Past exam of the quantum condensed matter course of the University of Cambridge / 2019 / Section B / 6 / b / Solution

At weak field or high temperature, ${\mu }_{B}B\ll k_{B}T$ and $\tanh x\simeq x$, soUsing $B\simeq {\mu }_{0}H$ for the applied-field response and neglecting demagnetizing corrections, the SI volume magnetic susceptibility isThis is Curie's law. If susceptibility is instead defined as $\partial M/\partial B$, its Curie constant is $n{\mu }_B^2/k_B$ without ${\mu }_0$; stating which field is used prevents a units error.