| Granular composite refers to a new kind material containing small particles embedded randomly in a host. The granular composites made of different materials often exhibit interesting physical phenomena and can be widely used in different application fields. So, it becomes a. popular thesis of condensed matter physics and many theoreticians and experimentalists are interested in investigating such granular composites. In this article, we study one kind of these composites named as magnetic granular composite. This kind material appears giant magnetoresistance (GMR) and other new interesting magnetic properties. By using Monte Carlo simulation or considering new theoretical method, we study the giant magnetoresistance effect and other magnetic properties of such granular composites.Though people begin to make the magnetic devices based on the giant magnetoresistance effect, it is still not complete to understand the giant ma.gnetoresistance in the microscope scale. In this article, we will theoretically study magnetic properties and the GMR effect of magnetic granular composite. We find that the GMR effect is much associated with the behavior of the-fine magnetic particles which are randomly distributed in nonmagnetic host. Therefore, we first discuss the magnetic behavior of the composite. We find that the size distribution of these fine magnetic particles is of great concern to the system抯 magnetization. We also study the hysteresis and other irreversible magnetic processes and find they are due to the irreversible transition of the magnetic particle moments. We distinguish the different contribution to the resistance caused by spin梔ependent conduction electrons which scatter among the superparamagnetic (SPM) particles and the blocked particles, then combine the tow梒hannel model and the effective medium theory (EMT), and average the spin-dependent scattering processes, and obtain the relations of GMR vs. applied field H, GMR vs. magnetic concentration, GMR vs. annealing temperature in the end. By considering the spin梔ependent scattering processes, We alsoV17suggest a phenoxnenological theory which can explain the experimental observation about the dependence of GMR on temperature. Based on extended Gittleman theory, we apply a Monte Carlo method to simulate the GMR effect. We compare the GMR wider different Hamiltonian form. We discuss the effect of size梔istribution of magnetic particles on GMR by considering the dipolar interactions. We combine the Monte Carlo method and random resistor network to study the GMR vs. magnetic concentration. We find the simulation result is in agreement with the experiments and the EMT is a good approximation to describe the granular composites. We also discuss the difference of GMR under two梔imensional and three-dimensional cases in this article.In the investigation of GMR, when the magnetic applied field is absent, the ma.ngnetic moments of these fine magnetic particles are randomly distributed iii the nonmagnetic host, as the spin梪p and spin梔own conduction electrons scatter between the randomly oriented magnetic moments, the resistance is high. While the applied magnetic field is added, these magnetic moments will be aligned along the field and in an ordering state. Then, one of the spin direction electrons have weak scattering between magnetic ordering particles so that give rise to a short-circuit effect, and therefore decrease the resistance of the system. Generally, the above process is also called as two梒hannel model which is associated with the scattering of spin-dependent conduction electrons. Because the GMR effect is related to the orientation of the magnetic moments of particles, to study the magnetic properties of randomly distributed particles is aslo an important aspect.In the investigation of the dependence of GMR on applied field, we first distinguish the magnetic particles into two parts according to the magnetic properties at some certain temperature. One part is called superparamaguetic (5PM) particl...
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