CND-18

Curie–Weiss susceptibility

χ = C / (T − θ). Mean-field magnet above a Curie (or Néel) temperature.

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Electrons in solidsCurie–Weiss

Governing equation

\chi=C/(T-\theta)

$T \in \left[5, 800\right]$

where

C: Curie constant (K)
\theta: Weiss temperature (K)
T: Temperature (K)
\chi: Susceptibility (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\chi=C/(T-\theta)

$T \in \left[5, 800\right]$

$T = 5$ $\chi = 6$

Along the curve

②

Domain of the variable — blue

T_{\min} = 5,\quad T_{\max} = 800

$T \in \left[5, 800\right]$

$T = 5$ $T = 5$

Along the curve

③

Response curve — green

\chi=C/(T-\theta)

$T \in \left[5, 800\right]$

$T = 5$ $\chi = 6$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\chi}{\mathrm{d}T}

$T \in \left[5, 800\right]$

$T = 10$ $\chi^{\prime} = 0$

Along the curve

Lecture brief

Historical brief

Drude electrons, Bloch waves, BCS pairing (1957) and Wiedemann–Franz heat are the first solids-and-metals laws. The lab is conductivity, gap and phonon heat in closed form. This sheet (CND-18 — Curie–Weiss susceptibility) is the form associated with Curie–Weiss. Working symbols: $C$ , $\theta$ , $T$ $\rightarrow$ $\chi$ . θ > 0 ferromagnetic, θ < 0 antiferromagnetic. Divergence is cut off by order.

Purpose

Purpose: compute

\chi

from

C

\theta

T

in Condensed matter via

\chi=C/(T-\theta)

χ = C / (T − θ). Mean-field magnet above a Curie (or Néel) temperature. Use it when a real condensed matter question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

C = 1.200\,\mathrm{K}

\theta = 100.000\,\mathrm{K}

T = 300.000\,\mathrm{K}

, the governing relation

\chi=C/(T-\theta)

yields

\chi = 0.006\,\mathrm{—}

. A 1/(T−θ) curve, a pole at θ. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Curie constant C1.2 KWeiss temperature \theta100 KTemperature T300 K

Outputs

Susceptibility \chi0.006 —

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Narration of this film

A 1/(T−θ) curve, a pole at θ.

θ > 0 ferromagnetic, θ < 0 antiferromagnetic. Divergence is cut off by order.

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