ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 29

The most powerful experimental technique available for studying
the details of the electronic structure in the vicinity of the Fermi level is
the de Haas-van Alphen (dHvA) effect (Shoenberg 1983), which allows
a precise determination not only of the shape of the Fermi surface, but
also of the effective masses of the electrons whose wave-vectors lie on it.
Unfortunately, the metallurgical diculties encountered in attempting
to fabricate pure single crystals have so far precluded the observation of
the effect in α -Ce, but Johanson et al. (1981) studied the related com-
pound CeSn 3 , and demonstrated that it contains itinerant f electrons
of large mass at low temperatures. More recently, a number of exam-
ples of heavy-fermion Ce compounds have been investigated (Reinders
et al. 1986; Lonzarich 1988) in which the effective masses, as deduced
either from the dHvA effect or the low-temperature heat capacity, are
enhanced by up to an order of magnitude compared with those deduced
from band structure calculations.
There is thus very convincing evidence that the f electrons in Ce
and its compounds can form bands and extend in coherent Bloch states
throughout the crystal. Photoemission experiments in α -Ce (Wieliczca
et al. 1982; Martensson et al. 1982) revealed a structure with two peaks,
which may plausibly be associated respectively with an itinerant f hole
near the Fermi level, and one localized for a finite time at a particular
ionic site (Norman et al. 1984; Mackintosh 1985). There are very few
indications of itinerant f behaviour in the other rare earth elements, al-
though the above-mentioned double-peaked structure is also observed in
γ -Ce and Pr (Wieliczka et al. 1984), in both of which the f electrons are
normally considered as localized, and as we shall see, there is evidence of
an f contribution to the binding energy in some of the light rare earths.
After this brief interlude, we will therefore leave the question of f bands
and return to the standard model of f electrons localized on the ions,
interacting with the surroundings but only indirectly with each other.
Pr, the neighbouring element to Ce, undergoes a phase transition at
high pressures (Wittig 1980) which is probably associated with the for-
mation of a band by the f electrons (Skriver 1981; Eriksson et al. 1990),
but at ambient pressures they are localized and may be considered as
part of the ionic core. Indeed, intermultiplet transitions, corresponding
to those occurring on Pr ions in insulators, but shifted due to screening
by the conduction electrons in the metal, have been observed by Taylor
et al. (1988), using inelastic neutron-scattering at relatively high ener-
gies. The 4 f states do not therefore appear in the energy bands of Fig.
1.9, which portrays broad sp bands hybridized with a much narrower d
band. As will be discussed later, Pr is paramagnetic above about 50 mK,
and in zero field the Fermi surface, which is relatively complex, may be
deduced from the figure to be composed of 2 electron pockets and 4 open