Solid State 2 – Exercise 6
1. Consider an ion with a partially filled shell of total angular momentum J , and
Z additional electrons in filled shells. Show that the ratio of the paramagnetic
susceptibility to the Larmor diamagnetic susceptibility is:
2
 par
2 J ( J  1)

 dia
Zk BT m r 2
and estimate its magnitude.
2. Compare Eqs. (4.9) and (4.15) from section 3, ie. Curie vs. Pauli magnetization, and
discuss the similarity and the difference between the two cases.
3. Show that the magnetization of a nondegenerate electron gas is precisely
given by the result
M 
N F N
  JBJ (  JH )
V H V
(3.26)
With J=1/2, by inserting the low density expansion of the Fermi function
f  e  (   )
into the following equation:
n   d  g (
 B H ) f ( )
4. A system of N non-interacting spins S=1/2 is placed in a magnetic field of
strength B0. Find and plot the specific heat capacity:
 U 
Cmagnetic  

 T V
(U is the energy of the system).
What is the meaning of this shape ? Does it have a name ?