A model paramagnetic salt has formula units per cubic metre

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetic materials · Magnetic materials

The Boundary-Value Problem, Ch Diamagnetism, paramagnetism and magnetic susceptibility

Problem

A model paramagnetic salt has

N_v = 5.0\times10^{26}

formula units per cubic metre. Each formula unit holds one ion with a permanent moment

m = 1.73\,\mu_B

and, counting every ion and water molecule in it,

Z = 200

electrons, which we describe by one representative radius

\langle r^2\rangle^{1/2} = 0.60\,\text{\AA}

. Its susceptibility is measured in a small field. ((a)) Show that the ratio of the salt's paramagnetic susceptibility to the size of its diamagnetic one is

2m_em^2/(e^2Z\langle r^2\rangle k_BT)

, and find the temperature

T^*

above which the diamagnetic term would be the larger. ((b)) Find the salt's total susceptibility at

100\,\mathrm{K}

and at

300\,\mathrm{K}

. ((c)) A student draws a Curie plot of

1/\chi_m

against

T

through these two measured values and reads the moment from its slope, ignoring the diamagnetic term. What moment does she find, and by what percentage is it wrong? ((d)) Suggest a way of plotting the same measurements that returns both the true moment and the diamagnetic term, and explain why it works.

Related theory

Magnetic materials

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