Environmental Engineering Reference
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Fig. 5.15.
The
c
-axis resistivity of Tb in the vicinity of
T
N
= 230 K,
after Hegland
et al.
(1963). As the helical ordering develops, the magnetic
superzones cause a sharp increase in the resistivity, which disappears at
T
C
= 220 K. The superzones may also be eliminated by a magnetic field
in the
b
-direction, which suppresses the helical structure.
The agreement obtained between simple model calculations of the
variation of
Q
and that observed experimentally is surprisingly good,
to some extent fortuitously so. The band electrons are far from free-
electron-like in the rare earth metals, and the approximation in which
I
(
n
k
,n
k
) is replaced by
j
(
k
−
k
+
) is rather crude. The effective free-
electron model, with
j
(
q
) proportional to a form factor
1+(
Aq
)
2
−
1
where
A
τ
0
.
2
˚
Aand2
k
F
≈
2
.
8 A
−
1
, leads to a maximum in
≈
J
(
q
)
0
.
3 A
−
1
at
q
parallel to the
c
-axis, in the paramagnetic phase. In
N
q
J
1
this model,
(
q
) is found to be an order of magnitude larger
than
J
(
0
), and the same is the case with the interband contributions
(
=
0
) to the exchange interaction, compared to the intra-band con-
tributions. However, various estimates indicate that all these terms are
of the same order of magnitude. Lindg ard
et al.
(1975) have made the
only existing
ab initio
calculation of
τ
(
q
) in a rare earth metal, consid-
ering the simplest case of Gd, and they obtained a reasonable account
of the dependence on wave-vector, even though the magnitude differed
by as much as a factor of four from that determined experimentally.
Their calculations show that the exchange integral is dominated by the
J
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