Environmental Engineering Reference
In-Depth Information
The study of the excitations by inelastic neutron scattering has pro-
vided diverse and detailed information on the magnetic interactions. A
glance at the dispersion relations of, for instance, Gd, Tb, and Pr im-
mediately reveals the relative importance of the exchange and crystal
fields in these elements. Careful measurements as a function of tem-
perature and external fields, combined with a systematic analysis, yield
an abundance of knowledge about these and other interactions. Further
information is contained in the neutron-scattering intensities, though
these have so far been relatively little utilized. However, in some cases,
relative intensities have allowed a discrimination between different mod-
els, and if the dicult experimental problems can be overcome, absolute
intensity measurements could provide a valuable supplement to the en-
ergies and lifetimes. The philosophy adopted in analysing measurements
of excitation spectra has generally been to use the simplest theory and
set of interaction-parameters which can provide a satisfactory fit to the
experimental results available at any particular time. The anisotropic
exchange may, for example, be subsumed in effective isotropic exchange
and crystal-field parameters, so that it is necessary to treat such quan-
tities with caution when comparing with values deduced from different
kinds of measurements, or from a fundamental theory.
The excitations to which the greatest efforts have been devoted are
the spin waves in the heavy rare earths. Gd, with negligible anisotropy,
is the simplest example and the dispersion relations have been carefully
measured over a range of temperatures, in an isotopically pure sample.
The lifetimes have also been studied, but not as a function of wave-vector
at low temperatures, which would allow an examination of the scattering
by the conduction electrons, without the interference by the magnon-
phonon interaction which partially disturbed the experiments on Tb.
Gd would also be the prime candidate for a detailed comparison with a
realistic theory, using the calculated band structure and measured Fermi
surface rather than the free electron model. The isotropy of the exchange
could be examined, to within the limitations of the experimental resolu-
tion, by applying a magnetic field, and a study of dipolar effects at long
wavelengths might also be possible. Despite the attention which has
been devoted to elucidating the excitation spectrum of Tb, a number of
questions remain. The relative importance of single- and two-ion contri-
butions to the macroscopic anisotropy and spin-wave energies could be
further clarified by more precise measurements in a field, taking full ac-
count of the influence of the dipolar coupling at long wavelengths. The
origin of the hard-axis axial anisotropy, and the discrepancy between
the macroscopic and microscopic hexagonal anisotropy, could thereby
be further investigated. The study of the magnon-phonon interaction,
which has earlier provided some fruitful surprises, could profitably be
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