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state is calculated to vary between 8.0 and 10.2 meV, while the exchange
field lies between 0 and 1.8 meV. Hence the exchange field acts as a minor
perturbation, and incommensurable effects above 32 K in the excitation
spectrum should be unimportant. In the low-temperature limit, the
magnetic excitations are spin waves; the MF ground state and the first
dipolar excited state are almost pure
−
depending on the site considered). The excitations propagating in the
c
-direction are found to lie between 8.5 and 10 meV (Fernandez-Baca
et al.
1990; McEwen
et al.
1991). The magnetic period is seven times
that of the lattice, and the exchange coupling splits the spin waves into
seven closely lying bands, which cannot be separated experimentally.
With a finite resolution, the exchange coupling leads to a single or, at
some wave-vectors, a double peak, whose shape and width change with
q
. At low temperatures, a relatively strong coupling between the spin
waves and the transverse phonons is observed, and when this coupling
is included in the determination of the RPA response functions, by the
method presented in Section 7.3.1 in the next chapter, good agreement
is obtained between the calculated neutron spectra and those observed
experimentally. At elevated temperatures, both below and just above
T
N
, other excitations between the excited crystal-field (MF) levels are
observed to be important, both in the transverse and the longitudinal
components of the response function, and good agreement is again found
between theory and experiment. With respect to its magnetic proper-
ties, Tm is thus an exceptional member of the heavy rare earths, as it
is the only one in which well-defined crystal-field excitations have been
detected. Hence it provides an appropriate termination of our discussion
of spin-waves, as well as a natural transition to the crystal-field systems
which are the topic of the next chapter.
|±
6
>
and
|±
5
>
levels (+ or
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