Curie-Weiss law
/ KYOOR-ee VYSE law /
As you cool a magnet toward the temperature where it is about to spontaneously order, it grows touchier and touchier — a smaller and smaller field produces a bigger and bigger response. The Curie-Weiss law is the simple rule that captures this rising eagerness: it says the material's susceptibility climbs steeply as you approach its ordering temperature from above.
Precisely, the law states that susceptibility is proportional to one divided by the temperature minus a special value, the Curie-Weiss temperature. As the temperature falls toward that value, the denominator shrinks toward zero and the susceptibility shoots up. That special value reflects how strongly the exchange interaction is pushing neighboring moments to cooperate; a positive one signals a leaning toward ferromagnetism, a negative one a leaning toward antiferromagnetism. So a single straight-line plot reveals both the strength and the type of magnetic coupling.
The Curie-Weiss law matters because it is the everyday workhorse for diagnosing a new magnetic material: measure susceptibility across a range of temperatures, plot it the right way, and read off the size of the atomic moments and the ordering tendency. The honest caveat is that it is an approximation that holds well only above the ordering temperature and away from it. Right at the transition, the simple law breaks down, and richer physics of fluctuations and critical behavior takes over.
For many paramagnets, plotting one-over-susceptibility against temperature gives a clean straight line. Where that line crosses zero on the temperature axis estimates the ordering temperature, and its slope reveals the size of the atomic moments — two numbers from one tidy graph.
Plotting one-over-susceptibility against temperature yields a line whose intercept and slope decode the magnet.
The Curie-Weiss temperature in the formula is close to, but not exactly, the true ordering temperature where magnetism actually sets in. The gap between the two is itself informative — a sign of competing interactions or frustration in the material.