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)


\(\begin{array}{l}{{overrightarrow{B}}_{Total}}\end{array} \)
= 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)

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


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

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