PERSPECTIVES FOR RARE EARTH RESEARCH - Rare Earth Magnetism: Structures and Excitations - page 371

The contribution of the spin-orbit coupling in the conduction-electron
gas to the single-ion anisotropy could also be estimated and compared
with the low-temperature experimental results, taking into account the
readily computed dipolar contribution. A knowledge of both the ex-
perimental and theoretical masses on a variety of orbits would allow a
stringent test of the theory of mass-enhancement by the spin waves. The
rich structure in the low-frequency dHvA spectrum of Pr may reflect the
hybridization with the 4 f electrons, which presumably gives rise to the
quasielastic neutron-diffraction central peak, and also apparently makes
a contribution to the binding in the light rare earths. An immediate
goal of a first-principles calculation of the indirect exchange in Pr would
be an explanation of the large anisotropy which is revealed by the dis-
persion relations for the magnetic excitations. This would require an
extension of the theory of the influence of the orbital angular momen-
tum on the two-ion coupling to more realistic electronic structures than
the free-electron model which is normally considered. If this could be
accomplished, a first-principles account of the observed scaling of the
exchange with the de Gennes factor in the elements could be envisaged.
An accurate knowledge of the electronic structure would also open
the way to a calculation of the source of the other primary interaction,
the crystal field, which is determined by the charge distribution. The
non-spherical terms, which give rise to the higher- l components of the
crystal field, are neglected in the averaging procedure adopted in the
construction of the mun-tin potential, but both they and the non-
uniformity of the charge distribution in the interstitial regions can in
principle be calculated self-consistently. Such a calculation for Y, for
example, would cast some light on the origin of the crystal-field split-
tings observed in dilute alloys with magnetic rare earths. However, the
main barrier to calculating the full crystal-field Hamiltonian again re-
sides in the other part of the problem, the screening of the fields by the
atomic core and the 4 f electrons themselves. This is indeed a formidable
diculty, but presumably not one which is insurmountable.
A constant theme, running in parallel with the steady improvement
of the standard model, has been the question of the nature of the 4 f
states in Ce and its compounds. As has been apparent for some time,
the standard model is not applicable to, for example, α -Ce, as the 4 f
electrons are itinerant, make a substantial contribution to the binding,
and must be described by the band model. We have said relatively
little about mixed-valent Ce compounds, primarily because they lie out-
side the main scope of this topic, but also because the subject is in a
very rapid state of development, making any kind of meaningful sum-
mary both dicult and ephemeral. Nevertheless, there is no question
that the study of the magnetic properties of these materials, and of the