# Curie-Weiss Law

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## Curie-Weiss law

A relation between magnetic or electric susceptibilities and the absolute temperature which is followed by ferromagnets, antiferromagnets, nonpolar ferroelectrics and antiferroelectrics, and some paramagnets. The Curie-Weiss law is usually written as the equation below,

where χ is the susceptibility,*C*is a constant for each material,

*T*is the absolute temperature, and Θ is called the Curie temperature. Antiferromagnets and antiferroelectrics have a negative Curie temperature. The Curie-Weiss law refers to magnetic and electric behavior above the transition temperature of the material in question. It is not always precisely followed, and it breaks down in the region very close to the transition temperature. Often the susceptibility will behave according to a Curie-Weiss law in different temperature ranges with different values of

*C*and Θ.

*See*Curie temperature, Electric susceptibility, Magnetic susceptibility

## Curie-Weiss Law

a temperature dependence of the specific magnetic susceptibility *Χ* of paramagnetic materials having the form

(1) *Χ* = *C′/(T -*Δ)

where *C*′ and Δ are constants for a given substance (P. Weiss, 1907). Equation (1) describes the experimental dependence of *Χ* on the temperature *T* with sufficient accuracy for most cases of paramagnetism of ions in crystals, as well as in crystals possessing atomic magnetic ordering at *T* > Ⓗ (above the Curie and Néel points). In many cases, the constant *C* ′, in practice, coincides with the constant *C* of Curie’s law for magnetic ions of a given type. The constant Δ characterizes the interaction of the magnetic ions with one another and with the crystal lattice field.

The magnetic susceptibility of paramagnetic substances, which become ferromagnetic at low temperatures, is described by equation (1) with a positive value of Δ close to the value of the Curie temperature Ⓗ. For substances that undergo a transition to an antiferromagnetic state at low temperatures, in most cases Δ is negative and agrees with the Néel temperature *T _{N}* only in order of magnitude.

The Curie-Weiss law is also applicable to ferroelectrics. At temperatures T , >> Ⓗ (where Ⓗ is the Curie temperature of the ferroelectric), the dielectric constant is ∊ = *B/(T* — Ⓗ), where *B* is a constant for the substance.