A magnetic susceptibility balance measures the volume susceptibility of a manganese…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Quantum Mechanics · Symmetry, angular momentum and spin

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

Problem

A magnetic susceptibility balance measures the volume susceptibility of a manganese ammonium sulphate salt, in which the number density of

\mathrm{Mn^{2+}}

ions is

N_v = 2.0\times10^{27}\,\mathrm{m^{-3}}

. The reciprocal of the measured volume susceptibility is read from the plotted Curie line at two temperatures:

T = 100\,\mathrm{K}

1/\chi_m = 547

T = 300\,\mathrm{K}

1/\chi_m = 1642

((a)) Find the slope of

1/\chi_m

against

T

and hence the Curie constant

C

(in kelvin), using

\chi_m = C/T

. ((b)) Use

C = \mu_0N_vm^2/3k_B

to extract the effective moment

m

per ion in units of the Bohr magneton

\mu_B = 9.274\times10^{-24}\,\mathrm{J\,T^{-1}}

, and compare with

g_J\sqrt{J(J+1)}\,\mu_B

for

\mathrm{Mn^{2+}}

(

S = 5/2

L = 0

g_J = 2

). ((c)) At

B = 2\,\mathrm{T}

and

T = 100\,\mathrm{K}

, evaluate

\mu_BB/k_BT

and say whether the salt is close to saturation at this field and temperature, i.e. whether the linear Curie law used above is justified.