Curie temperatures – relation between ferromagnetic Curie temperature (Q_f) and paramagnetic Curie temperature (θ) Considering the Curie–Weiss behavior of real ferromagnets, what is the most appropriate general statement about the relationship between the ferromagnetic Curie temperature Q_f (often denoted T_c) and the paramagnetic Curie temperature θ appearing in χ = C / (T − θ)?

Introduction:
Magnetic phase transitions are characterized by the Curie temperature T_c (here denoted Q_f) at which a ferromagnet becomes paramagnetic. Above T_c, the Curie–Weiss law often describes susceptibility with a parameter θ called the paramagnetic Curie temperature. Understanding how θ compares with T_c in real materials is important for interpreting experimental susceptibility data.

Given Data / Assumptions:

• Curie–Weiss law in the paramagnetic region: χ = C / (T − θ).
• Real materials show deviations from ideality due to interactions, anisotropy, and band effects.
• θ is obtained from a linear fit of 1/χ vs T extrapolated to zero.

Concept / Approach:

In the simplest mean-field model for an ideal ferromagnet, θ equals T_c. However, in real ferromagnetic and ferrimagnetic materials, θ extracted from high-temperature fits can differ from T_c due to short-range order, crystal-field effects, itinerant-electron contributions, or measurement range limitations. Consequently, θ may be slightly greater than, less than, or approximately equal to T_c (Q_f).

Step-by-Step Solution:

Verification / Alternative check:

Experimental 1/χ plots for different ferromagnets show varying θ relative to T_c; some itinerant ferromagnets yield θ > T_c, while localized systems may show θ ≈ T_c or θ < T_c depending on interactions.

Why Other Options Are Wrong:

Options A–C impose a strict inequality or limited relation that does not universally hold; Option E is arbitrary and incorrect.

Common Pitfalls:

Assuming ideal mean-field behavior applies perfectly to all materials; ignoring experimental uncertainties and fitting ranges that shift the apparent θ.

Final Answer:

θ may be equal to less than or more Q_f