= Solution
Room-temperature iron is ferromagnetic: interactions among its electronic moments produce spontaneous local order. The independent-ion <Curie law> therefore needs an interaction and an ordered-state description. In a Weiss mean-field approximation, replace the applied field by $H_{\rm eff}=H+\Lambda M$. Above the ordering <temperature>, linearizing the single-ion response yields
$$
M=\frac{C_\chi}{T}(H+\Lambda M),\qquad
\boxed{\chi_H=\frac{C_\chi}{T-T_C},\qquad T_C=\Lambda C_\chi.}
$$
This is the Curie–Weiss approximation on the paramagnetic side. Merely substituting room <temperature> below $T_C$ into that high-temperature formula would produce a negative response and is not a valid model of stable iron.
Below $T_C$, use the full nonlinear moment response to the effective field; it has nonzero zero-field solutions. On a chosen ordered branch the local small-field response has the form $M\simeq M_s(T)+\chi_{\rm diff}(T)H$, rather than $M\propto H/T$ through the origin. Macroscopic <magnetic domains> and <hysteresis> further determine the measured net moment. Exchange interactions, arising from electronic quantum statistics and Coulomb correlations, supply the alignment <energy>; bare dipolar fields alone do not explain ordinary iron's strong <ferromagnetism>. A localized-ion Weiss model describes the qualitative ordering, while iron's itinerant electronic structure limits a literal independent-fixed-ion interpretation.
Back to article page