MAGNETIC STRUCTURES - Rare Earth Magnetism: Structures and Excitations - page 120

whole interval between T C and T N , but it is possible that a non-collinear
basal-plane component is present in some of the commensurable struc-
tures just above T C .

Fig. 2.6. The calculated mag-
netic structure in Er at 48 K. Each
arrow represents the magnitude and
orientation, in the a - c plane, of the
ordered moment in a specific plane
normal to the c -axis, relative to the
magnitude of the moment at abso-
lute zero (9 µ B ), indicated by the
length of the line along the a -axis.
The hodograph is very close to an
ellipse, with semi-axes of length 6.5
and 2.2 µ B , and this structure can be
considered as comprising four planes
of moments with a positive compo-
nent along the c -axis, followed by
three with a negative moment, with
the designation (43).

The structure shown in Fig. 2.6 comprises four planes of moments
with a positive component along the c -axis, followed by three with a neg-
ative moment. The basic wave-vector is therefore 2/7, and we may de-
scribe the structure as (43). The other commensurable structures listed
above are then respectively 2 (44443),

(444443), and (44) where, in each case, blocks of n moments with a
positive component along the c -axis alternate with negative blocks, and
the doubling is necessary to ensure periodicity if the number of blocks is
odd. These calculations give a good account of the neutron-diffraction
results of Cowley (1991). The lattice strains associated with a number
of these structures have been studied with synchrotron X-rays by Gibbs
et al. (1986). The fundamental wave-vector for the oscillating c -axis
strain in a structure like (44), which has inversion symmetry, is twice
that of the magnetic structure. However, the other examples above do
not have inversion symmetry, so charge-scattering of X-rays may occur
at the fundamental magnetic wave-vector. In the cone phase, the X-ray
scattering at the fundamental wave-vector of the helical component is
anomalously large, even though the longitudinal lattice-strain must be
very small. There is however also a contribution from charge scattering
associated with a transverse strain, discussed at the end of the previ-
ous section, which may arise when the mirror symmetry normal to the
c -axis is broken, as it is in this structure. The hexagonal symmetry of a

× (443), 2 × (4434443), (4443), 2 ×