MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

34 Chapter 3
The dichotomy between the two types of polarons seems unnecessary
when considering their spatial extent, but the conductivity of the two types of
polarons are vastly different. Large polarons move with significant mobilities
μ > 1 cm 2 /V sec, that decrease with increasing temperature (metal-like). In
contrast, small polarons move with very low mobilities, μ Θ D /2) the electrical
conductivity is predicted [58] to be σ = 3ne 2 ωa 2 /2k B T -1 exp(-E A /k B T). Here n is
the number density of charge carriers, a is the site-to-site hopping distance, ω
is the longitudinal optical phonon frequency and e is the electronic charge.
The Hall mobility may behave like the drift mobility with 1/3 of the
activation energy, but in the adiabatic approximation the form is much more
complicated [58].
In the theory of small polaron hopping, it was found that the motion of
the polaron is only weakly dependent on the magnetic order, and changes
little as the temperature is raised above the Curie temperature [61, 62].
Small polarons were first studied in the non-adiabatic regime, where the
electron transfer integral and hence the bandwidth is small [60, 63-65]. In the
high temperature limit this gives a factor of T 3/2 instead of a T in the drift and
Hall mobilities. There are some unphysical assumptions required for the
non-adiabatic analysis to be valid. The assumptions behind the adiabatic