Magnetic moment inferred from an entropy derivative ($m(T,B)=\alpha B/T+m_0(B)$)

With magnetic Helmholtz free energy convention $dF=-SdT-mdB$, a measured $(\partial S/\partial B{)}_T=-\alpha B/T^2$ fixes $(\partial m/\partial T{)}_B$ to the same value. Integrating determines the displayed inverse-temperature term but leaves a temperature-independent function $m_0(B)$. An independent constitutive or boundary condition is needed to fix it. Requiring zero moment at infinite temperature recovers Curie's law without that offset.