Definitions

# Curie constant

Curie's constant is

$C = frac\left\{N g^2 mu_B^2 J\left(J+1\right)\right\}\left\{3 k_B\right\}$,

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

$C = frac\left\{N mu^2 \right\}\left\{k_B\right\}$

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

$chi = frac\left\{C\right\}\left\{T\right\}$.

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 $H$:

$chi = frac\left\{M\right\}\left\{H\right\}$,

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