MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

114 Chapter 5
A high, temperature independent carrier concentration is consistent with
Hall effect measurements (sect 4.2.4) on La 0.67 Ca 0.33 MnO 3 .
5. 2. 3 Variable Range Hopping
The resistivity of the manganites has also been attributed to variable range
hopping due to Anderson localization [148]. At temperatures less than 150K,
this picture produces a somewhat better fit to our data (Figure 5-7), but is
clearly inferior to the polaron model at high temperatures (Figure 5-6). The
fit to R 0 exp(T 0 /T) 1/4 gives T 0 = 1.7 × 10 9 K. In the theory of variable range
hopping [71, 149], k B T 0 ≈ 21/(ζ 3 N(E F )) where ζ is the decay length of the
localized wave function, and N(E F ) is the density of localized states at the
Fermi level. For ζ ≈ a = 3.9Å, the distance between neighboring Mn atoms,
this implies N(E F ) ≈ 2.4 × 10 18 eV -1 cm -3 which is typical for disorder
semiconductors but about 1500 times less than the density of states found in
the specific heat of manganites which become metallic at low temperatures
(≈ 5 mJ mol -1 K -2 )[124].
5.3 X-ray Absorption Fine Structure
The primary quantity in XAFS data analyses is χ(k)=(µ(k)-µ 0 (k))/µ 0 (k)),
where k is the ejected photoelectron wave vector, µ(k) is the total absorption
due to the absorbing atomic species, and µ 0 (k)) is the portion of µ(k) that does
not include the photoelectron backscattering off neighboring atoms. This
backscattering causes an interference at the absorbing atom which is manifest
as oscillations in χ(k). A Fourier transform of kχ(k) thus produces peaks that
correspond to the distribution of atoms around the absorbing atom.
Figure 5-8 shows these Fourier transforms.