Ferromagnetism is a type of magnetism exhibited by certain materials, such as iron, nickel, and cobalt, where they exhibit a strong and permanent magnetization even in the absence of an external magnetic field. In ferromagnetic materials, the magnetic moments of individual atoms or ions are aligned in the same direction, resulting in a net magnetic moment that gives rise to a magnetic field.

This alignment of magnetic moments is due to a quantum mechanical phenomenon known as exchange interaction, which arises from the overlapping of the electron orbitals of neighbouring atoms. When these electron spins are aligned in the same direction, the exchange interaction is maximized, leading to a lower energy state and a more stable arrangement of atoms.

Ferromagnetic materials can be magnetized in an external magnetic field, and once magnetized, they retain their magnetization even after the field is removed. This is because the aligned spins maintain their orientation due to the exchange interaction, resulting in a stable magnetization.

Ferromagnetism is important for a wide range of technological applications, such as in magnetic storage devices like hard drives, electric motors, and transformers, as well as in magnetic resonance imaging (MRI) in medicine.

Main features in this case is given as

1. The magnetic dipole moment per unit volume M produced in such substance is very high even in the presence of weak magnetic field.

2. The value of M is not linearly proportional to applied magnetic field Ba. In other words, the magnetic susceptibility χ = μ M / Ba is not constant but varies with Ba.

3. Ferromagnetic materials have a Curie temperature, which is the temperature above which the material loses its ferromagnetic properties and becomes paramagnetic, meaning its magnetic moments become disordered and no longer align.

4. The variation of magnetisation with field strength exhibits well known hypothesis.

Overall, the key features of ferromagnetism are the spontaneous alignment of magnetic moments, a large magnetic susceptibility, a memory effect, and a Curie temperature. These properties make ferromagnetic materials important for a wide range of technological applications.

Weiss field theory is a theoretical framework developed to explain the origin of ferromagnetism in materials. The theory was developed by French physicist Pierre Weiss in the early 20th century, and it is based on the idea that the magnetic moments of atoms in a ferromagnetic material interact with each other and with an external magnetic field.

The Weiss theory describes the magnetic behavior of ferromagnetic materials using a mean field approach, where the interaction between magnetic moments is replaced by an effective magnetic field, known as the Weiss field. The Weiss field is a self-consistent field that takes into account the interaction between magnetic moments in a material, and it is used to calculate the magnetization of the material at a given temperature.

In the Weiss theory, the magnetic moments in a ferromagnetic material are assumed to be aligned spontaneously at low temperatures due to the exchange interaction, and this alignment is maintained by the Weiss field. The Weiss temperature is a critical temperature above which the Weiss field becomes weaker than the thermal energy, and the material loses its ferromagnetic properties.

The Weiss theory has been successfully used to explain the magnetic properties of a wide range of ferromagnetic materials, including metals, alloys, and magnetic oxides. However, it has some limitations, particularly in explaining the behaviour of ferromagnetic materials at very low temperatures, where quantum mechanical effects become important.

Weiss field theory based upon

1. A ferromagnetic specimen of macroscopic dimension certain a small regions known as domains which are spontaneously magnetised.

2. There exists a molecular magnetic field within each domain and field tends to produces a parallel alignment of individual localised atomic moments.

In mean field approximation each magnetic atom experiences a field proportional to magnetisation.

If the external magnetic field Ba is applied then the effective field acting on ion or atom is

Consider a ferromagnetic substance containing N atoms per unit volume each having a total angular momentum quantum number then magnetisation is

For spontaneous magnetisation where there is no external magnetic field then

Suppose when all domains are aligned along magnetic field, the magnetic moment per un it volume known as saturation magnetisation is given by

The simultaneous equation 8 and 6 can be solved by plotting (M/ Ms) against x in accordance with 8 for T>Tc, T = Tc and T<Tc and we plot against M/Ms against Bj (x) in accordance with 7 for T = Tc.

a. At critical temperature: At Tc, the straight line given by 8 is tangent to the curve given by equation 6 at origin. The slope of straight line is given by

For x<<l, Brillouin function becomes

Tangent to the curve at the origin has slope and is given by

Equating 9 and 10, we get

This shows that Tc is proportional to 𝜆

b. Below Tc (T< Tc): Below Tc, straight line given by 8 intersect the curve given by 6 at two points x=0 and 'p'.

Ms is the maximum value of spontaneous magnetisation on temperature.

c. Above Tc: In this case, magnetisation occur when external magnetic field Ba is applied . There is no spontaneous magnetisation. This region is known as paramagnetic region. As in paramagnetic case,

This is Curie - Weiss Law. It states that the magnetic susceptibility (χ) of a material is proportional to the inverse of the difference between its temperature (T) and a critical temperature (Tc), known as the Curie-Weiss temperature.

The Curie-Weiss law is important because it provides a simple model for the behaviour of magnetic materials near their Curie temperature. When the temperature of a magnetic material is above its Curie temperature, the material loses its magnetic properties and becomes paramagnetic, meaning it is only weakly attracted to magnetic fields. Conversely, when the temperature is below the Curie temperature, the material exhibits ferromagnetism, with its magnetic moments aligning spontaneously.

The Curie-Weiss law provides a useful tool for predicting the behaviour of magnetic materials near their Curie temperature, and it has been widely used in the study of magnetism and in the design of magnetic materials for technological applications. However, it is important to note that the law is only an approximation and does not account for all the complexities of magnetic behaviour, particularly at very low temperatures or in strongly interacting systems.

This note is a part of the Physics Repository.

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