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 T_c^cluster. 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 T_block and T_c^system below T_c^cluster. Here T_block is the blocking temperature due to the anisotropy energy of clusters, while T_c^system is the freezing temperature due to interactions between clusters. If T_c^system is lower than T_block, the system behaves as a normal superparamagnetic material, characterized by a relatively weak effect of cluster correlation and/or dipole interaction. If T_c^system is higher than T_block, 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 T<T_c^system, superparamagnetism with correlation when T_c^system<T<_c^cluster, and paramagnetism when T>T_c^cluster. The freezing due to cluster interactions is characterized by a significant increase of remanence, while high coercivity is obtained below T_block. 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.