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The observed
σ
15
dependence on the magnetization indicates that the
magnetoelastic term dominates. As illustrated in Fig. 1.22,
C
and
A
have been accurately determined by Rhyne and Legvold (1965a) from
macroscopic strain-gauge measurements and, since the elastic constant
is known (Jensen and Palmer 1979), the relative magnetoelastic and
crystal-field contributions to (1.5.33) may readily be determined.
At
absolute zero, the former is 1.14 K/ion and the latter is
0
.
60 K/ion,
rapidly becoming negligible as the temperature is increased. On account
of the sign of the Stevens factor
γ
for Tb, the crystal-field contribution
is expected to be positive, and this may be another indication of the
importance of anisotropic two-ion coupling in the magnetically ordered
phases.
−
Fig. 1.22.
The temperature dependence of the magnetostriction pa-
rameters
C
and
A
in Tb, after Rhyne and Legvold (1965a). The full lines
show the results of the Callen-Callen theory presented in Section 2.2.
The magnetoelastic energy (1.5.32) is substantial in the ferromag-
netic phase. In particular the term
2
c
γ
C
2
, which results from a magne-
toelastic strain of
cylindrical
symmetry, is relatively important at high
temperatures, because it renormalizes roughly as
σ
4
, and is therefore
still about 0.3 K/ion in Dy at 85 K, the temperature at which a first-
order transition occurs from the helical to the ferromagnetic phase. The
hexagonally
symmetric contribution proportional to
CA
is small at all
temperatures in Dy, since
A
1
−
0 (Martin and Rhyne 1977). In the
helical phase, the lattice is
clamped
(Evenson and Liu 1969), so that
the
γ
-strains are zero, and the magnetoelastic contribution to the sta-
bilization energy is therefore absent. At
T
C
, this energy, plus a minor
≈
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