A model of the magnetic properties of a dispersion of interacting superparamagnetic particles in a solid matrix is presented. The model uses Monte Carlo techniques and is capable of predicting the time and temperature dependence of the magnetic properties. The model is applied to the study of the magnetic behavior of a cobalt granular system, particularly the low-field susceptibility. It is shown that strongly interacting systems at high density exhibit non-Langevin behavior and give a strongly nonlinear variation of susceptibility with packing density. The temperature dependence of the initial susceptibility shows the characteristic peak observed experimentally, with the peak temperature increasing with packing density. The field cooled (FC) and zero field cooled (ZFC) magnetization are also studied. The field dependence of the FC magnetization is shown to depend on the interparticle interactions and also on the orientational easy axis distribution. The FC magnetization is found to exhibit a peak resulting from the interactions. This behavior is finally related to the energy barrier distribution of the system (and its dependence on the interactions) using the temperature decay of remanence. It is also shown that the remanence calculated from the complete hysteresis loop at each temperature differs from the values obtained by increasing the temperature of a system initially at saturation remanence. The evolution of magnetic properties as a function of the magnetic state and history points to the importance of collective phenomena. Calculations of a spin-spin correlation function show the existence of a state with short-ranged order at low temperatures.

• Received 6 March 2000

DOI:https://doi.org/10.1103/PhysRevB.63.024410