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so that the constant angle φ in the plane between any moment and the
nearest b -axis is only 5.8 , as shown in Fig. 2.5(a), compared with the 15
which corresponds to a uniform helix. As the temperature is increased,
the expectation value
O 6
decreases with the relative magnetization,
roughly like σ 21 ,and φ increases correspondingly. Simultaneously Q
tends to increase, reflecting the change in the position of the maximum
Fig. 2.5. The self-consistent periodic structures in Ho, calculated at
different temperatures. Each circle represents the magnitude and direc-
tion of the ordered moment in a specific plane, relative to the size of the
moment at absolute zero (10 µ B ), indicated by the length of the horizon-
tal lines. The orientation of moments in adjacent planes is depicted by
the positions of neighbouring circles.
(a) The 12-layer zero-spin-slip structure at 4 K. The open circle in the
centre indicates the ferromagnetic component in the cone structure.
(b) The 11-layer one-spin-slip structure at 25 K. The bunched pairs of
moments are disposed unsymmetrically with respect to the easy axis in
the vicinity of the spin slip.
(c) The 19-layer structure at 50 K. The orientation of the moments in
successive layers is determined by following first the filled circles in an
anticlockwise direction, as indicated, and then the open circles.
(d) The 9-layer trigonal structure at 75 K. This may be looked upon as
a three-spin-slip structure, but the bunching is so slight that it is more
useful to regard it as an almost regular helix, in which every third plane
aligns its moments close to an easy axis, in order to reduce the anisotropy
energy.
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