68 CHAPTER 7. ITINERANT-ELECTRON MAGNETISM
Fig. 7.3.2b corresponds to the inequality sign in Eq. (7.3.4): The magnitude of and
the corresponding band shift is larger than required for reaching the maximum moment
for the degree of 3d-band filling considered in this figure. This situation is referred to as
strong ferromagnetism. Note that the top of the majority-spin subband falls below the Fermi
energy.
Which of these two types of ferromagnetism is reached in a given compound depends
on the actual shape of the density of states curve, the total number of 3d electrons and the
value of The most interesting example is formed by the 3d metals themselves and
their alloys. These systems usually have a bcc structure for which each of the two spin
subbands is fairly well divided into two parts with a high density of states separated by a
pronounced minimum in the density of states (as has been assumed in Fig. 7.3.2). It can
be shown by means of Eq. (7.3.4) that for such a shape of N(E) the depletion of the 3d
band with decreasing number of 3d electrons proceeds as follows. Starting from a full 3d
band, first one of the two spin subbands will become partially depleted (minority band)
and this depletion continues until the upper portion of this subband is empty. This then
leads to a further decrease of the number of 3d electrons to partial depletion of the other
spin subband (majority band). This implies a simultaneous change from weak to strong
ferromagnetism.
It is plausible that the increasing depletion of only the minority band in the regime of
strong ferromagnetism leads to an increase of the magnetic moment with decreasing number
of 3d electrons. This moment increase comes to an end, however, when the majority band
also becomes more depleted. The reason for this can be described as follows. The Fermi
level in the majority band, the latter being only slightly depleted, is in a region of a
high density of states. By contrast, the density of states at in the minority band is at or
close to the minimum in the density of states (as shown in the upper left part of Fig. 7.3.3).
Consequently, when 3d electrons are further withdrawn from the 3d band, most of these
electrons will come from the majority band where the density of states is high. This leads to
a decreasing difference in the number of electrons of opposite spin direction, and hence to