$C\; =\; frac\{N\; g^2\; mu\_B^2\; J(J+1)\}\{3\; k\_B\}$,

where $N$ is the number of magnetic moments, $g$ is the Landé g-factor, $mu\_B$ 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

$C\; =\; frac\{N\; mu^2\; \}\{k\_B\}$

It comes from Curie's Law, which is the relationship between magnetic susceptibility and temperature of a paramagnetic material

$chi\; =\; frac\{C\}\{T\}$.

This equation was first derived by Pierre Curie (Marie Curie's husband.)

Because of the relationship between magnetic susceptibility $chi$, magnetization $M$ and applied magnetic field $H$:

$chi\; =\; frac\{M\}\{H\}$,

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

See also

• Curie's law
• Paramagnetism