Magnetic susceptibility ($\chi$)

Magnetic susceptibility measures the linear change of magnetization or magnetic moment with an applied magnetic field. With the relevant convention stated explicitly, $\chi =\partial M/\partial B$.

For independent moments of angular momentum $J$ at small ${\mu }_B|B|/(k_{B}T)$, the zero-field variance is $⟨m^2⟩=J(J+1)/3$. Differentiating the canonical mean gives the magnetic susceptibilityThus 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.