A crystal of a gadolinium salt has ions 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 crystal of a gadolinium salt has

N_v=2.0\times10^{26}

\mathrm{Gd^{3+}}

ions per cubic metre, each with effective moment

m=7.94\,\mu_B

read from a Curie plot. ((a)) Use the Curie law

\chi_m=\mu_0N_vm^2/3k_BT

to find

\chi_m

T=300\,\mathrm{K}

B=1.0\,\mathrm{T}

. ((b)) At

T=2.0\,\mathrm{K}

in a field

B=6.0\,\mathrm{T}

, compute

mB/k_BT

and decide whether the same linear Curie-law calculation could be trusted at this temperature and field.