CRYSTAL-FIELD EXCITATIONS IN THE LIGHT RARE EARTHS - Rare Earth Magnetism: Structures and Excitations - page 348

Fig. 7.7. The field dependence
of the coecient γ of the linear elec-
tronic heat capacity of Pr at low
temperatures. The experimental re-
sults of Forgan (1981) are compared
with a theory including the renor-
malization of the mass, due to the in-
teraction of the conduction electrons
with the magnetic excitations, and
also taking into account the phonon
enhancement and the dependence of
the Fermi level on magnetic field.
The dashed line shows the results of
the theory when the change of the
Fermi energy with field is neglected.

The mass-enhancement due to the crystal-field excitations is re-
flected directly in the effective mass measured in the de Haas-van Alphen
effect, and in the linear term in the low-temperature electronic specific
heat, analogously to the spin-wave system. The former effect has been
studied by Wulff et al . (1988), who find that the theory of Fulde and
Jensen (1983) accounts very well for the field dependence of the masses
of several orbits, using the same values of the sf -exchange integral I ,
about 0.1 eV, as reproduce the variation of the orbit areas discussed
in Section 1.3. The substantial field dependence of the electronic heat
capacity, measured by Forgan (1981), is shown in Fig. 7.7, and com-
pared with values calculated from eqn (7 . 3 . 21 b ), taking into account the
field dependence of the electronic state density at the Fermi level, calcu-
lated by Skriver (private communication), and the phonon enhancement
(Skriver and Mertig 1990). At higher temperatures, the imaginary part
of ( q ,ω ) in (7.3.16) gives rise to the same contribution to the magnetic

heat capacity as the extra term in (5.7.52) in the spin-wave case, with
ζ ( q ) α χ αα ( q ,ω

J

0) replacing 2Γ q /E q . This contribution should be
added to the non-linear corrections to the total low-temperature heat
capacity calculated by Fulde and Jensen (1983).

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