Domain Theory of Ferromagnetism

DOMAIN THEORY OF FERROMAGNETISM

The domain in ferromagnetic solid is understandable from the thermodynamical principle, (i.e.,) in equilibrium the total energy of the system is minimum. For this, first we consider the total energy of the domain structure and then how it is minimised. The total energy of the domain comprises the sum of following energies. viz.

 (i) Exchange energy

(ii) Anisotropy energy

(iii) Domain wall energy

(iv) Magneto-strictive energy.

(i) Exchange energy (or) magnetic field energy (or) magneto-static energy

The interaction energy which makes the adjacent dipoles to align themselves is known as exchange energy (or) magnetic field energy. The exchange energy has established a single domain in a specimen of ferromagnetic and it is shown in Fig. 3.17.

Because of the development of the free poles at the ends of the domain, an external field will be produced around it and the configuration will have a high value of magnetic field energy. In other words it is the energy required in assembling the atomic magnets into a single domain and this work done is stored as potential energy.

The magnetic energy can be reduced by dividing the specimen into two domains as shown in Fig. 3.18 and 3.19. The process of subdivision may be carried further, until the reduction of magnetic energy is less than the increase in energy to form another domain and its boundary. This boundary is called as domain wall (or) Block wall.

Note:

Closure domains: The triangular domains complete the flux path and hence will not produce any poles. Therefore there is no magnetic field associated with the magnetisation. These domains are called closure domains. It is shown in Fig. 3.20.

 (ii) Anisotropy energy

In ferromagnetic crystals there are two directions of magnetisation. viz,

(i) Easy direction (ii) Hard direction

In easy direction of magnetisation, weak field can be applied and in hard direction of magnetisation, strong field should be applied. For producing the same saturation magnetisation along both the hard and easy direction, strong fields are required in the hard direction than the easy direction.

For example in Iron easy direction is [100], medium direction is [110] and the hard direction is [111] and it is as shown in Fig. 3.21. From the figure we can see that very strong field is required to produce magnetic saturation in hard direction [111] compared to the easy direction [100].

Therefore the excess of energy required to magnetise the specimen along hard direction over that required to magnetise the specimen along easy direction is called Crystalline anisotropy energy

(iii) Domain wall energy (or) Bloch wall energy

Bloch wall is a transition layer which separates the adjacent domains, magnetised in different directions. The energy of domain wall is due to both exchange energy and anisotropic energy.

Based on the spin alignments, two types of Bloch walls may arise, namely (i) Thick wall (ii) Thin wall

Thick Wall: When the spins at the boundary are misaligned and if the direction of the spin changes gradually as shown in Fig. 3.22, it leads to a thick Bloch wall. Here the misalignment of spins are associated with exchange energy.

Thin Wall: When the spins at the boundaries changes abruptly, then the anisotropic energy becomes very less. Since the anisotropic energy is directly proportional to the thickness of the wall, this leads to a thin Bloch wall.

Note: The Bloch wall should have thickness, balancing these two energies.

(iv) Magnetostrictive energy

When the domains are magnetised in different directions, they will either expand (or) shrink. Therefore there exists a deformation (i.e.,) change in dimension of the material, when it is magnetised. This phenomenon is known as magnetostriction and the energy produced in this effect is known as magnetostriction energy.

The deformation is different along different crystal directions and the change in dimension (increase or decrease) depends upon the nature of the material. For example, in Ni the length decreases; and in permalloy the length increases. But both the increase (or) decrease is due to the mechanical stress generated by domain rotation.