What is "curie's law"

n. (context physics English) a law which shows that the magnetic susceptibility of a paramagnetic dipole is inversely proportional to the absolute temperature; the basis of operation of magnetic thermometers

In a paramagnetic material the magnetization of the material is (approximately) directly proportional to an applied magnetic field. However, if the material is heated, this proportionality is reduced: for a fixed value of the field, the magnetization is (approximately) inversely proportional to temperature. This fact is encapsulated by Curie's law:

$$\mathbf{M} = C \cdot \frac{\mathbf{B}}{T},$$

where

M
is the resulting magnetisation

B
is the magnetic field, measured in teslas

T
is absolute temperature, measured in kelvins

C
is a material-specific Curie constant.

This relation was discovered experimentally (by fitting the results to a correctly guessed model) by Pierre Curie. It only holds for high temperatures, or weak magnetic fields. As the derivations below show, the magnetization saturates in the opposite limit of low temperatures, or strong fields.