MAGNETIC STRUCTURES - Rare Earth Magnetism: Structures and Excitations - page 126

as many as five different phases at some temperatures. The structures
in a magnetic field were investigated with neutron diffraction by Koehler
et al. (1967), who identified two intermediate phases which they called
fans and characterized by the intensity distribution of the Bragg peaks.
These phenomena have been elucidated by means of calculations of
the effect of a magnetic field on the commensurable structures of Fig.
2.5 (Jensen and Mackintosh 1990). At low temperatures, the hexagonal
anisotropy has a decisive influence on the magnetic structures, ensuring
that a first-order transition occurs from the helix or cone to the ferro-
magnet, without any intermediate phases. Below about 20 K, where the
cone is the stable structure in zero field, the cone angle is almost indepen-
dent of the applied field in the basal plane, but at the transition to the
ferromagnet, the c -axis moment disappears. When the field is applied
in the hard direction at these temperatures, the moments just above the
ferromagnetic transition do not point along the field direction, but are
aligned very closely with the nearest easy axis, so that

· √ 3 / 2,
as illustrated in Fig. 1.20. As the field is further increased, they turn
towards it, becoming fully aligned through a second-order phase transi-
tion at a critical field which is estimated from B 6 to be about 460 kOe
at absolute zero. At low temperatures, the hexagonal anisotropy also
hinders the smooth distortion of the helix in a field. The moments jump
discontinuously past the hard directions as the field is increased, giving
first-order transitions which may have been observed, for example, as
low-field phase boundaries below 20 K in the measurements of Akhavan
and Blackstead (1976).
Above about 40 K, when the hexagonal anisotropy is not so domi-
nant, intermediate stable phases appear between the helix and the fer-
romagnet. The nature of these phases may be appreciated by noting
that the helix can be considered as blocks of moments with components
alternately parallel and antiparallel to the field, as is apparent from the
structures illustrated in Fig. 2.5. If we write this pattern schematically
as (+

J 8

), then the fan structure may be described as (+ + + +).
The intermediate structures, the helifans, then correspond to patterns
of the type specified in Table 2.2. The notation helifan( p )isusedto
designate a structure whose fundamental period is p times that of the
helix (the single number p is not generally adequate for discriminating
between the different helifans). It is clear that these structures repre-
sent compromises between the demands of the exchange for a periodic
structure, and the field for a complete alignment of the moments. They
are not due to the hexagonal anisotropy which, on the contrary, tends
to suppress them, and occur both when the field is applied along the
easy and hard directions in the plane. The free energies of the various
magnetic phases as a function of magnetic field in the easy direction at

− + −