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low temperatures. Since the anisotropy energy is very small just below
the critical temperature, the exchange dominates and gives rise to peri-
odic magnetic structures in the heavy rare earths, except in Gd where
the peak in
( q ) occurs at q = 0 . As the temperature is lowered, the
anisotropy forces become relatively more important, and phase transi-
tions occur to structures in which their influence is apparent. A less
obvious but nevertheless important effect is that
J
( q ) itself changes
substantially with temperature. As was mentioned in the last section,
the peak reflects a maximum in the conduction-electron χ ( q ), which is
determined by the form of the Fermi surface. Because of the interaction
(1.3.23) between the local moments and the spins of the conduction elec-
trons, the latter experience a potential with a period which is generally
different from that of the lattice, and therefore generates extra energy
gaps in the band structure. These magnetic superzone gaps, which we
shall discuss in more detail in Section 5.7, may be of the order of 10 mRy
and therefore perturb the energy spectrum of the conduction electrons
significantly. In particular, the regions of the Fermi surface responsible
for the peak in
J
( q ) are severely modified, as has been verified through
calculations on Tm by Watson et al. (1968). The result is that both
the position of the peak is changed and its magnitude is reduced. As a
consequence, periodic magnetic structures tend to be self-destructive; as
they become established they try to eliminate the characteristic of the
exchange which ensures their stability. These effects were studied by
Elliott and Wedgwood (1964), who used a free-electron model to ex-
plain the variation of Q in the heavy metals. Although their model is
greatly over-simplified, it illustrates the essential features of the prob-
lem. We shall see in Chapters 2 and 5 that this variation in
J
( q )is
necessary to explain the change in both the magnetic structures and
excitations with temperature.
Whereas the magnetic structures of the heavy rare earths can be
accounted for by recognizing the dominant role of the exchange, and
considering the crystal fields and magnetoelastic effects asperturbations,
whose essential role is to establish favoured directions for the moments
in the lattice, the balance in the light elements is not so clear-cut. Since
g is generally close to 1, the exchange is relatively weak, and the larger
values of
J
r l
towards the beginning of the series are expected to make
crystal-field effects relatively important. As a result, the latter are able
to hinder the moments from attaining their saturation values of B J ,
even in high fields at low temperatures, as illustrated in Table 1.6.
The most remarkable manifestation of the influence of the crystal
fields is found in Pr, where they are able effectively to frustrate the efforts
of the exchange to produce a magnetically ordered state. As illustrated
in Fig. 1.16, the ground state on the hexagonal sites is the
|
J ζ
=0 >
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