Curie–Weiss law for paramagnetism and ferromagnetism above the Curie point Which of the following expresses the Curie–Weiss law relating magnetic susceptibility to temperature?

Introduction / Context:The Curie–Weiss law generalizes Curie’s law by incorporating internal (molecular) fields via the Weiss temperature θ. It describes the temperature dependence of magnetic susceptibility χ for paramagnets and for ferromagnets when measured above their Curie temperature. This law is widely used to extract key parameters from high-temperature susceptibility data.

Given Data / Assumptions:

• Linear response regime in modest applied fields.
• Temperatures well above any ordering temperature for the material under test.
• Material behaves as an assembly of local moments with mean-field coupling.

Concept / Approach:Curie’s law states χ = C / T for non-interacting moments. Weiss introduced an internal field proportional to the magnetization, shifting the effective temperature scale. The result is the Curie–Weiss law: χ = C / (T − θ), where C is the Curie constant and θ (Weiss temperature) captures the strength and sign of spin–spin interactions (positive for ferromagnetic-like correlations, negative for antiferromagnetic-like correlations).

Step-by-Step Solution:Start with Curie law: χ = C / T.Introduce molecular field H_m = λ M, giving an effective field H_eff = H + λ M.Mean-field treatment leads to χ = M / H = C / (T − θ) with θ proportional to λ.

Verification / Alternative check:Plotting 1/χ versus T yields a straight line with slope 1/C and intercept θ on the temperature axis, a standard experimental diagnostic for magnetic materials.

Why Other Options Are Wrong:χ = C / T is Curie’s law (no interaction). χ = C * T and χ = (T − θ) / C invert the correct dependence. χ = C / (T + θ) gives the wrong intercept sign and fails to describe ferromagnetic precursors correctly.

Common Pitfalls:

• Applying Curie–Weiss below the Curie temperature where spontaneous magnetization invalidates the linear relation.
• Misinterpreting the sign of θ; positive θ usually indicates ferromagnetic correlations.

Final Answer:χ = C / (T − θ)