# Curie constant

The Curie constant is a material-dependent property that relates a material's magnetic susceptibility to its temperature.

The Curie constant, when expressed in SI units, is given by

$C = \frac{\mu_0 \mu_B^2}{3 k_B}N g^2 J(J+1)$[1]

where $N$ is the number of magnetic atoms (or molecules) per unit volume, $g$ is the Landé g-factor, $\mu_B$ (9.27400915e-24 J/T or A·m2) is the Bohr magneton, $J$ is the angular momentum quantum number and $k_B$ is Boltzmann's constant. For a two-level system with magnetic moment $\mu$, the formula reduces to

$C = \frac{1}{k_B}N \mu_0 \mu^2$

The constant is used in Curie's Law, which states that for a fixed value of a magnetic field, the magnetization of a material is (approximately) inversely proportional to temperature.

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

This equation was first derived by Pierre Curie.

Because of the relationship between magnetic susceptibility $\chi$, magnetization $\scriptstyle\mathbf{M}$ and applied magnetic field $\scriptstyle\mathbf{H}$:

$\chi = \frac{\mathbf{M}}{\mathbf{H}}$

this shows that for a paramagnetic system of non-interacting magnetic moments, magnetization $\scriptstyle\mathbf{M}$ is inversely related to temperature $T$ (see Curie's Law).