Random walk simulation of magnetotransport in magnetic granular systems

An integral series for the conductivity of magnetic inhomogeneous systems was previously derived from the real-space Kubo formula and semiclassical Boltzmann equation independently. In this work, we show that the integral series can be evaluated by using a random-walk sampling technique. The approach is applied first to a simple nonmagnetic single-granule system, and then to the giant magnetoresistance (GMR) effect of magnetic granular systems. It is well suitable for the granular systems in which the granular size is smaller than the electron mean free path, where the macroscopic approach becomes invalid. The GMR is found to always increase with decreasing size of granules. Optimum GMR could be obtained by a proper adjustment of the spin-dependent scattering strengths due to interfacial roughness and bulk impurities.