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