SPIN WAVES IN PERIODIC STRUCTURES - Rare Earth Magnetism: Structures and Excitations - page 309

Fig. 6.5. The energies of the magnetic excitations propagating in
the c -direction in the 19-layer and 9-layer spin-slip structures of Fig. 2.5.
The solid lines indicate the positions of the main peaks in the calculated
spectrum, whereas the dashed extensions designate peaks of relatively
lower intensities. The energy gaps due to the reduced symmetry are not
resolved in the experimental measurements of Nicklow (1971).

as illustrated in Fig. 6.5. The dispersion relations are broken into short
segments by a succession of energy gaps, which may however be dicult
to identify because of intrinsic broadening effects, neglecting in the RPA,
which become more and more pronounced at increasing temperatures.
At temperatures above about 50 K, when

O 6

in Ho is small and
the distortion of the helix correspondingly weak, the large B 6 still plays

an important role in mixing J z > molecular-field (MF) states. Indeed,

as the temperature is increased and the exchange field decreases, this
effect becomes relatively more important, so that, for example, the en-
ergy difference between the two lowest MF levels varies by an order of
magnitude as the moment on the site moves from an easy to a hard
direction at elevated temperatures, while this variation is much smaller
in the low-temperature limit. The large changes in the MF states from
site to site tend to disrupt the coherent propagation of the collective
modes, providing a mechanism for the creation of energy gaps in the
excitation spectrum. The spectrum thus becomes similar to that of the
incommensurable longitudinal phase, illustrated in Fig. 6.3.
Whenever the moments are not along a direction of high symmetry,
B 6 mixes the transverse and longitudinal components of the single-site
susceptibility, so that the normal modes are no longer either pure trans-
verse spin waves or longitudinal excitations. At low temperatures, where

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