Environmental Engineering Reference
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tions are thereby increased, while the dispersion becomes smaller. If
the field is applied along the
ξ
-axis, the
ξ
-mode parameters are changed
approximately twice as much, relative to their zero-field values, as the
η
-mode parameters. At
H
=43
.
5 kOe, the total molecular field, which
determines the energies in Fig. 7.12, is 100 kOe, and ∆
ξ
=4
.
29 meV,
whereas ∆
η
=3
.
86 meV. This means that the field produces the largest
effects on the excitations polarized (predominantly) parallel to it, which
in Fig. 7.14 are the transverse modes, both when
q
is along ΓM and
along ΓKM. The
γ
-strain coupling opposes the splitting of the trans-
verse and longitudinal modes, but only quadratically in the field. The
hexagonal anisotropy does not affect the effective (
J
= 1)-excitations in
zero field, but
B
6
causes a splitting between the
|
3
s
>
and
|
3
a
>
-states
of nearly 5 meV. As
B
6
3
s
>
which, according to Fig. 1.16 or 7.12, should lie only 0.9 meV above
the
is negative, the lower of the two states is
|
1
s,a
>
-states. The magnetic field induces a coupling between this
neighbouring level and the doublet excitations, so that it acquires a sig-
nificant scattering cross-section at the energies indicated by the dashed
lines in Fig. 7.14. Although the extra peak was not suciently distinct
to be detected directly in the neutron-scattering experiments, the pres-
ence of this level is clearly manifested in the behaviour of the doublet
excitations. The absolute minimum in the excitation spectrum at zero
field is found along ΓM, whereas at
H
=43
.
5 kOe the energy minimum
in the ΓK-direction has become the lowest. The
|
3
s
>
-excitations are
coupled to the doublet excitations polarized along the
ξ
-axis, both when
the field is along the
ξ
-andthe
η
-axis. This means that the energy
increase of the longitudinal (optical) mode in the ΓK-direction is dimin-
ished, due to the repulsive effect of the field-induced coupling to the
|
|
3
s
>
-excitations. When the field is along the
ξ
-direction, the longitu-
dinal modes in the ΓM-direction are coupled to the
3
a
>
-excitations,
which lie at much higher energies and only perturb the lower modes very
weakly. The basal-plane anisotropy is also clearly reflected in the field
dependence of the elastic constant
c
66
, shown in Fig. 7.5.
The effects of the field on the hexagonal doublet-excitations are
very strong. In comparison with the zero-field result of Fig. 7.1, the
minimum-energy modes have more than doubled their energies, while
the overall width of the excitation bands has been reduced by nearly
a factor of two. Because of these large changes, the measurement of
the field dependence of the excitation spectrum allowed a rather precise
determination of ∆ and the relative position of the
|
|
3
s
>
crystal-field
level. With the assumption that
B
6
(77
/
8)
B
6
, these results then
led to the crystal-field level-scheme for the hexagonal ions shown in
Figs. 1.16 and 7.12, leaving only the position of the highest-lying level
somewhat arbitrary. The field experiment also determined the value of
=
−
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