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whose zero-frequency limit is a longitudinal-wave structure along the
b
-
axis, and the electronic moment induced by the hyperfine coupling, in
the zero-temperature limit, is
2
M
η
∆(1
χ
J
(0)
J
η
(
Q
)
0
IA
(
Q
)
=
IA
R
0
)
,
(7
.
4
.
1)
1
−
χ
J
(0)
J
−
multiplied by
gµ
B
, corresponding to about 0.6
µ
B
. Determining the elec-
tronic moment from the neutron-diffraction intensities is complicated by
the coherent nuclear scattering of neutrons at the same
Q
, due to the
induced polarization of the nuclei. The two contributions can however
be separated with the help of polarized neutrons, and Kawarazaki
et al.
(1988) thereby deduced that the electronic moment on the hexagonal
sitesisabout0.4
µ
B
at 30 mK, while there is also an induced moment
an order of magnitude smaller on the cubic sites. The nuclear polariza-
tion on both types of site is substantial at this temperature, which is
consistent with the observation by Lindelof
et al.
(1975) and Eriksen
et
al.
(1983) of a dramatic increase in the nuclear heat capacity, indicating
a second-order transition of the nuclear spins to an ordered structure at
about 50 mK.
As may be seen in Fig. 7.8, the magnetic ordering is preceded by
a strong precursor scattering, which has been observed in single crys-
tals by a number of investigators at temperatures as high as 10 K, and
was first investigated in the millikelvin range by McEwen and Stirling
(1981). The figure shows that the peak actually comprises two contribu-
tions, one centred at the critical wave-vector, and a broader component
at a slightly smaller wave-vector. The narrower peak, which is usually
known as the
satellite
, appears around 5 K and increases rapidly in in-
tensity as
T
N
is approached, at which temperature it transforms into
the magnetic Bragg peak. Since the width in
of this peak is greater
than the instrumental resolution, at temperatures above
T
N
,itdoesnot
reflect the presence of true long-range magnetic order, but rather very
intense fluctuations, with a range of several hundred A, which presum-
ably also vary slowly in time. The RPA theory predicts such a peak
only because of the elastic scattering from the nuclear spins, as given
by eqn (7.3.29). However, the peak produced by this mechanism is es-
timated to be visible only very close to
T
N
, below 200 mK, and cannot
therefore explain the observations. The satellite above
T
N
may be in-
terpreted as a critical phenomenon, due to the strong increase in the
fluctuations, neglected in the RPA, which develop as the second-order
transition is approached. When the electronic susceptibility has satu-
rated below about 7 K, the critical fluctuations in Pr would be expected
κ
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