ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 11

one 4 f electron, and Tm, which has one 4 f hole in the atom, though
two in the metallic state. The angular dependences of the 4 f wavefunc-
tions are depicted in Fig. 1.2. The charge clouds are highly anisotropic,
with pronounced multipoles whose magnitudes and signs change dra-
matically with m l . As we shall see, this anisotropy is clearly manifested
in the magnetic properties of the metals.
Since they are among the heavier elements, relativistic effects are of
substantial importance in the rare earths. These are most straightfor-
wardly taken into account by solving the Dirac equation in the central
Fig. 1.1. The radial components of atomic wavefunctions for Ce, which
has one 4 f electron, and Tm, which has 13 4 f electrons, or one 4 f hole.
The Tm wavefunctions are contracted, relative to those of Ce, due to the
incomplete shielding of the greater nuclear charge. As a consequence, the
amplitude of the 4 f wavefunction at the indicated Wigner-Seitz radius
is much greater in Ce than in Tm, which has important consequences
for the character of the 4 f states in the metals.