# Explain curie-weiss theory in details

Curie – Weiss theory which explains the qualitative explanation of the ferromagnetism. We also call it as molecular field theory. In this theory we treat the Ferromagnetic materials as a special case of paramagnetic material. In which there is an internal field besides in addition to applied external field.

The total field experienced by the ferromagnetic material is given as

$${{overrightarrow{B}}_{Total}}={{overrightarrow{B}}_{operatorname{int}}}+{{overrightarrow{B}}_{ext,app}}$$ … (1)

Where

$${{overrightarrow{B}}_{Total}}$$ = Net field

$${{overrightarrow{B}}_{operatorname{int}}}$$ = internal magnetic field (or) Weiss field

$${{overrightarrow{B}}_{ext,app}}$$ = externally applied field.

$${{overrightarrow{B}}_{operatorname{int}}}propto$$ Magnetization (M)

$${{overrightarrow{B}}_{operatorname{int}}}=lambda {{mu }_{0}}M$$ … (2)

$${{mu }_{0}}$$- magnetic permeability of free space

$$lambda$$- constant

M – magnetization

Sub equation (2) in equation (1)

$${{overrightarrow{B}}_{Tot}}=lambda {{mu }_{0}}M+{{overrightarrow{B}}_{ext}}$$

As we know, magnetic susceptibility (χ) is given by

$$chi =frac{{{mu }_{0}}M}{{{B}_{Total}}}$$ … (3)

$$chi =frac{{{mu }_{0}}M}{{{B}_{app}}+lambda {{mu }_{0}}M}$$ … (4)

Assuming temperature dependence of magnetic susceptibility (χ) is given by curie law

$$chi =frac{C}{T}$$ … (5)

Where C – is constant

T – is Temperature

This equation is known as curie law for paramagnetism.

By comparing equation (4) and (5)

$$frac{C}{T}=frac{{{mu }_{0}}M}{{{B}_{app}}+lambda {{mu }_{0}}M}$$ $$Cleft( {{B}_{app}}+lambda {{mu }_{0}}M right)={{mu }_{0}}MT$$ $$C,{{B}_{app}}=left( T-Clambda right){{mu }_{0}}M$$ $$frac{C}{T-Clambda} = frac{mu_oM}{B_{app}}$$ $$frac{C}{T-Clambda} = chi$$

Where $$Clambda = theta$$ $$frac{C}{T-theta }=chi$$ … (6)

θ – characteristic temperature (or) curie temperature we call this above equation (6) as curie – Weiss law.

Case I: T > θ

For Ferromagnetic material θ = is positive and this curie – Weiss law holds good for ferromagnetic material. The behaviour of ferromagnetism doesnot exist to above the certain characteristics temperature (θ) – is identified as critical temperature (or) curie temperature of the material. Material behaves as paramagnetic material.

When T > θ

Internal field of the magnetic material vanishes. Now the atomic magnetic moment will not aligned with respect to one another.

Case (II): T < θ

Temperature below the characteristic temperature (or) curie temperature the magnetic material behaves as Ferromagnetic material. Which means there is spontaneous magnetization.

There is a strong internal field which aligns the atomic magnetic moments even in the absence of external applied field.