Editing Curie temperature (section)

== Curie–Weiss law ==
{{main|Curie–Weiss law}}
The Curie–Weiss law is an adapted version of [[Curie's law]].

The Curie–Weiss law is a simple model derived from a [[Mean-field theory|mean-field]] approximation, this means it works well for the materials temperature, {{mvar|T}}, much greater than their corresponding Curie temperature, {{math|''T''<sub>C</sub>}}, i.e. {{math|''T'' ≫ ''T''<sub>C</sub>}}; it however fails to describe the [[magnetic susceptibility]], {{mvar|χ}}, in the immediate vicinity of the Curie point because of correlations in the fluctuations of neighboring magnetic moments.<ref name=Jullien153>{{harvnb|Jullien|Guinier|1989|pp=153}}</ref>

Neither Curie's law nor the Curie–Weiss law holds for {{math|''T'' < ''T''<sub>C</sub>}}.

Curie's law for a paramagnetic material:<ref name=Hall205>{{harvnb|Hall|Hook|1994|pp=205–06}}</ref>

<math display="block">\chi = \frac{M}{H} =\frac{M \mu_0}{B} =\frac{C}{T} </math>

{|
|-
! Definition !!
|-
| {{mvar|χ}} ||the magnetic susceptibility; the influence of an applied [[magnetic field]] on a material
|-
| {{mvar|M}} ||the [[magnetic moments]] per unit volume
|-
| {{mvar|H}} || the macroscopic magnetic field
|-
| {{mvar|B}} ||the magnetic field
|-
| {{mvar|C}} ||the material-specific [[Curie constant]]
|}

The Curie constant {{mvar|C}} is defined as<ref name=Levy201>{{harvnb|Levy|1968|pp=201–02}}</ref>
<math display="block">C = \frac{\mu_0 \mu_\mathrm{B}^2}{3 k_\mathrm{B}}N_\text{A} g^2 J(J+1)</math>
{|
|-
| <math>N_\text{A}</math>
| the [[Avogadro constant]]
|-
| {{math|''µ''<sub>0</sub>}} || the [[permeability of free space]]. Note: in [[CGS]] units is taken to equal one.<ref name=Kittel1996>{{harvnb|Kittel|1996|p=444}}</ref>
|-
| {{mvar|g}} || the [[Landé g-factor|Landé ''g''-factor]]
|-
| {{math|''J''(''J'' + 1)}} || the eigenvalue for eigenstate J<sup>2</sup> for the stationary states within the incomplete atoms shells (electrons unpaired)
|-
| {{math|''µ''<sub>B</sub>}} || the [[Bohr magneton]]
|-
| {{math|''k''<sub>B</sub>}} || the [[Boltzmann constant]]
|-
| total magnetism || is {{mvar|N}} number of magnetic moments per unit volume{{clarify inline|reason=This isn't a variable used in the above and N is also undefined. If it's the Avogadro number then first it should be N_A not N, second it's per mole (unit amount), not per "unit volume"|date=October 2024}}
|}

The Curie–Weiss law is then derived from Curie's law to be:

<math display="block">\chi = \frac{C}{T-T_\mathrm{C}}</math>

where:

<math display="block">T_\mathrm{C} = \frac{C \lambda }{\mu_0}</math>

{{mvar|λ}} is the Weiss molecular field constant.<ref name=Levy201/><ref name=Myers>{{harvnb|Myers|1997|pp=334–345}}</ref>

For full derivation see [[Curie–Weiss law]].