Based on the probability-conserved Boltzmann equation, we develop a formal and general transport theory for the conductivity in inhomogeneous systems. In particular, we show that the local current density inside the sample can be expressed as a boundary value integral, so that the local electric field need not be calculated explicitly. The theory is first applied to multilayer systems and shown to recover the previous theory. More importantly, by including spin-dependent interface scattering and bulk scattering, we employ our theory successfully to account for the giant magnetoresistance in magnetic granular systems. © 1996 The American Physical Society.

• Received 8 May 1995

DOI:https://doi.org/10.1103/PhysRevB.53.8203