PERSPECTIVES FOR RARE EARTH RESEARCH - Rare Earth Magnetism: Structures and Excitations - page 378

this phase, but the full characterization of the excitations as a function
of the strain, temperature, and field is clearly a major enterprise. Of
immediate interest would be a renewed effort to observe the amplitude
mode, which should be visible at low temperatures.
Despite the impressive range of information which has been attained
by accurate measurements of the magnetic structures and excitations
under various external conditions, the investigation of the two-ion inter-
actions which supplement the dominant isotropic RKKY exchange is by
no means complete. Low-symmetry two-ion couplings are clearly impor-
tant in Pr and Nd. In addition to the anisotropic contribution ( ij )in

(2.1.41), which accounts for the stability of the longitudinal ordering of
the moments and the splitting of the doublet-excitations in Pr, a further
term must be included to explain the c -axis moments on the cubic sites
in Nd, which are induced by the ordered basal-plane moments on the
hexagonal sites. In the heavy rare earths Tb and Er, there is indirect but
weighty evidence that anisotropic interactions are essential for explaining
the excitation spectra. The strong optical-phonon - acoustic-magnon in-
teraction in the c -direction of Tb is of fundamental significance, since it
reveals that the spin-orbit coupling of the conduction electrons results
in a spatially varying deviation between the direction in which their
spins are polarized and that of the ferromagnetic ionic moments. The
spin-orbit coupling may also be important for explaining the possible
occurrence of interactions, such as the example given in (2.1.39), which
reflect the reduced three-fold symmetry of the c -axis in the hcp lattice.
Indications that this kind of coupling is present in Ho have appeared in
the possible detection by Cowley and Bates (1988) of a modulated c -axis
moment in the commensurable helical structures, and the unusual sta-
bility of the Q = π/ 2 c -structure around 96 K (Noakes et al. 1990). The
c -axis moments should alternate in sign between each pair of planes in
the spin-slip structures of Fig. 2.5, being zero on the spin-slip planes, so
that Q c =2 π/c

K

3 Q = π/c in the twelve-layered zero-spin-slip structure.
The aforementioned mutual solubility of the rare earth elements
gives unlimited possibilities for fabricating systems with adjustable mag-
netic properties. Dilute alloys of magnetic ions in non-magnetic hosts
such as Y have proved particularly interesting, largely because the crys-
tal fields may be studied in the absence of the exchange interaction and
its possible anisotropy. The crystal-field levels have primarily been deter-
mined by measurements of the magnetic moments, but further neutron-
scattering studies, which are possible with modern experimental tech-
niques even in very dilute systems, would be even more enlightening,
especially in a magnetic field. These systems can also be effectively
investigated by the straightforward means of measuring the electrical
resistivity as a function of temperature and field, and comparing with

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