Curie constant

In magnetism, the Curie constant is a material-dependent property that relates a material's magnetic susceptibility to its temperature through Curie's law.

The Curie constant when expressed in SI units, is given in kelvins (K), by

$C={\frac {\mu _{0}\mu _{\rm {B}}^{2}}{3k_{\rm {B}}}}ng^{2}J(J+1)$ ,

where $n$ is the number of magnetic atoms (or molecules) per unit volume, $g$ is the Landé g-factor, $\mu _{\rm {B}}$ is the Bohr magneton, $J$ is the angular momentum quantum number and $k_{\rm {B}}$ is Boltzmann's constant. For a two-level system with magnetic moment $\mu$ , the formula reduces to

$C={\frac {1}{k_{\rm {B}}}}n\mu _{0}\mu ^{2}$ ,

while the corresponding expressions in Gaussian units are

$C={\frac {\mu _{\rm {B}}^{2}}{3k_{\rm {B}}}}ng^{2}J(J+1)$ ,
$C={\frac {1}{k_{\rm {B}}}}n\mu ^{2}$ .

The constant is used in Curie's law, which states that for a fixed value of an applied magnetic field $\mathbf {H}$ , the magnetization of a material is (approximately) inversely proportional to temperature.

$M={\frac {C}{T}}H$ .

This equation was first derived by Pierre Curie.

Because of the relationship between magnetic susceptibility $\chi$ , magnetization $\mathbf {M}$ and applied magnetic field $\mathbf {H}$ is almost linear at low fields, then

$\chi ={\frac {\mathrm {d} M}{\mathrm {d} H}}\approx {\frac {M}{H}}$ ,

this shows that for a paramagnetic system of non-interacting magnetic moments, magnetization $\mathbf {M}$ is inversely related to temperature $T$ .