Environmental Engineering Reference
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Fig. 5.14. A comparison of the measured and calculated resistivity of
a Tb single crystal, as a function of temperature, after Hessel Andersen
and Smith (1979). The residual resistivity has been subtracted from the
experimental results. The full line includes the calculated contributions
from both the magnon scattering and the phonons. The rapid increase
around 20 K is predominantly due to the excitation of magnons across
the energy gap.
electron gas remain unchanged. If the resistivity of the unpolarized
electrons is ρ total ( T ) and their density of states at the Fermi surface is
N
( ε F ), the polarization (5.7.16) of the conduction electrons in the ferro-
magnetic state leads to a scaling of the total resistivity, which according
to eqn (5.7.55) is
ρ total ( T )= 1+ ζ ( T ) ρ total ( T ); ζ ( T )= N (
ε F )+
N (
ε F )
1 .
2
N
( ε F )
(5 . 7 . 61)
In ρ total ( T ), the residual resistivity is temperature independent and the
magnetic contribution is determined by the above result, if
N σ ( ε F )in
(5 . 7 . 57 b ) is replaced by its paramagnetic value
( ε F ). The modifica-
tion ζ ( T ), due to the polarization of the conduction electrons, depends
on the temperature via the magnetization, and ζ ( T )
N
2 at small
J z
magnetization.
The most important effect on the resistivity produced by the spin-
polarization of the electronic states results from the change in the density
of states at the Fermi surface, taken into account by ζ ( T ) in (5.7.61).
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