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ance of higher harmonics in neutron diffraction (Koehler
et al.
1966). As
illustrated in Fig. 2.4, the peak in
(
q
) simultaneously moves to smaller
values of
q
,andthe
Q
of the magnetic structure decreases correspond-
ingly. However this change does not occur uniformly with temperature,
but rather a series of
commensurable
wave-vectors is traversed, with ap-
parently discontinuous jumps between them (Gibbs
et al.
1985). At 20
K, a second-order transition to a shallow cone structure, with an opening
angle which decreases continuously towards 80
◦
as the temperature is
lowered, is observed. The helical component is commensurable with the
lattice, with an average turn angle of 30
◦
, but the moments are strongly
bunched around the easy
b
-axes, as shown in Fig. 1.20.
To interpret this rich variety of phenomena, we will use the model
of Larsen
et al.
(1987). The Hamiltonian which they constructed has
J
Fig. 2.4.
The Fourier transform, for wave-vectors in the
c
-direction,
of the indirect-exchange interaction in Ho at different temperatures, de-
duced from the magnetic excitations and used in the calculation of the
structures. The maximum in
J
⊥
(
q
) increases in magnitude and moves to
larger wave-vectors as the temperature is increased, leading to a decrease
in the repeat distance of the periodic structures.
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