= Curie's law
{c}
{title2=$\chi=C/T$}
{wiki}
= Curie law
{c}
{synonym}
For independent moments of angular momentum $J$ at small $\mu_B|B|/(k_BT)$, the zero-field <variance> is $\langle m^2\rangle=J(J+1)/3$. Differentiating the canonical mean gives the <magnetic susceptibility>
$$
\chi=\frac{N\mu_B^2J(J+1)}{3k_BT}.
$$
Thus susceptibility is inversely proportional to temperature. The small-field or high-temperature condition distinguishes this law from the exponentially vanishing fixed-field susceptibility of a saturated paramagnet at low temperature.
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