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Fig. 7.12. The crystal-field levels of an isolated hexagonal ion in Pr,
as a function of an applied magnetic field in the a -and c -directions. The
zero-field wavefunctions are specified more precisely in Fig. 1.16.
and, as < 1 a |
3 s > is non-zero, it has a significant effect on ∆ η ( t 11 ).
A calculation which includes all the crystal-field levels of Pr predicts
the critical uniaxial pressure
O 2 |
T 11 along the ξ -axis to be 0.7 kbar. As
may be seen in Fig. 7.10, such a calculation is in good agreement with
the experimental observations of McEwen et al. (1983), at temperatures
suciently high that the hyperfine coupling is of no importance, and also
accounts very well for the critical pressure at higher temperatures, where
the thermal population of the magnetic excitons becomes significant.
The dependence of the ordered moment at 1.5 K on the uniaxial pressure
is also very well reproduced by this theory, as illustrated in Fig. 7.11.
The stable configurations of the moments at zero pressure are expected
to be analogous to those found in Nd and discussed in Sections 2.1.6
and 2.3.1, i.e. a single- Q structure at small values of the magnetization
and a double- Q configuration when the first harmonic of the moments is
larger than about 0.2-0.3 µ B . This behaviour has not been established
experimentally, but a suggestive rotation of the ordering wave-vector
away from the symmetry axis, as expected in the double- Q structure,
has been detected (McEwen et al. 1983). Uniaxial pressure stabilizes a
longitudinal wave with Q along the b -axis perpendicular to the strain,
and a modest pressure of about 0.1 kbar is estimated to be sucient
to quench the double- Q structure. Accordingly, the theoretical curve in
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