ALBERTO BOLLERO REAL

2.2 Magnetic properties
(i) The rare-earth (R) series
The rare-earth series presents an incomplete filling of the 4f shell. The number of
electrons in the inner 4f shell varies from 0 to 14 through the series La (atomic number in
the periodic table: Z = 57) to Lu (Z = 71). The total magnetic moment of an R-atom has
both orbital and spin components. However the 4f shell is not the outermost shell of the
atom. Figure 2.2 illustrates the position of the 4f shell for Nd (Z = 60) where the 3
electrons with unpaired spin are localised. The R-R exchange-coupling between two R
atoms in a solid is indirect because the direct overlap between the 4f shells of adjacent
rare-earth atoms is negligible. The resulting weak magnetic interaction with the 4f
electrons of neighbouring atoms, results in low Curie temperatures of the ferromagnetic
rare-earth metals; in fact, all of them have a T C below room temperature (only Gd has a
Curie temperature as high as ambient temperature, T C = 20°C).
Nd
Fe
3d shell
4f shell
5d shell
0.21nm
0.36nm
0.25nm
Fig. 2.2: Positions of the unpaired electron shells in Nd and Fe atoms (from Coey [3]).
(ii) The transition-metal (T) elements: Fe, Co and Ni
There are three ferromagnetic transition elements: Fe, Co and Ni. The 3d electrons of
these atoms are localised in the outer shell (see Fig. 2.2). Hence in solids the 3d electrons
are considerably less localized than the 4f electrons of the rare earths. Therefore the orbital
momentum of T atoms or ions is nearly completely removed (“quenched”) by the
interaction in the solid which, of course, is not rotationally invariant and does not allow the
orbital momentum to be a good quantum number. Usually the (spin) magnetism of the T
elements in metals and intermetallic compounds is described by delocalised electrons. Fe is
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