Weiss Theory of Ferromagnetism

Langevin’s theory of paramagnetism was extended by Weiss to give a theoretical explanation of the behavior of ferromagnetic. He made the following two assumptions:

(i)    Weiss assumed that a ferromagnetic specimen contains a number of small regions (domains) which are spontaneously magnetized. The total spontaneous magnetization is the vector sum of the magnetic moments of the individual domains.

(ii)    The spontaneous magnetization of each domain is due to the existence of an internal molecular field. This tends to produce a parallel alignment of the atomic dipoles.

Weiss also assumed that the internal molecular filed Hi is proportional to the magnetization M, i.e., Hi = γ M where γ is a constant called Weiss constant. If now an external field H acts on the dipole, then the effective field Heff is given by
        H_eff = H + Hi + γ M                            … (1)

According to Langevin’s theory of paramagnetism, at high temperatures,

        M = nm² μ₀ H / 3kT

Weiss suggested that the corresponding result for ferromagnetic could be obtained by replacing H by Heff. Hence for ferromagnetic,

        M = nm² μ₀ / 3kT [H + γ M]

Or        M = nm₂ μ₀ H / 3k (T – nm2 γ μ₀ / 3k)                    … (2)

The susceptibility X_ferro is,
       
        X_ferro = M/ H = nm2 μ0 / 3k (T – nm2 γ μ0 /3k) = C / (T – θ)            … (3)

Here, nm2 μ₀ /3k is called the Curie constant.

 θ = nm2 μ₀ /3 is called the Curie temperature.

It is the temperature below which the material shows ferromagnetic behavior.
For values of temperature above θ, the ferromagnetic substance behaves like a paramagnetic substance.

Eq. (3) is called the Curie – Weiss law for ferromagnetic.

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