6.4 Diamagnetism

Diamagnetic materials are those in which the electron motions are such that they produce net zero magnetic moment in the absence of any magnetic field. Typically these are atoms with closed or filled outer electron shells.

Examples of such materials are inert gases, hydrogen, many metals (e.g. Ag, Au, Cu etc.), most non-metals (e.g. Si)  and many organic compounds such as polymers.

Imagine a circular orbit of radius, r, around an atom with its center coinciding that of the atom. Now, we turn on the magnetic field in its vicinity.

Hence, according to Faraday’s law, as the magnetic field changes, it generates an electric field by magnetic induction. The electric field, E, tangent to the circular path is given as

OR

(6.14)

This electric field produces a torque equivalent to -eE.r (i.e. F.r) which must be equal to the rate of change of angular momentum, J, i.e.

(6.15)

Two minuses cancel each other. Now integrating with respect to time with zero field, we get

(6.16)

This expression represents the extra angular momentum provided to the electrons when the field is applied.

Now, since the motion of electron is taking place in the orbits, the change in magnetic moment (Δμ_m) which is orbital in nature is given as       

(6.17)

Replacing B = μ₀H, we get

(6.18)

For atoms with spherical symmetry, , hence,

(6.19)

So, here we have a magnetic moment which is negative in sign to the magnetic field strength because it opposes the applied field. This magnetic moment is the moment for one electron.

So, if there are N electrons per unit volume, then magnetization, M, is given as

(6.20)

Hence magnetic susceptibility χ_m is given as

(6.21)

This equation shows the opposite nature of the magnetic susceptibility of the diamagnetic behaviour.
Remember that diamagnetism is something which is present in all materials except that many materials also have other effects which completely overshadow the diamagnetic effect.