# Curie-Weiss Law

## Curie Law

Curie law states that the magnetization of paramagnetic substances is directly proportional to an applied magnetic field, but the case is not the same when the substances is heated. When it is heated, the relation is reversed i.e. the magnetization becomes inversely proportional to temperature.

In other words, we can say that magnetization of paramagnetic substances is directly proportional to external magnetic field and inversely proportional to Absolute Temperature at high temperature.

Mathematically, it is written as-

M ∝ C x (B / T)

or, M = C x (B / T)

Where-

M is the magnetization

B is the magnetic field

T is the absolute temperature

C is a material-specific Curie constant.

Curie law obeyed after Curie Temperature (T_{C}) in the above graph.

This relation was discovered experimentally by Pierre Curie. This concept holds good for high temperatures and weak magnetic fields. Various experiments showed that for many substances the susceptibility is inversely proportional to the absolute temperature T.

χ ∝ 1/T.

or, χ = C/T.

This relationship is defined as the Curie's law. The constant 'C' is called the curie constant.

The above equation may also be modified to-

χ = C/(T − θ), where θ is a constant. This equation is called the Curie–Weiss Law.

## Curie-Weiss Law

Curie-Weiss Law is to one of the most important laws in the field of electromagnetism. It states that the magnetic susceptibility of a material above a specific temperature (called Curie Temperature), becomes ferromagnetic.

χ = C/(T-T_{C})

Here C is a material specific Curie constant

T is the absolute temperature in Kelvin

T_{C} is the Curie Temperature in Kelvin (Temperature where magnetic materials lose their ferromagnetic characteristics)

When T = T_{C}, the value of the susceptibility becomes infinite. Below this temperature, the material exhibits spontaneous magnetization (i.e., it becomes ferromagnetic). Hence, the magnetic properties of such a material are also quite different from those in the paramagnetic or high-temperature stage. By applying some magnetic field, the magnetic moment can be changed but the amount of moment attained in a given field may vary depending on the last magnetic, thermal or mechanical treatment of the sample.

However, when T ≫ T_{C} the expression of the Curie–Weiss law still holds good, but T_{C} replaced by a temperature 'Θ' that is somewhat higher than the actual Curie temperature 'T_{C}'. Θ is called the Weiss constant used to distinguish it from the temperature of the actual Curie point.

## Limitation of Curie – Weiss Law

The Curie-Weiss law holds not good in many materials to describe the susceptibility. Instead, there is a critical behaviour of the form.

X = 1/ (T – T_{C})^{γ}

At temperature T >> T_{C} the expression of the law still holds good. But, with the T_{C} will be replaced by temperature (Θ) is higher than the Curie temperature.

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