CRYSTAL-FIELD EXCITATIONS IN THE LIGHT RARE EARTHS - Rare Earth Magnetism: Structures and Excitations - page 362

Fig. 7.14. Dispersion relations for the excitations propagating on
the hexagonal sites of Pr at 6 K, in an applied field of 43.5 kOe. The
field is in the basal plane and perpendicular to the wave-vector, so that
there is a discontinuity at M, corresponding to a rotation of the field
through 90 ◦ . Compared with Fig. 7.1, the energy of the magnetic exci-
tations has increased, and the field has induced couplings between the
magnetic excitons and the transverse-acoustic phonons polarized in the
basal plane, indicated by dashed lines. These phonons are coupled to the
acoustic and optical longitudinal magnetic modes in the ΓM-direction,
and to the (predominantly) acoustic longitudinal and optical transverse
modes (the two branches of intermediate energy) in the ΓK-direction
(Jensen 1976a). The full lines show the results of an RPA calculation of
the magnetic excitations, neglecting the coupling to the phonons. The
predicted low-intensity higher-lying modes, corresponding to transitions
to the predominantly | 3 s > crystal-field state, were not observed directly
in the experiments, but their influence may be seen in the lowest branch
along ΓK, since it is their mixing with this mode which holds the energies
below those along ΓM.

a field is applied in the basal plane at low temperature. The dispersion
relation was measured at three values of the field (14.5, 29.0, and 43.5
kOe), and the results obtained at the highest field are shown in Fig.
7.14.
The most important effect of the field is the admixture of

| 1 s,a >

into the ground state. This causes ∆ ξ and ∆ η to increase, and the

matrix elements M ξ and M η to decrease. The energies of the excita-