SPIN WAVES IN PERIODIC STRUCTURES - Rare Earth Magnetism: Structures and Excitations - page 298

Fig. 6.2. Spin-wave dispersion relations in the c -direction, in the cone
phase of Er at 4.5 K, after Nicklow et al. (1971a). The closed and open
symbols represent the + q and −q branches respectively. The solid lines
are the results of the spin-wave calculation described in the text, and
the dashed lines are the dispersion relations for the transverse phonons
originating from 2 π/c ± 2 Q .

only the isotropic part of the coupling, but this requires a value of L 35

meV, and the intensity ratio, in the interval π/c < q < 2 π/c , is found
to be wrong by a factor of three or more.
It has been suggested (Lindg ard 1978) that the necessity of intro-
ducing anisotropic two-ion coupling in the description of the spin-waves
in Er may be an artifact due to a breakdown of the linear spin-wave
theory. As discussed in Section 5.3.2, the linear theory is not valid in
strongly anisotropic systems, i.e. when the numerical value of the b -
parameter is large and the length of the moments is significantly smaller
than their saturation value, in the low-temperature limit. However,
the model for Er presented in Section 2.3, which describes the mag-
netic structure as a function of temperature and magnetic field reason-
ably well, predicts that σ ( T = 0) is only reduced by 1-2%, and that
| b | 0 . 08. The excitation spectrum in the cone phase may be derived,