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the pure solvent element. As the concentration is increased, magnetic
ordering is observed at correspondingly higher temperatures. Because
of the long range of the indirect exchange interaction, all systems of rare
earth Kramers-ions in Y which have so far been studied order in the
c
-
direction at suciently low temperatures, although there may be some
disorder in the plane (Caudron
et al.
1990). It would be interesting to
examine by neutron diffraction even more dilute systems, to clarify the
mechanism by which the moments are aligned. As the concentration
of heavy rare earths in Y is further increased, the alloys change rather
rapidly from crystal-field to exchange-dominated systems. This process,
and especially the transition from crystal-field to spin-wave excitations
(Wakabayashi and Nicklow 1974), deserves detailed examination.
The potentiality for adjusting the interactions to fabricate concen-
trated alloys with novel magnetic properties is restricted only by the
imagination. The Ho-Er system is a good example, in which the rich-
ness of the phase diagrams of the two constituents, and the competing
crystal-field anisotropies, give rise to a great variety of structures, es-
pecially in a magnetic field. The excitations of such binary alloys have
only been investigated to a limited extent. The most systematic studies
have so far been those on Tb alloys, which are well described by the av-
erage crystal or virtual crystal approximations. It would be interesting
to examine a system in which lifetime effects are suciently pronounced
to allow a comparison with the predictions of the coherent potential ap-
proximation; Pr alloys may be good candidates in this context. It would
also be informative to investigate the behaviour of light rare earths dis-
solved in the heavy elements, and vice-versa. Preliminary studies have
been made of Er in Pr, and Pr in Tb would be a natural choice for a
complementary system. We have only peripherally discussed compounds
of rare earths with other elements, but they may possess novel and inter-
esting properties. Of particular significance are compounds with mag-
netic transition metals, such as ErFe
2
(Clausen
et al.
1982) and HoCo
2
(Castets
et al.
1982), which display a striking interplay between itin-
erant and localized magnetism. As mentioned earlier, Ce compounds
constitute a field of magnetism in themselves. Their properties vary
from highly localized magnetism, often with very anisotropic interac-
tions, through mixed-valent systems with heavily quenched moments,
to non-magnetic heavy-fermion superconductors. They are thus ideally
suited for investigations of the limits and breakdown of the standard
model.
It is a vain ambition for any authors to aspire to write the last word
on any subject; there is always more to say. We have rather attempted
to summarize the present state of knowledge and understanding of rare
earth magnetism, and indicate some directions for future research. It is
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