Environmental Engineering Reference
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Fig. 5.10.
Isotropic and anisotropic two-ion coupling parameters
I
(
q
)
(upper curve) and
K
(
q
) (lower curve) for Tb at 4 K, deduced from the
field dependence of the spin-wave energies. The former is closely related
to
J
[
J
(
0
)
−J
(
q
)], an estimate of which is indicated by the dashed line.
The magnon-phonon interaction causes relatively large uncertainties at
intermediate wave-vectors.
anisotropy
(
q
)is
very small. The
φ
-dependent anisotropy is detected very clearly in the
experiments, since it gives rise to a change in the dispersion
E
q
(
T
),
when the moments are rotated from the the easy to the hard planar
direction.
C
(
q
) is about the same magnitude as
K
(
q
), while
D
(
q
)isthe
q
-dependent generalization of the
φ
-dependent
anisotropy ∆
M
in
A
0
+
B
0
, introduced in the previous section, and
∆
M
C
q
.
As mentioned in Section 5.4.1, the corrections to the field depen-
dence of the magnon energies in (5.5.17) were included in an effective
fashion, neglecting changes due to the rotation of the moments and as-
suming
η
−
≈−C
(
q
)
σ
−k
,where
k
may be estimated to be
about 0.3. The renormalization effects are thus taken as proportional to
σ
raised to a power which depends on the term considered. We estimate
that the effects neglected in this approach only introduce corrections
of the order of the experimental uncertainties. The two-ion coupling
1
/η
+
{
1
−
b
(
T
=0)
}
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