Magnetic moment from a Schottky heat-capacity tail ($\mu =B^{-1}\sqrt{3a{k}_B/2}$)

For one three-level unit with energies $-\mu B,0,\mu B$, the high-temperature heat capacity is $C\simeq 2{\mu }^2{B}^2/(3k_B{T}^2)$. A measured coefficient $C=a/T^2$ therefore gives the displayed magnetic moment. If the heat capacity instead represents $N$ independent units, replace $a$ by $a/N$; the normalization must be established before extracting a single-unit moment.