The work done on a material to change its magnetization M in an external field H is dw = HdM. Its Gibbs free energy is
\(G(T, H)=-\left(γ T+\frac{a H^2}{2 T}\right)\),
where γ, a > 0 are constants. The material is in equilibrium at a temperature T = T0 and in an external field H = H0. If the field is decreased to \(\frac{H_0}{2}\) adiabatically and reversibly, the temperature changes to
1
2T0
2
\(\frac{T_0}{2}\)
3
\(\left(\frac{a}{2 \gamma}\right)^{\frac{1}{4}} \sqrt{H_0 T_0}\)
4
\(\left(\frac{a}{\gamma}\right)^{\frac{1}{4}} \sqrt{H_0 T_0}\)