CurieWeiss

Curie–Weiss law describes the magnetic susceptibility of many paramagnetic materials in the high-temperature regime and represents a refinement of Curie's law by incorporating a mean-field interaction. It is attributed to Pierre Curie and, later, to Pierre Weiss, who proposed that the moments experience an internal molecular field proportional to the magnetization.

The law is expressed as χ = C /(T − Θ), where χ is the molar or volume susceptibility, T is the absolute temperature, C is the Curie constant, and Θ (the Weiss temperature) encodes the strength and sign of the effective interactions among magnetic moments. For a molar susceptibility χ_m, C_m = μ0 N_A μ_eff^2 /(3 k_B), with μ0 the vacuum permeability, N_A Avogadro’s number, k_B Boltzmann’s constant, and μ_eff the effective magnetic moment per formula unit. The practical upshot is that χ grows as T approaches Θ from above.

The sign of Θ indicates the dominant interaction: Θ > 0 suggests ferromagnetic interactions, Θ < 0 suggests antiferromagnetic interactions, and Θ ≈ 0 implies weak or canceled interactions. The law typically applies well above any magnetic ordering temperature, where the material behaves paramagnetically; near the ordering temperature, critical fluctuations cause deviations.

Limitations include the mean-field nature of the model, which neglects fluctuations and spatial correlations; it fails to accurately describe critical behavior near Tc and complex magnets. Nevertheless, Curie–Weiss analysis remains a standard tool for estimating the effective moment and inferring the nature of magnetic interactions in many solids.