Description:
In granular solids, the magnetoresistance is directly related to the macroscopic magnetization, but this relationship is extremely complex due to the distribution of grain size and intergranular interaction. The dependence of the magnetoresistance on the temperature and external magnetic field are investigated here by means of a theoretical approach that is developed, taking explicitly into account the grain-size distribution and the percolative character of the tunneling conductance in the transport network. Within this model, it is found that the optimal path that consists of grains of a particular size is strongly temperature dependent. Such a selective tunneling mechanism between metallic grains complicates the dependence of magnetoresistance on the temperature and external magnetic field, other than the square of reduced magnetization. Compared with previous theoretical results, a steeper decrease of magnetoresistance at high temperatures and a steadier state at low temperatures are found. Particularly, for the band-bending effects at the grain boundaries of manganites, the selective tunneling mechanism leads to the extraordinarily large magnetoresistance in their ultrafine powder compacts. These results agree well with experimental observations.