A FORMAL THEORY OF THE CONDUCTIVITY AND APPLICATION TO THE GIANT MAGNETORESISTANCE

The transport in a system with inhomogeneous elastic scattering is des cribed in terms of a probability-conserved Boltzmann equation. We demo nstrate that the spatially varied current density depends only on the voltage drop between the ends of the sample. This fact enables us to d evelop a formal and general theory for the conductivity without determ ining: the actual electric field inside the sample. The theory is firs t applied to multilayer systems and shown to recover the previous theo ry. By including the spin-dependent interface scattering and bulk scat tering, we employ our theory to account for the giant magnetoresistanc e (MR) in magnetic granular systems with both spherical and cylindrica l granules. The results obtained reproduce the experimental dependence of the MR on annealing temperature.