Diamagnetism

Diamagnetism

Diamagnetism is based on the interaction between electrons and the magnetic field. Since all materials contain electrons, all materials are diamagnetic. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism the material is called a diamagnet. Diamagnets were first discovered when Sebald Justinus Brugmans observed in 1778 that bismuth and antimony were repelled by magnetic fields. 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. He adopted the term diamagnetism after it was suggested to him by William Whewell.


One of the forms of magnetism. A diamagnet gets pushed out of an inhomogeneous magnetic field. You can test it with the carbon rods inside a mechanical pencil. Carbon is an easy to come by diamagnet. You take one of the little rods from a mechanical pencil and hang it at the end of a thin piece of string. If you move a strong magnet towards one of the ends of the rod, it will start to turn away from the magnet.

Law

According to Lenz's law, any current induced by a magnetic field gives rise to a magnetic field opposing the original inducing field. This follows from the application of the right-hand rule both on induction of a current by a field and vice versa. For this reason, diamagnetic susceptibility is always negative, i.e. the density of B-field lines is reduced by diamagnetism.

In a semi-classical view of an atom (left figure), an electron can be regarded as orbiting the nucleus at a fixed distance. If placed in a magnetic field, a precession of the vector linking the electron with the nucleus around the field axis is observed. The frequency ω of that precession is given by the Larmor theorem:

ω=eB2me

where e and me are the electron's charge and mass, respectively. Given that a current is the number of charges flowing through a point per unit time, the current IFlowing in an atom due to the Larmor precession is

I=−Zeω2π=−Ze2B4πme

where the factor −Z adds up all the electrons in the atom and acknowledges the fact that electrons have negative charge.

Given a current, we we can determine the magnetic moment induced by it. For this purpose, it helps comparing the Larmor current in the atom with a current flowing around a single wire loop (right figure). The magnetic moment pm induced by a current I is proportional to the current and the area enclosed by it, pm=AI (and pointing in the direction normal to that area). For a circular loop, A=πr2, and

pm=πr2I=−Ze2B4me⟨r2⟩

where ⟨r2⟩ stands for the median distance of all the electrons from the field axis in the case of the atom.This fairly crude classical interpretation gives us a good estimate of the induced magnetic moment in an atom due to the interaction of the material's electrons with the magnetic field. Given the chemical composition and density (and hence electron density) of a material, we can calculate its diamagnetic susceptibility. This simple model produces adequate results except in the case of conduction electrons in metals. Since they are delocalised over many atoms within the lattice, the idea of a Larmor current doesn't do them justice.

In metals, The Langevin theory does not apply to metals because they have non-localized electrons. The theory for the diamagnetism of a free electron gas is called Landau diamagnetism, and instead considers the weak counter-acting field that forms when their 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.

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