Pauli paramagnetism

Pauli paramagnetism is the weak positive magnetic response produced when a magnetic field shifts the two spin Fermi surfaces of a degenerate electron gas. At zero temperature, if $g(E_F)$ includes both spin states, its total magnetic moment and susceptibility are

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.