CRYSTAL-FIELD EXCITATIONS IN THE LIGHT RARE EARTHS - Rare Earth Magnetism: Structures and Excitations - page 355

The quasielastic peak cannot be classified as an additional critical
phenomenon, because it is not centred at the critical ordering wave-
vector. Furthermore, even though its intensity increases in the para-
magnetic phase, as the system approaches criticality, it is still present,
with a non-zero width in

-space, below the transition and its intensity
continues to increase as the temperature is further reduced (Burke et al .
1981; Bjerrum Møller et al. 1982; McEwen 1986). The dynamic effects
associated with this quasielastic peak are very modest, as observed by
Jensen et al. (1987); its width in energy is estimated to be less than 0.1
meV. Nevertheless, its integrated intensity is too large to be explained
as a static phenomenon due to scattering from local short-range ordering
of the crystal near the surface or around bulk defects, such as magnetic
impurities or lattice defects. The only remaining possibility appears to
be that the quasielastic peak is associated with the magnetic response of
the itinerant electrons. This is consistent with one of the results of the
neutron-scattering studies by Leuenberger et al. (1984) of the hexagonal
insulator Cs 3 Cr 2 Br 9 , in which the Cr dimers form a singlet-triplet sys-
tem which has a number of analogies to Pr. Even though this system is
very close to magnetic ordering, and the lowest excitation energies are
only about 0.2 meV, there is no sign of either a satellite or a quasielastic
peak. The spin fluctuations of band electrons are not normally expected
to give rise to a quasielastic peak of the intensity observed in Pr, and its
occurrence may therefore indicate the formation of resonant states near
the Fermi surface in Pr, due to hybridization of the conduction electrons
with the 4 f electrons. As discussed in Section 1.3, the 4 f electrons in Pr
are very close to delocalization, and the incipient magnetic instability
of the localized electrons would therefore be expected to be reflected in
fluctuations in the conduction electron-gas. An indication of the sensi-
tivity of the conduction electrons to the ordering process is provided by
the resistivity measurements of Hauschultz et al. (1978), who found an
increase of almost fifty per cent, over the temperature range in which
the quasielastic peak develops, in the c -direction, where superzone effects
in the ordered phase are expected to be of minor importance. Further
studies of the quasielastic peak, and associated changes in the conduc-
tion electrons, particularly under high pressures with the corresponding
progressive increase in 4 f hybridization, would clearly be of interest.
Antiferromagnetism can also be induced in Pr by an internal cou-
pling to magnetic impurities. Assuming that the susceptibility of the
single impurities of concentration c is proportional to 1 /T , we find that
eqns (5.6.5-6) of the virtual crystal approximation lead to an ordering
temperature determined by

κ

c

T N = T N ( c )=

c ) R ( T N ) T N ( c =1) ,

(7 . 4 . 2)

1 − (1 −