Diamagnetism — Question 6

Question 6

Two temperatures separate a diamagnetic background from a Curie term

A sample follows $\chi(T)=\chi_d+C/T$ with constant negative $\chi_d$. Measurements give $\chi(100\,\mathrm K)=2.0\times10^{-5}$ and $\chi(300\,\mathrm K)=-2.0\times10^{-5}$.

1. Find C and the diamagnetic background.

2. Find the temperature at which the net susceptibility vanishes and determine the sign above that temperature.

Question 6 - Solution

Two temperatures separate a diamagnetic background from a Curie term

(a) Method and calculation

$$\chi(100)-\chi(300)=C(1/100-1/300)\Rightarrow\boxed{C=6.0\times10^{-3}\,\mathrm K}.$$$$\boxed{\chi_d=2.0\times10^{-5}-C/100=-4.0\times10^{-5}}.$$

(b) Interpretation and further calculation

$$0=\chi_d+C/T_*\Rightarrow\boxed{T_*=-C/\chi_d=150\,\mathrm K}.$$$$T>T_*\Rightarrow C/T<|\chi_d|\Rightarrow\boxed{\chi(T)<0}.$$

Physical check

The change of sign reflects competing responses in the specified model; it is not a change in the sign of the diamagnetic contribution.