72 CHAPTER 7. ITINERANT-ELECTRON MAGNETISMCloser inspection of the bands in Fig. 7.4.3 reveals the following. The spin-up and
spin-down rare-earth 5d-band states mix with the transition-metal 3d-band states but do
so to a different degree. The reason for this is the exchange splitting between the spin-
up and spin-down 3d bands. For the spin-down electrons it leads to a smaller separation
in energy between the 5d- and 3d-electron bands than for the spin-up electrons. There
fore, the mixing of 3d-band states and 5d-band states is larger for spin-up electrons than
for spin-down electrons. As is indicated by the black and white areas in Fig. 7.4.3, the
5d(R)–3d(T) mixing leads to a larger 3d character of the 5d spin-down band than of the
spin-up band. Consequently, the overall 5d(R) moment is antiparallel to the overall 3d(T)
moment.
This mixing scheme is true for any rare-earth element R, independent of whether a 4f
moment is present on the R atoms or not. When a 4f moment is present, one has ferro
magnetic intra-atomic exchange interaction between the 4f-spin moment and the 5d-spin
density, so that also the 4f-spin moment is antiparallel to the 3d moment. Summarizing these
results, one can say that the rare-earth 5d electrons act as intermediaries for the coupling