SPIN WAVES IN THE FERROMAGNETIC HEAVY RARE EARTHS - Rare Earth Magnetism: Structures and Excitations - page 254

Fig. 5.11. Excitations in the c -direction of Tb 90 Tm 10 at 4 K. The
Tb magnon modes, the crystal-field excitations on the Tm ions, and
the transverse phonons polarized parallel to the magnetization mutu-
ally interfere to produce the calculated dispersion relations shown by the
thick lines. The dashed lines indicate the unperturbed Tb magnons, and
the short and long dashes the phonons. A and O signify acoustic and
optical respectively.
of Jensen et al. (1975) of the magnon dispersion relations. The magnon-
phonon interaction, which plays an important role in determining the
dispersion relations, was incorporated in the calculations by the method
which will be presented in Section 7.3.1, which leads to results consis-
tent with those derived in Section 5.4.2. The effective exchange between
the moments on the different ions was scaled as in eqn (5.6.1-2), but
γ was given the value 0.24, instead of the 0.33 which (5.6.2) yields, in
order to fix correctly the energy of the first excited state on the Tm
ions. Such a departure from the simple de Gennes scaling is not partic-
ularly surprising for ions with very different orbital angular momenta.
In the system Pr 95 Er 5 , for example, Rainford et al. (1988b) found that