Physics of Magnetism

66 CHAPTER 7. ITINERANT-ELECTRON MAGNETISM

This quantity describes the magnetic susceptibility in metallic systems in which there is no

interaction between the band electrons. This means that and thus that the Stoner

enhancement factor reduces to unity. By contrast, the enhancement

factor can reach fairly high values when there is a strong interaction between the electrons

and/or when the density of electron states at is high, in fact, the Stoner enhancement

factor can become extremely high for metallic systems close to magnetic instability, that

is, when the Stoner criterion is fulfilled. We mentioned already that such a situation occurs

for Pd metal. Experimentally, one finds that the susceptibility of Pd metal is roughly one

order of magnitude larger than, for example, of Zr metal.

7.3. STRONG AND WEAK FERROMAGNETISM

In order to explain the principles of 3d-electron magnetism, up to now we have used a
simplified model with rectangular 3d bands (Fig. 7.1.1). In a more realistic treatment, one
has to take account of the actual shape of the 3d band in the energy range of interest (Friedel,
1969). This means that the density of states is no longer a constant over the whole energy
range considered but may vary strongly as a function of the energy when moving from the
bottom of the 3d band to the top. Generally, one finds that the density of states of the 3d
band first increases when moving from the bottom of the 3d band in upward direction. After
reaching a region where the density of states is high, one passes into a region where the
density of states is fairly low. Moving further to the top of the band, one encounters again
a region where the density of states is high.
When, for a given degree of 3d-band filling, the Fermi energy happens to be located in
a region where the density of states is relatively low, the Stoner criterion may not be met and
a spontaneous moment may form only if higher and lower lying states are included where
the density of states is higher than in the immediate vicinity of the Fermi energy. Such a
situation is schematically represented in Fig. 7.3.1.
Owing to the high kinetic-energy expenditure in the region where the density of states is
low, no formation of a spontaneous moment will occur for small amounts ofelectron transfer,
that is, for small 3d moments. The average energy expenditure is lower and spontaneous
moments may form when electron states in the region with higher density of states are
included. This implies that the formation of a spontaneous moment is only possible if the