MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

122 Chapter 6
The Hall effects are contained in the antisymmetric part of σ and ρ and
therefore can be expanded in odd powers of H and M. The first two terms in
the Hall resistivity is R H H×J + R A M×J, where R H is the normal Hall coefficient
and R A is the anomalous Hall coefficient. Since there is no evidence to prefer
the Hall conductivity of equation 1 (≈ -R H /H 2 ) to the Hall resistivity, the Hall
effect is analyzed using R H and R A .
It is possible that the observed magnetoconductivity could be reduced to
terms involving only M 2 and (E•M)M since M ≈ M 0 + χH gives the same field
dependence described above. This would imply a strict relationship among
the various β i (T) and γ i (T) which could be determined by simultaneous
measurements of M and the magnetoconductivity. The resistivity saturates
in a magnetic field [113, 158] more rapidly than does the magnetization
(giving M 2 behavior only at small M), indicating again that it is probably the
conductivity not the resistivity which is proportional to M 2 . This is discussed
in more detail in chapter 7.
The reciprocal nature of the conductivity and resistivity leads to only an
abstract distinction between them. Thus, the simpler, empirical description of
the resistivity in terms of a magnetoconductivity may be accidental.
Nevertheless, it warrants further consideration. The standard additive
scattering time interpretation of the magnetoresistivity requires a more
complex H dependence to describe the suppression of magnetic scattering by a
magnetic field. The simplicity of the magnetoconductivity expression may
signify the basis of an alternative transport interpretation. Taken literally, the
magnetic field appears to open parallel channels of conduction with a simple,
physical functional dependence.