Monte Carlo simulation of a cluster system with strong interaction and random anisotropy

The Monte Carlo method is used to study magnetic properties of amorphous rare-earth (RE) and transition-metal alloys, based on a model in which the magnetic units are magnetic clusters. Each cluster is assumed to possess a certain magnetic moment, which decreases with increasing temperature, and a Curie temperature (formula presented) A random distribution is assumed for the magnetic easy directions of the clusters. Monte Carlo simulations were carried out to simulate magnetization curves after zero-field cooling and magnetic hysteresis loops at different temperatures. The simulation results showed presence of two other critical temperatures (formula presented) and (formula presented) below (formula presented) Here (formula presented) is the blocking temperature due to the anisotropy energy of clusters, while (formula presented) is the freezing temperature due to interactions between clusters. If (formula presented) is lower than (formula presented) the system behaves as a normal superparamagnetic material, characterized by a relatively weak effect of cluster correlation and/or dipole interaction. If (formula presented) is higher than (formula presented) as in the case of many amorphous rare-earth and transition-metal alloys, it is possible to have three magnetic states, depending on the temperature: ferromagnetism when (formula presented) superparamagnetism with correlation when (formula presented) and paramagnetism when (formula presented) The freezing due to cluster interactions is characterized by a significant increase of remanence, while high coercivity is obtained below (formula presented) The simulation results were compared with the experimental measurements. The magnetic behaviors of amorphous rare-earth and transition-metal alloys are well described by the model.