Two-state Curie law ($C={\mu }_{0}n{\mu }^2/k_B$)

For independent magnetic moments constrained to ${\mu }_z=\pm \mu$, the one-site partition function is $2\cosh [\mu {\mu }_{0}H/(k_{B}T)]$. The weak-field magnetization is $M={\mu }_{0}n{\mu }^{2}H/(k_{B}T)$, so the SI magnetic susceptibility obeys $\chi =C/T$ with $C={\mu }_{0}n{\mu }^2/k_B$. If $\mu =gS{\mu }_B$, this involves $S^2$, not the unrestricted-spin factor $S(S+1)/3$. The constraint on allowed moment orientations must be specified before using a Curie law coefficient.