 # 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

$$\begin{array}{l}{{overrightarrow{B}}_{Total}}={{overrightarrow{B}}_{operatorname{int}}}+{{overrightarrow{B}}_{ext,app}}\end{array}$$
… (1)

Where

$$\begin{array}{l}{{overrightarrow{B}}_{Total}}\end{array}$$
= Net field

$$\begin{array}{l}{{overrightarrow{B}}_{operatorname{int}}}\end{array}$$
= internal magnetic field (or) Weiss field

$$\begin{array}{l}{{overrightarrow{B}}_{ext,app}}\end{array}$$
= externally applied field.

$$\begin{array}{l}{{overrightarrow{B}}_{operatorname{int}}}propto\end{array}$$
Magnetization (M)

$$\begin{array}{l}{{overrightarrow{B}}_{operatorname{int}}}=lambda {{mu }_{0}}M\end{array}$$
… (2)

$$\begin{array}{l}{{mu }_{0}}\end{array}$$
- magnetic permeability of free space

$$\begin{array}{l}lambda\end{array}$$
- constant

M – magnetization

Sub equation (2) in equation (1)

$$\begin{array}{l}{{overrightarrow{B}}_{Tot}}=lambda {{mu }_{0}}M+{{overrightarrow{B}}_{ext}}\end{array}$$

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

$$\begin{array}{l}chi =frac{{{mu }_{0}}M}{{{B}_{Total}}}\end{array}$$
… (3)

$$\begin{array}{l}chi =frac{{{mu }_{0}}M}{{{B}_{app}}+lambda {{mu }_{0}}M}\end{array}$$
… (4)

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

$$\begin{array}{l}chi =frac{C}{T}\end{array}$$
… (5)

Where C – is constant

T – is Temperature

This equation is known as curie law for paramagnetism.

By comparing equation (4) and (5)

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

Where

$$\begin{array}{l}Clambda = theta\end{array}$$
$$\begin{array}{l}frac{C}{T-theta }=chi\end{array}$$
… (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. (0) (1)