MAGNETIC STRUCTURES - Rare Earth Magnetism: Structures and Excitations - page 130

the exchange is suciently short-range, the helix, helifans and fan are
almost degenerate at the critical field; it is the interaction between the
blocks which differentiates between these structures. One of the most
remarkable features of the helifans is the large number of hexagonal
layers involved in a single period, a characteristic which they share with
the commensurable structures observed in zero field in Ho and Er, which
were discussed in the preceding sub-section.
Helifans, or analogous structures, may also occur in other rare
earth systems where periodic ordering is observed. For example, the
modulated structures in Nd discussed previously may be described as
(+

), indicating blocks of moments with a component
parallel or antiparallel to a magnetic field applied in the basal plane. A
periodic reversal of ( − ) blocks will then generate subharmonics of the
basic Q -vector. Thus the sequence (+ + +

− + − + − + −

− − −

) generates Q / 4,

+ +

)gives Q / 2, both of which have been observed
by neutron diffraction in a magnetic field (Zochowski et al. 1991).

− −

and (+++ +++

2.3.3 Films and superlattices
The development of the technique of molecular-beam epitaxy has allowed
the fabrication on a substrate of films of rare earth metals, with thick-
nesses ranging from a few to thousands of atomic planes. In addition,
superlattices ,or multilayers ,oftheform[A l | B m ] n may be produced, in

which blocks comprising l planes of element A, followed by m planes of
element B, are replicated n times. It is clear that an endless variety of
such systems may be constructed, and the field is in a stage of rapid de-
velopment. We will restrict ourselves to a discussion of some of the new
physical principles involved in understanding the magnetic properties of
such structures, illustrated by a few specific examples.
The essential difference between these structures and a bulk crystal
lies, of course, in the boundary conditions. Films and superlattices are
finite in one dimension, whereas a bulk crystal is assumed to be essen-
tially unbounded, and the magnetic layers are terminated by a medium
which may have very different magnetic properties, be it a vacuum, a
rare earth with quite different moments and interactions, or a nominally
non-magnetic metal such as Y, which is a very popular choice for the
intermediate layers in superlattices.
The influence of the finite size on the orientation of the ordered mo-
ments is illustrated in Fig. 2.11, which depicts the results of a mean-field
calculation, based on the model of Larsen et al. (1987), for a 15-plane
slab of Ho at 4 K. The bunched commensurable helix encompassing the
inner 12 planes is enclosed by a single and a double plane, aligned almost
ferromagnetically with the respective outer planes. These ferromagnetic
clusters distort the adjacent bunched pairs in a manner reminiscent of