to field minima, and there can be a minimum in B² in free space (in fact $\nabla ^{2}\mathbf {B} ^{2}\geq 0$). The important distinction is that the sign of the induced magnetization in a diamagnet opposes the applied field, hence the attraction to minima in the field strength. Other materials with magnetization proportional to the applied field, but with the opposite sign, called "paramagnets", also obey Earnshaw's theorem and cannot be levitated by any fixed combination of magnetic, electrical, and gravitational fields.

A thin slice of pyrolytic graphite, which is an unusually strong diamagnetic material, can be stably floated in 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.

The Radboud University Nijmegen, the Netherlands, has conducted experiments where water and other substances were successfully levitated. Most spectacularly, a live frog (see figure) was levitated.

In September 2009, NASA's Jet Propulsion Laboratory in Pasadena, California announced they had successfully levitated mice using a superconducting magnet, an important step forward since mice are closer biologically to humans than are frogs. They hope to perform experiments regarding the effects of microgravity on bone and muscle mass.

Recent experiments with studying the growth of protein crystals has led to a technique that utilizes powerful magnets to allow growth in ways that counteract Earth's gravity.

A simple homemade device for demonstration can be constructed out of bismuth plates and a few permanent magnets that will levitate a permanent magnet.

See also

• Magnetic field
• Magnetic moment

External links

• Video of a museum-style magnetic elevation train model which makes use of diamagnetism
• Videos of frogs and other diamagnets levitated in a strong magnetic field
• Video of levitating pyrolytic graphite
• Video of Meissner-Ochsenfeld effect involving liquid nitrogen
• Video of a piece of neodymium magnet levitating between blocks of bismuth.
  • Website about this device, with images (in Finnish).