MAGNETIC STRUCTURES - Rare Earth Magnetism: Structures and Excitations - page 118

in ( q ), so that the structure at 25 K has reduced its periodicity to 11

layers by introducing a regularly-spaced series of spin slips ,atwhichone
plane of a bunched doublet is omitted while the remaining member ori-
ents its moments along the adjacent easy axis. The configuration of Fig.
2.5(b), in which one spin slip is introduced for each repeat distance of
the perfect commensurable structure, is the primordial spin-slip struc-
ture and has a number of interesting features. It is particularly stable,
existing over a range of temperature (Gibbs et al. 1985), possesses a
net moment, and the bunching angle is still rather small. Although the
angle 2 φ between two bunched planes is almost constant, the exchange
interaction distorts the structure near the spin slips so that the moments
are not symmetrically disposed around the easy axis. As the tempera-
ture is increased further, the bunching decreases and the concept of spin
slips becomes less useful. Thus the configuration of Fig. 2.5(d) can be
considered as a distorted three spin-slip structure, but it is simpler to
regard it as a commensurable, almost regular helix in which every third
plane aligns its moments close to an easy axis in order to reduce the
anisotropy energy.
The spin-slip structures of Ho have been subjected to a careful and
extensive neutron-diffraction study by Cowley and Bates (1988). They
interpreted their results in terms of three parameters:
b - the number of lattice planes between spin slips,
2 α - the average angle between the moments in a bunched pair,
σ G - a Gaussian-broadening parameter for α .
In a perfect, undistorted structure, α = φ and σ G = 0. The parameter
σ G takes into account two effects; the distortions which occur in perfect
periodic structures such as that illustrated in Fig. 2.5(b), and possible
irregularities in the positions of the spin-slip planes. The former is in
principle included in the calculations, whereas the latter is not. From
the calculated magnetic structures, such as those illustrated in Fig. 2.5,
it is possible to deduce the corresponding neutron-diffraction patterns
and hence, by fitting the peak intensities, determine the values for α
and σ G (Mackintosh and Jensen 1990). The parametrization suggested
by Cowley and Bates is in practice rather satisfactory; it allows a fit of
all the calculated neutron-diffraction intensities, which vary over about
five orders of magnitude, with a relative error of in all cases of less than
20%. Furthermore, the parameter α is close to the average values of
the angle φ determined directly from the calculated structures. The
measured and calculated values of α are in good agreement, taking into
account the experimental uncertainties, but there are some discrepan-
cies in σ G . It is noteworthy that the agreement between the predicted
and observed neutron-diffraction intensities is very good for the b = 11,
one-spin-slip structure, but that the experimental values of σ G otherwise

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