Magnetism

Langevin’s theory of Diamagnetism (Qualitative treatment)

Diamagnetic materials are those which acquire feeble magnetism opposite to the applied magnetic field. i.e., they exhibit negative susceptibility. The order of susceptibility is around 10^-6. Copper, Bismuth, Lead, Zinc, Inert gases etc. are examples.

Here all the electrons rotating in clockwise direction will have magnetic moment in one direction and the remaining electrons which rotate in the anticlockwise direction will have magnetic moment in opposite direction. Thus net magnetic moment in any direction must be zero.

When magnetic field is applied, the electrons rotating in clockwise direction will experience a Lorentz force directed radially outwards. Now to maintain equilibrium, electrons reduce its velocity which results in the reduction of magnetic moment in the direction of applied magnetic field.

Meanwhile the electrons which revolve in the anticlockwise direction will experience a force directing radially inwards. Now to maintain equilibrium, electrons increase its velocity which results in an increase of magnetic moment in a direction opposite to the magnetic field.

Thus, when a magnetic field is applied to a diamagnetic material, a net magnetic moment develops in a direction opposite to the applied field. Based on this, Langevin derived an expression for the magnetic susceptibility of diamagnetic material and is given by,

where N = The number of atoms per unit volume, Z = Number of electrons in the atom (Atomic number), r_i = Radius of electron orbit, e = The charge on an electron, m = The mass of an electron and m₀ = The permeability of free space.

Langevin’s theory of Paramagnetism (Qualitative treatment)

Paramagnetic substances acquire feeble magnetism in the direction of applied magnetic field. i.e., they exhibit positive magnetic susceptibility. The order of susceptibility is around 10^-6. Chromium, Platinum, Aluminium etc. are examples.

In paramagnetic materials, atoms/molecules/ions possess permanent magnetic dipole moments which are oriented randomly in the absence of an external magnetic field. As a result net magnetic moment in any direction will be zero. When an external magnetic field is applied, the dipoles tend to align themselves in the direction of the field.

Langevin proposed a theory for paramagnetism and developed an expression for magnetic susceptibility which is given by,

where N = The number of atoms per unit volume, m_B = The Bohr magneton, k = The Boltzman constant, T = The absolute temperature and m₀ = The permeability of free space.

The above expression can also be written as,

This is called Weiss law.

Weiss theory of Ferromagnetism (Qualitative treatment)

When ferromagnetic materials are placed in a magnetic field, it become strongly magnetized in the direction of the field. Order of magnetic susceptibility is 10⁶. They continue to retain magnetic property even after the magnetizing field is removed. Iron, Cobalt, Nickel etc. are examples.

In 1907, Weiss proposed a theory to explain the ferromagnetism. The important features of this theory are

1. In ferromagnetic materials, an additional magnetic field known as internal molecular field exist which leads to spontaneous magnetization. Later Heisenberg explained the origin of internal molecular field is due to quantum exchange interaction between the electrons.

2. The spontaneous magnetization exists in the material only below the Curie temperature T_C. Magnetic susceptibility of a ferromagnetic material is given by,

The above equation is called Curie-Weiss law where C is Curie constant.

3. The net magnetic moment of a ferromagnetic material in the absence of a magnetic field is zero. To explain this Weiss proposed ferromagnetic domain concept.

The entire ferromagnetic volume splits into a large number of small regions of spontaneous magnetization. These regions are called domains. In the absence of magnetic field, the relative orientation of the magnetic moments of various domains will be completely random, and thus the resultant magnetic moment of the material as a whole turns out to be zero.

Antiferromagnetism and ferrimagnetism

When the magnetic moments of sublattices in a crystal unit cell are equal in magnitude but opposite in direction, they cancel each other giving rise to antiferromagnetism. Their susceptibility is of the order of 10^-3 to 10^-5. MnO is an example for antiferromagnetic material. If the temperature of the antiferromagnetic material is raised above Neel temperature, material becomes paramagnetic.

When the magnetic moments of sublattices in a crystal unit cell are not exactly equal in magnitude and oriented in opposite in direction, the crystal possess a net resultant magnetic moment. This type of materials is called ferromagnetic materials whose saturation magnetization value is not as high as for ferromagnetic materials. Ferrites are examples for ferrimagnetic material.

Ferrites

Ferrites are mixed metal oxides with the general formula MFe₂O₄ or MO Fe₂O₃. By varying composition, we can appreciably vary the magnetic and other properties of ferrite materials. Metal ions can occupy tetrahedral A sites (surrounded by 4 oxygen ions) or octahedral B sites (surrounded by 6 oxygen ions). In ZnFe₂O₄ and CdFe₂O₄ F³⁺ ions occupy octahedral sites and Zn²⁺/Cd²⁺ ions occupy tetrahedral sites. They are called normal spinel ferrites. In NiFe₂O₄, CoFe₂O₄ and CuFe₂O₄, Fe³⁺ ions occupy both octahedral and tetrahedral sites while Ni²⁺, Co²⁺ and Cu²⁺ ions occupy octahedral sites. Hence they are called inverse spinel ferrites.

B-H graph in ferromagnetic materials

When a ferromagnetic material is taken through a cycle of magnetization, a curve as shown below is obtained.. This curve is known as hysteresis curve (B-H curve).

When a magnetic field H is applied to a ferromagnetic material, the magnetic flux density B (or magnetisation M) will vary. As the magnetic field is increased, the flux density (or magnetisation) increases and reaches a saturation value B_s (or M_s). When the field intensity is reduced to zero, the flux density will not become zero, but will have a finite value which is called remanent flux density B_r ( or remanent magnetisation M_r). This remanent flux density may be reduced to zero by applying a magnetic field in the opposite direction. The field H_c required to reduce the flux density to zero is called the coercive field.

Soft and hard magnetic materials

Magnetic materials which are easily magnetized and demagnetized are known as soft magnetic materials. They are characterized by thin hysteresis loop (loop area small) with low coercive field, low hysteresis loss and high initial permeability. All these properties are by virtue of the domain wall motion that occurs easily in soft magnetic materials. Permalloy, Silicon-Iron alloy and ferrites are examples.

Hard magnetic materials are those which have a high resistance to demagnetization. They are characterized by large hysteresis loop (loop are large) with high coercive field, high hysteresis loss and low initial permeability. In these materials, domain walls are highly immobile. Alnico alloy, Invar, Platinum-Cobalt alloy etc. are examples.

Applications of magnetic materials

High resistivity soft magnetic materials are used in the transformer cores since in ac conditions hysteresis loss factor and eddy current loss are important and for high resistivity soft magnetic materials these factors are low. Ferrites are used for high frequency applications. Hard magnetic materials are used in fabrication of permanent magnets. Magnetic materials are also used in memory devices, loud speakers, generators, switching devices, tape-recorders, telephones, electrical instruments, TV tubes etc.