Diamagnetism : Langevin Theory, Properties, and Types

Diamagnetism is the phenomenon of a material that can create a magnetic field in response to an external magnetic field. It is also called Magnetism. 

A diamagnetic material is a material that is repelled by a magnetic field. The most common example of diamagnetism is when a piece of paper or other thin material is held over a bar magnet and observed. The paper will be attracted towards the magnet, but will not be pulled down because it is not strong enough to overcome gravity.

• A diamagnet is an object made from materials that can be magnetized, but do not in themselves produce a magnetic field.
• There are no atomic dipoles in the material as the magnetic moment is zero in each atom .
• They can be repelled by magnets. 
• These materials have a strength to move from strong to weak parts in a magnetic field.
• Materials like Copper, Bismuth, Zinc, Silver, Gold, and Antimony are Diamagnetic in nature.

Read also: Force of Attraction 

Key terms: Diamagnetism, Magnetic Materials, Magnetic field, Magnets , Diamagnetic Materials, Ferromagnetic

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Types of Magnetic Materials 

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A material's magnetic properties are its response to an external magnetic field. According to the magnetic properties of solids, they can be divided into five types.

• Diamagnetism: A substance with no net magnetic moment. Not attracted to magnets.
• Paramagnetism: A substance that has a net magnetic moment, but is too small to detect with the naked eye.
• Ferromagnetism: Attracts substances with a large net magnetic moment to a magnet.
• Ferrimagnetism: The magnetic fields associated with individual atoms are spontaneously aligned, some aligned in parallel or in the same direction.
• Antiferromagnetism: Neighboring ions acting like tiny magnets spontaneously align in an opposite or antiparallel arrangement.

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What is Diamagnetism?

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Diamagnetism is a type of magnetism displayed by certain materials, including copper, silver, gold, and other non-magnetic materials, that causes them to be weakly repelled by a magnetic field. Diamagnetism simply occurs in materials that have no magnetic moment of their own.

• The diamagnetic effect is the result of the fact that all electron in an atom act like tiny magnets and these magnetic moments are directed in the opposite direction to the direction of the external magnetic field.
• This effect was first discovered by Michael Faraday in 1845. He found that when bismuth, silver, and copper were brought close to a magnet, the magnet repelled them.
• Faraday concluded that "the cause of this repulsive force must lie in the atoms or in the space between atoms".

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Langevin Theory of Diamagnetism

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Diamagnetism, the orbit motion of the atom negatively charged electrons creates tiny current-carrying rings creating a magnetic field. In the absence of an external magnetic field, the total magnetic moment is zero because the vector sum of all magnetic moments in the direction of electron orbits inside an atom is zero.

The current loop formed by an electron e with charge -qe per unit time is:

Z Current in atoms with electrons,

I= -q^e/t

The current of the atom with Z electrons in it,

 I= - Z^e/t …………………………………………………….(1)

When a magnetic field of intensity B acts on an electron of charge and mass m, it produces an angular frequency ω known as the Larmor frequency, with revolutions per unit time equal to ω/2π. .

Then the current produced per atom is:

 I= -Ze²B/4Πm …………………………………………….(2)

The magnetic moment produced by this energized loop is the product of the energized loop I times the area of the loop.

If "a" is the average radius of the loop:

μ=I × Π(a²) ………………………………………..(3)

Now , we get

μ= Ze²B/4Πm × Π(a²)

Simplifying the equation gives the result: I suspect diamagnetism, then:

μ= -Ze²B/4m (a²) ………………………………(4)

 If the magnetic field is in z direction and orbit plane is in x-y direction:

(a²) = (x²) + (y²)

The mean square distance (r²) of electron from the nucleus:

(r²) = (x²) + (y²) + (z²) ……………………………………………… (5)

(x²) = (y²) = (z²)

From this equation:

(r²) = 3/2 (a²)

Replace the value of a² in eq.4 :

μ=-Ze²B/4m × ⅔(r²)

Getting the equation:

μ=-Ze²B/6m × (r²) ………………………………………………….(6)

Then, M=N*μ ………………………………………………………(7)

From equation 6 and 7

M= -NZe²B/6m × (r²) …………………………………………………(8)

Since, B=μ0 H and 

is diamagnetic suspect then:

X_dia = -NZe²μ₀/6m × (r²) ……………………………………………….(9)

Now if N is a number. Number of atoms per volume:

From the equation, the diamagnetic susceptibility of any material does not depend on the external magnetic field and external temperature. It is proportional to the number of atoms per unit volume. The higher the number of atoms in the volume, the higher the diamagnetic energy of the material.

Read also: Faraday Constant

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What is a Diamagnetic Material?

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Diamagnetic materials are those that exhibit a weak, negative susceptibility to magnetic fields. When subjected to an external magnetic field, diamagnetic materials produce a magnetic field in the opposite direction, which weakens the applied field.

• A diamagnetic material creates a magnetic field in the opposite direction to the applied external magnetic field. 
• A diamagnet is attracted by a magnet and repelled by an applied electric field.
• Examples of diamagnetic materials include bismuth, magnesium, nickel, platinum and silver.
• Diamagnetism induces no net magnetization in the direction of an applied magnetic field. Diamagnetism, or negative magnetism, is a physical property that is repelled by a magnetic field due to relative motion between a particle and an external source.
• The term diamagnetism was introduced in 1882 by William Henry Bragg and William Lawrence Bragg.

Diamagnetic Material

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Properties of Diamagnetic Materials

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Now that we understand what diamagnets are, the next step is to understand their properties.

• Diamagnets have no atomic dipoles. This is because the net magnetic moment of each atom is zero due to the pair of electrons.
• A diamagnet is repelled by a magnet.
• These materials are weakly repelled by magnetic fields, so in a non-uniform magnetic field, they tend to move from strong to weak areas of the external magnetic field. 
• The relative permeability is slightly less than 1.

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Things to Remember

• Diamagnetic materials are repelled by magnetic fields and are not attracted to a magnet.
• A diamagnet is an object made from materials that can be magnetized, but do not themselves produce a magnetic field.
• Diamagnetism is the phenomenon by which certain materials are repelled by a magnetic field, and can be thought of as magnetism from the opposite direction. 
• The materials are attracted to magnetic fields, but if the magnetic field is strong enough, they will be pushed away.
• Diamagnetism is universal. It is present in all materials. But it is weak and hard to detect if the substance is para- or ferromagnetic.

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