 # 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.