ELEMENTS OF RARE EARTH MAGNETISM - Rare Earth Magnetism: Structures and Excitations - page 50

assume that all terms in (1.4.24) which are not forbidden by symmetry
are present, to calculate their influence on the magnetic properties, and
to determine their magnitude by judicious experiments.
The hyperfine interaction between the 4 f moment and the nuclear
spin I may be written

H hf = A
i

I i · J i . (1 . 4 . 27)

Since A is typically of the order of micro-electron-volts, the coupling to
the nuclei normally has a negligible effect on the electronic magnetism
in the rare earth metals, but we shall see in Sections 7.3 and 7.4 that it
has a decisive influence on the low-temperature ordering in Pr.

1.5 Rare earth magnetism
The interactions discussed in the preceding section are the origin of the
characteristic magnetic properties of the rare earth metals. The long-
range and oscillatory indirect exchange gives rise to incommensurable
periodic structures , the crystal fields and anisotropic two-ion coupling
induce a magnetic anisotropy which may require fields up to hundreds
of tesla to overcome, and the magnetoelastic interactions cause magneto-
strictive strains which may approach one per cent. In the following, we
shall give a brief description of some features of rare earth magnetism, as
a prelude to a more detailed discussion of selected structures in the next
chapter, and as a necessary basis for our later treatment of magnetic
excitations. We have emphasized general principles, with appropriate
illustrations, and have not attempted an exhaustive description of the
magnetic properties of each element. This task has been accomplished by
McEwen (1978), following earlier surveys by Rhyne (1972) and Coqblin
(1977), and we shall refer to his comprehensive review article for further
details, while quoting more recent investigations where appropriate.
Below the critical temperatures, listed in Table 1.6 on page 57, the
rare earth metals form magnetically ordered phases. In the heavy ele-
ments, the maximum moment of gµ B J per ion is approached in moderate
fields at low temperatures. As is also apparent from Table 1.6, there is an
additional contribution from the conduction electrons, which is almost
10% of the total moment in Gd, and appears to fall with S , as expected
from (1.3.23). In their ordered phases, all the moments in a particular
plane normal to the c -axis are aligned but, as illustrated in Fig. 1.19,
their relative orientations may change from plane to plane. The mag-
netic structures of the heavy rare earths, which have been thoroughly
reviewed by Koehler (1972) and Sinha (1978), derive basically from two
different configurations of moments. In the helix , the expectation values