SECTION 7.4. INTERSUBLATTICE COUPLING IN ALLOYS OF RARE EARTHS AND 3d METALS 71
means of an extension of the itinerant-electron model, as will be briefly described below. At
first sight, an explanation in terms of the itinerant-electron model seems somewhat strange
because we have treated 4f moments as strictly localized in Chapter 1. Also, in the present
section we will deal with 4f electrons as localized, but additionally we will discuss the role
played by the 5d valence electrons of the rare-earth elements. These 5d valence electrons
are accommodated in narrow 5d bands, in a similar way as the 3d electrons of 3d transition
metals are accommodated in 3d bands. In the rare-earth elements La and Lu, there are no 4f
moments (see Table 2.2.1). From the magnetic properties of these elements it can be derived
that the 5d electrons are not able to form 5d moments of their own. The reason for this is
that the Stoner criterion (see Section 7.1) is not satisfied for the corresponding 5d bands.
Nevertheless, these 5d electrons play a crucial role in the magnetic coupling between the
4f and 3d moments. Below, we will closely follow the treatment presented by Brooks and
Johansson (1993).
Let us consider an isolated molecule of the compound A schematic represen
tation of the relative positions of the Lu 5d and Fe 3d atomic levels is shown in Fig. 7.4.1
before and after the two types of atoms have been combined to form a molecule. In the
molecule, mixing of states leads to bonding and antibonding states, both states having a
mixed 3d–5d character. Although this is of no particular concern in the present treatment,
we will briefly mention that the electronic charges corresponding to the bonding states are
accumulated mainly between the participating atoms. In the antibonding states, the elec
tronic charges are accumulated mainly on the participating atoms. The bonding as well as
the antibonding states broaden into bands when forming the solid compound, as illustrated
in the left part of Fig. 7.4.2. Using the same simplified picture of rectangular bands as was
done in the first part of Section 7.1, one can represent this situation by means of the diagram
shown in the right part of Fig. 7.4.2.
Up to now, we have dealt equally with spin-up and spin-down electrons. However,
from the fact that the Fe atoms carry a magnetic moment in we know that the 3d
band splits into a spin-up and a spin-down band, as discussed in the previous sections. This
3d-band splitting is illustrated in Fig. 7.4.3. The spin-up band, shown in the lower left part
of the figure, is seen to be completely occupied. The spin-down band, shown in the lower
right part is partly unoccupied. In fact, this difference in occupation reflects the presence
of 3d moments on the Fe atoms.