Environmental Engineering Reference
In-Depth Information
Tab l e 2 . 2 .
The arrangement of blocks of spins in the helifan
structures. The first row shows the relative number of (
−
)
blocks in the different structures.
Helifan
Helix
(4)
(3)
(3/2)
(2)
Fan
1/2
3/8
1/3
1/3
1/4
0
+
+
+
+
+
+
−
+
+
+
+
+
+
+
+
−
+
+
−
−
−
+
−
+
+
+
+
+
+
+
−
−
−
−
+
+
+
+
+
+
+
+
−
−
+
+
−
+
+
+
+
−
+
+
−
+
−
+
+
+
+
+
+
+
+
+
−
−
−
−
−
+
50 K are shown in Fig. 2.9. In these calculations, the wave-vector
Q
was allowed to vary in small, discrete steps, by changing the repeat dis-
tance, and the absolute minimum in the free energy for the structure
thereby determined, as illustrated in the insert to Fig. 2.9, leading to
the prediction that the stable magnetic structures follow the sequence
helix
→
→
→
ferromagnet as the field is increased. The
helifan(3/2) is depicted in Fig. 2.10. In a narrow interval between the he-
lix and the helifan(3/2), other stable phases appear, e.g. the helifan(4
)
(+ +
helifan(3/2)
fan
), and similarly a sequence of helifans with
m
(+)
blocks followed by a (
−
++
−
+
−
3) occurs in the close neighbourhood of
the fan phase. The various structures are associated with characteristic
neutron-diffraction patterns. An examination of the neutron-diffraction
intensities which Koehler
et al.
(1967) associate with the phase which
they designate as 'Fan I' reveals a striking correspondence with the heli-
fan(3/2) pattern, with a very weak fundamental at
Q
0
/
3, where
Q
0
is approximately the wave-vector of the helix, strong second and third
harmonics, and a weak fourth harmonic. The basic periodicities of this
structure are 2
Q
0
/
3 for the component of the moments parallel to the
field, and
Q
0
for the perpendicular component; the weak
Q
0
/
3peak
arises as the result of interference between them. Similar but more de-
tailed neutron-diffraction results have more recently been obtained by
Axe
et al.
(1991). The changes in the basic wave-vector are substantial,
−
)(
m
≥
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