Curie temperature

The Curie temperature T_c is the sharp threshold above which a ferromagnet gives up its spontaneous order. Below T_c, quantum exchange interactions between neighbouring atomic moments energetically reward parallel alignment, and the material carries permanent magnetization. Above T_c, thermal motion k_B T overwhelms the exchange energy: the moments wobble too violently for neighbours to stay aligned, and the spontaneous magnetization drops to zero. The material becomes an ordinary paramagnet, with susceptibility now following the Curie–Weiss law χ = C/(T − T_c).

The transition is a genuine thermodynamic phase transition — a continuous (second-order) one, in Landau's classification. The spontaneous magnetization vanishes smoothly as T → T_c from below, typically as M ∝ (T_c − T)^β with β ≈ 0.326 for three-dimensional ferromagnets (the 3D-Heisenberg universality class). The magnetic heat capacity diverges logarithmically at T_c. The susceptibility above T_c blows up as T approaches T_c from above. Every experimental signature of a second-order transition is present, and indeed the Curie transition was the first phase transition for which Landau's mean-field theory (via Pierre Weiss's 1907 molecular field) gave quantitatively correct predictions near T_c.

Different ferromagnets have dramatically different Curie temperatures. Iron: 1043 K (770 °C). Nickel: 627 K (354 °C). Cobalt: 1388 K (1115 °C). Gadolinium: 292 K (just below room temperature) — which is why a gadolinium sphere at room temperature is only weakly magnetic but becomes a strong ferromagnet when refrigerated. Some permanent-magnet alloys are engineered for very high T_c: samarium-cobalt magnets stay ferromagnetic up to 1000 K, making them the standard choice for high-temperature applications like aerospace motors. Below T_c, the exchange coupling wins; above, thermal noise does. The crossover is sharp, universal, and the founding example in the whole theory of critical phenomena.