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The effects of interactions (dipolar and exchange) on the magnetic behavior of granular solid systems are examined using a Monte Carlo model capable of predicting the temperature and time dependence of the magnetic properties. Using this model the interaction effects on the magnetization and the magnetoresistance are studied. The results show that these properties depend critically on the strength and nature of the interactions. Magnetostatic interactions are found to decrease both remanence and coercivity and Hc is predicted to decrease linearly with concentration. It is shown that spatial disorder may be responsible for an increase of coercivity with exchange coupling which has been observed in some experimental studies. In systems with no hysteresis, magnetostatic interaction effects are found to increase the superparamagnetic transition temperature, in agreement with experimental data and previous analytical treatments. Calculations of the giant magnetoresistance (GMR) show that magnetostatic interaction effects give rise to a finite positive resistivity at zero field which increases with concentration. This causes the value of the maximum change in resistivity, which occurs near the coercivity, to be greater than the value at zero field. These calculations are in agreement with experimental observations of GMR in granular solids. It is predicted that the GMR is strongly dependent on the spin diffusion length via the local spin–spin correlation function.

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A mixture of bi(acetylacetonato) zinc(II)hydrate and tri(dimethylglyoximato)gadolinium(III) complexes was used to synthesize Gd-doped ZnO powder. The synthesis was a result of the complexes’ thermal codecomposition. Magnetic characterizations have shown that the sample with the atomic ratio 3.5% Gd exhibited a clear ferromagnetic behavior at room temperature (RT) and demonstrated the highest saturation magnetization at 0.05 emu/g. When all the Gd ions were considered to be ferromagnetically coupled (successful doping) the analysis of moments per Gd atom resulted in a very low value (≈0.01 μB). However, when the uncorrelated spins that are responsible for the paramagnetic component were taken into account, the analysis of moment per Gd atom gave a high value (≈9 μB). These results led us to believe that successful but not complete doping may be responsible for the observed RT magnetization in these Gd doped ZnO systems. Further analysis for the irreversible component of the sample with 3.5% Gd has shown that the activated moment, upon reversal, is large (μact=1.78×106 μB). This result hints at the existence of largely correlated regions of spins. Moreover, the obtained distribution of activation energies demonstrates that the reversal mechanism cannot be due to independent regions of correlated spins. This result explains the low values of the remanence ratio and coercivity that are usually observed in such systems.