Temperature and magnetic field dependent transports in granular structures

We study the temperature and magnetic field dependent transports of a two-dimensional granular system near percolation threshold. We consider a model system that consists of ferromagnetic, metallic nano-sized particles randomly distributed on a 2D non-magnetic and insulating surface. The particles (grains) do not touch one another, but electrons can quantum tunnel from one grain to another. We assume a temperature range where phonon-assisted hopping is not important and quantum tunneling dominates the transports between the particles. However, the temperature is still high enough so that the phase coherence between different tunneling events is lost. In this case the whole system can be treated as a classical percolation network with resistance between gains determined by quantum tunneling. Spin-dependent scattering is also considered in our system