MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

3. Electronic and Magnetic Measurements
3.1 Transport Properties
Transport properties: Resistivity, dielectric constant, thermalconductivity,
thermopower, Hall effect, etc. are often a prime concern when engineering a
new material for a particular use. Even if the purpose of the material is not
related to transport, the material may still be required to have certain
transport characteristics. For example, the liquid crystal in a liquid crystal
display should have a low electrical conductivity to minimize resistive losses.
3. 1. 1. 1 Ohm’s Law
Most materials, whether metals, semiconductors or insulators, obey
OhmÕs law to a good extent: the current I flowing in a wire is proportional to
the potential drop V along the wire V = IR (linear response). R is the
resistance of the wire and it depends on the size and shape of the wire. One
generally prefers to use intensive quantities to characterize a material. Thus
OhmÕs law can be used to define the resistivity ρ which is defined to be the
proportionality constant between the electric field E and the current density j
that it induces: E = ρj. Since E and j are vectors, ρ is a second order tensor.
Any deviations of OhmÕs law can be easily described by adding terms with
higher powers of j. The conductivity σ is the inverse of the resistivity (σ = ρ -1 )
such that j = σE. In an isotropic or cubic substance the resistivity tensor ρ has
off diagonal elements equal to zero and three equal diagonal elements ρ (a
scalar), then the conductivity tensor σ has the same form with diagonal
elements σ where σ = 1/ρ. For an orthorhombic substance (for which ρ and σ
have no nonzero off diagonal terms in the appropriate coordinate system),
the conductivity along a principle direction is equal to the inverse of the
resistivity along the same principle direction. Because of these simple
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