Curie–Weiss temperature dependence of magnetic susceptibility According to the Curie–Weiss law, how does the magnetic susceptibility χ of a material vary with absolute temperature T (for T sufficiently above any ordering temperature)?

Introduction / Context:The Curie–Weiss law extends Curie’s law by including mean-field interactions via the Weiss temperature θ. It is widely used to analyze susceptibility data of paramagnets and ferromagnets above the Curie temperature.

Given Data / Assumptions:

• Linear response regime and temperatures well above ordering temperature.
• Local-moment picture with mean-field coupling.

Concept / Approach:For interacting moments, the effective field is H_eff = H + λM, which shifts the temperature scale. This yields χ = C / (T − θ), so χ varies inversely with (T − θ). The sign and magnitude of θ reveal the nature and strength of magnetic interactions.

Step-by-Step Solution:Start from Curie law: χ = C / T for non-interacting spins.Introduce mean-field interaction: replace T by (T − θ).Conclude: χ ∝ 1 / (T − θ).

Verification / Alternative check:Plotting 1/χ versus T gives a straight line with intercept θ. This is a standard diagnostic in magnetism labs.

Why Other Options Are Wrong:Proportionalities to T, T^2, or independence of T contradict data for local-moment systems. T^-2 is not the Curie–Weiss form.

Common Pitfalls:

• Applying Curie–Weiss law below Tc or in itinerant magnets where deviations occur.
• Misinterpreting negative θ as antiferromagnetic correlations.

Final Answer:χ ∝ 1 / (T − θ)