16 CHAPTER 3. PARAMAGNETISM OF FREE IONSThe magnetic splitting of the ground-state multiplet level (J = L – S = 5 –5/2 = 5/2)
and the first excited multiplet level (J = L – S + 1 = 5 – 5/2 + 1 = 7/2) is illustrated in
Fig. 3.2.2. Note that the equidistant character is lost not only due to the energy gap between
the J = 5/2 and J = 7/2 levels but also due to a difference in energy separation between
the levels of the J = 5/2 manifold (g = 2/7 and the levels of the J = 7/2 manifold
(g = 52/63).
Generally speaking, it may be stated that the Curie law as expressed in
Eq. (3.2.3), is a consequence of the fact that the thermal average calculated in Eq. (3.1.4)
involves only the 2J + 1 equally spaced levels (see Fig. 3.1.1) originating from the effect of
the applied field on one multiplet level. Deviations from Curie behavior may be expected
whenever more than these 2J + 1 levels are involved (as for and or when these
levels are no longer equally spaced. The latter situation occurs when electrostatic fields in
the solid, the crystal fields, come into play. It will be shown later how crystal fields can also
lift the degeneracy of the 2J + 1 ground-state manifold. The combined action of crystal
fields and magnetic fields generally leads to a splitting of this manifold in which the 2J + 1