Curie–Weiss law

In its common form, the Curie–Weiss law is χ = C/(T − θCW). Here χ is magnetic susceptibility, T is absolute temperature, C is the Curie constant, and θCW is the Curie–Weiss temperature. The equation extends Curie’s inverse-temperature relation by accounting, approximately, for interactions among magnetic moments through Weiss’s molecular-field idea. For a simple paramagnet with negligible interactions, θCW is near zero and the equation reduces to Curie-like 1/T behaviour. In experiments, susceptibility conventions and units depend on whether data are expressed per volume, mass, or mole, so the units and definition used must be stated when comparing fitted constants.

In the mean-field picture, each magnetic moment experiences the applied field together with an effective field representing the average influence of neighbouring moments. A positive θCW commonly indicates net ferromagnetic interactions, while a negative value commonly indicates net antiferromagnetic interactions; a value near zero may indicate weak net interactions. These interpretations are useful but not universal proofs of a particular ordered state. In a region where the law applies, a plot of inverse susceptibility against temperature is approximately linear, and its extrapolated temperature-axis intercept is θCW. The Curie constant is related to the strength and concentration of the magnetic moments, although material-specific contributions and modelling assumptions affect its interpretation.

Researchers use Curie–Weiss fits to characterize magnetic materials in their paramagnetic regime, often as an initial way to estimate effective moments and the scale or sign of interactions. Temperature-dependent magnetic susceptibility measurements can also help identify transitions to ordered or frozen states. A fit is most informative when the sample’s magnetic contributions are understood, the applied field is appropriate, and the chosen fitting interval is supported by the data rather than selected solely to produce a straight line.

The Curie–Weiss law is a mean-field approximation, not a universal formula. Close to an ordering transition, correlations and critical fluctuations can cause deviations. Additional temperature-independent contributions—such as diamagnetic, Pauli, or van Vleck susceptibility—can curve a plot of inverse susceptibility and may require an amended model. Crystal-field effects, low-dimensional interactions, frustration, spin-state changes, or itinerant-electron magnetism can also alter the response. In itinerant magnets, a Curie–Weiss-like fit may describe data over a range without giving the same microscopic meaning to fitted parameters as in a localized-moment model. Consequently, θCW and an effective moment should be interpreted alongside other measurements and a physically justified model.