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heavy rare earths and their temperature dependences, utilizing a phe-
nomenological
molecular-field model
. A similar approach was taken by
Miwa and Yosida (1961), while Nagamiya, Nagata, and Kitano (1962)
calculated the effect of a magnetic field on some of these structures,
showing that a
fan
structure may exist between the helix and the ferro-
magnet. In these papers, the standard model first attained a coherent
formulation.
The transport properties, particularly the
electrical resistivity
,were
elucidated in the same period. De Gennes (1958) considered the
mag-
netic disorder scattering
, showing that it is proportional to the de Gennes
factor in the paramagnetic phase, while Kasuya (1959) gave a very com-
plete discussion of the same subject, including not only the paramag-
netic phase but also scattering by spin waves and rare earth impuri-
ties. The first resistivity measurements on single crystals were made
on Er by Green, Legvold, and Spedding (1961). The unusual temper-
ature dependence of the resistance in the
c
-direction was explained by
Mackintosh (1962) as a consequence of the incommensurable magnetic
ordering, leading to
magnetic superzones
. Miwa (1963) and Elliott and
Wedgwood (1963) made calculations of the magnitude of this effect, us-
ing the free electron model, which were in semi-quantitative agreement
with the experimental results. Mackintosh (1963) pointed out that the
spin-wave energy gap should also give rise to an exponential increase in
the magnetic scattering at low temperature and deduced that the gap in
Tb is about 20 K, a value later substantiated by direct measurements.
Until this time, the conduction electrons in the rare earths had
been described by the
free-electron model
, but Dimmock and Freeman
(1964) demonstrated that this simplification was unjustified when they
calculated the
band structure
of Gd by the APW method. The con-
duction electrons were found to be largely
d
-like, as in the transition
metals, and the Fermi surface far from spherical. At that time, sin-
gle crystals of the purity required to allow conventional Fermi surface
experiments were unavailable, so Gustafson and Mackintosh (1964) em-
ployed
positron annihilation
, initially in polycrystalline samples. Their
most striking observation was that the number of 4
f
electrons in Ce does
not change greatly at the
γ
-
α
transition, in contradiction to the promo-
tional model, and hence to the standard model. Later measurements on
single crystals of the heavy rare earths showed that the conduction elec-
trons are indeed far from free electron-like, and the experimental results
could be well accounted for by relativistic APW calculations (Williams,
Loucks, and Mackintosh 1966).
As the ground-state properties of the rare earth metals became
progressively clarified, interest turned towards the
magnetic excitations
.
Niira's pioneering theoretical work was followed by the calculation of
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