Diamagnetism

In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field.

In most materials, diamagnetism is a weak effect which can be detected only by sensitive laboratory instruments, but a superconductor acts as a strong diamagnet because it entirely expels any magnetic field from its interior (the Meissner effect).

Diamagnetism was first discovered when Anton Brugmans observed in 1778 that bismuth was repelled by magnetic fields.

[1] In 1845, Michael Faraday demonstrated that it was a property of matter and concluded that every material responded (in either a diamagnetic or paramagnetic way) to an applied magnetic field.

Diamagnetic materials are those that some people generally think of as 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, like water, or water-based materials, have a relative magnetic permeability that is less than or equal to 1, and therefore a magnetic susceptibility less than or equal to 0, since susceptibility is defined as χv = μv − 1.

However, since diamagnetism is such a weak property, its effects are not observable in everyday life.

Nevertheless, these values are orders of magnitude smaller than the magnetism exhibited by paramagnets and ferromagnets.

This is the case for gold, which has a magnetic susceptibility less than 0 (and is thus by definition a diamagnetic material), but when measured carefully with X-ray magnetic circular dichroism, has an extremely weak paramagnetic contribution that is overcome by a stronger diamagnetic contribution.

Superconductors may be considered perfect diamagnets (χv = −1), because they expel all magnetic fields (except in a thin surface layer) due to the Meissner effect.

[8][9] 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.

A thin slice of pyrolytic graphite, which is an unusually strongly 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 and relatively convenient demonstration of diamagnetism.

The Radboud University Nijmegen, the Netherlands, has conducted experiments where water and other substances were successfully levitated.

[11] In September 2009, NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California announced it had successfully levitated mice using a superconducting magnet,[12] an important step forward since mice are closer biologically to humans than frogs.

[13] JPL said it hopes to perform experiments regarding the effects of microgravity on bone and muscle mass.

[15] The electrons in a material generally settle in orbitals, with effectively zero resistance and act like current loops.

Thus it might be imagined that diamagnetism effects in general would be common, since any applied magnetic field would generate currents in these loops that would oppose the change, in a similar way to superconductors, which are essentially perfect diamagnets.

However, since the electrons are rigidly held in orbitals by the charge of the protons and are further constrained by the Pauli exclusion principle, many materials exhibit diamagnetism, but typically respond very little to the applied field.

The Bohr–Van Leeuwen theorem proves that there cannot be any diamagnetism or paramagnetism in a purely classical system.

Paul Langevin's theory of diamagnetism (1905)[17] applies to materials containing atoms with closed shells (see dielectrics).

A field with intensity B, applied to an electron with charge e and mass m, gives rise to Larmor precession with frequency ω = eB / 2m.

The Langevin theory is not the full picture for metals because there are also non-localized electrons.

The theory that describes diamagnetism in a free electron gas is called Landau diamagnetism, named after Lev Landau,[19] and instead considers the weak counteracting field that forms when the electrons' trajectories are curved due to the Lorentz force.

Landau diamagnetism, however, should be contrasted with Pauli paramagnetism, an effect associated with the polarization of delocalized electrons' spins.

[20][21] For the bulk case of a 3D system and low magnetic fields, the (volume) diamagnetic susceptibility can be calculated using Landau quantization, which in SI units is where

This formula takes into account the spin degeneracy of the carriers (spin-1/2 electrons).

In doped semiconductors the ratio between Landau and Pauli susceptibilities may change due to the effective mass of the charge carriers differing from the electron mass in vacuum, increasing the diamagnetic contribution.

[22][23] Additionally, for strong magnetic fields, the susceptibility of delocalized electrons oscillates as a function of the field strength, a phenomenon known as the De Haas–Van Alphen effect, also first described theoretically by Landau.