MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

22 Chapter 3
inadequate. l ≈ a is known as the Ioffe-Regel limit. To calculate l, the average
speed (not velocity) must be known. Unfortunately, this is the Fermi velocity
which depends strongly on the band structure. For an electron gas of density
n with a spherical Fermi surface, the Fermi velocity v F is
v
.
F ≈ 309 3
m n
h
h σ
so that l ≈ 309 . 2 2 .
3 e n
3. 1. 1. 4 Hall effects
The Hall effect is the transverse electric field that is produced by the
presence of a magnetic field perpendicular to the flow of charged carriers.
This can be described by antisymmetric off diagonal terms in the resistivity
tensor which are a function of the magnetic field. The Hall effect is normally
linear with respect to an applied field. For an isotropic substance E y = j x R H H,
where H is the magnetic field, j x is the current along the x direction and E y is
the transverse electric field. R H is known as the Hall coefficient. An internal
magnetic field due to a nonzero magnetization of the material may cause a
Hall effect. This anomalous Hall effect is proportional to the internal
magnetization M, E y = j x R A M. The angle between E and j caused by the Hall
effect is known as the Hall angle.
For simple metals and semiconductors, the Hall effect (combined with
other data) can reveal the sign and density of the charge carriers. The Hall
coefficient for an electron gas is -1/nec. If there is more than one type of
carrier, the Hall effect is the weighted average of the Hall effect of the
individual carriers and becomes nonlinear in H. This nonlinearity can be
used to determine the sign and density of the individual carriers Ð assuming
field independent mobilities and Hall coefficients for each carrier type [50].
3. 1. 2 Measurement
The primary concern for reliable transport measurements of new
materials is the identification and elimination of systematic errors. Thermal
and electrical noise lower the precision but usually not to an important extent