SPIN WAVES IN THE FERROMAGNETIC HEAVY RARE EARTHS - Rare Earth Magnetism: Structures and Excitations - page 239

applies. If q is parallel to the magnetization, the spin-wave energies
are unchanged from the values deduced in Sections 5.2-4, provided that
the lattice-sum contribution is included in the axial anisotropy term
(5 . 5 . 11 b ), and eqn (5.4.38) is still valid. On the other hand, when q is
in the basal-plane and perpendicular to the magnetization, the ultrasonic
Fig. 5.9. Dispersion relations, in the double-zone representation, for
magnetic excitations propagating in the c -direction of Ho 90 Tb 10 in the
ferromagnetic phase (upper branch), and the bunched helical structure
(lower branch). The full and dashed lines for the ferromagnetic phase
show the theoretical dispersion relations at 4 K and 16 K respectively, and
the open and filled symbols are the corresponding experimental results.
The calculated long-wavelength energies in the basal plane are shown to
the left of the ordinate axis and the discontinuity, which is due to the
dipole-dipole interaction, is clearly manifested in the neutron-scattering
spectra in the inset. This discontinuity also appears in the helical phase,
and the bunching causes an energy gap on the ALH face of the Brillouin
zone, which is not resolved in these measurements.