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and it may be described by a few interplanar coupling parameters of the
type used for other two-ion interactions. Cohen and Keffer (1955) have
calculated the
q
-dependence for the three cubic Bravais lattices, and
their results also determine approximately
D
αβ
(
q
), with
q
along the
c
-
axis, in the hcp lattice with the ideal
c/a
-ratio, since this is equivalent to
q
along a (111)-direction in the fcc crystal. In the distorted case, with
c/a
=0
.
963
8
/
3 (corresponding to Ho), a numerical calculation gives
=
0
.
9190 + 0
.
0816 cos (
qc/
2)
0
.
0006 cos (
qc
)
4
π
3
D
ξξ
(
q
)+0
.
0221
4
π
3
−
when
q
10
/L
, so that the
q
-dependence in the
c
-
direction is very weak, exceptforthejumpatsmall
q
, which is illustrated
for the example of Ho in Fig. 5.7.
In a uniform ferromagnet, the demagnetization factor leads to a pos-
itive contribution to the internal energy. Without any external applied
c
-axis and
q
≥
Fig. 5.7.
Parallel and perpendicular components of the Fourier trans-
form, for
q
along the
c
-direction, of the two-ion coupling in Ho, deduced
from the spin-wave energies. The coupling is assumed to comprise an
isotropic indirect-exchange contribution and the classical dipole-dipole
interaction, which gives rise to the discontinuity at
q
=
0
in the parallel
component, and stabilizes the cone structure at low temperatures.
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