Critical Magnetic Behavior of the Rare Earth-Based Alloy GdN: Monte Carlo Simulations and Density Functional Theory Method

In this study, we use Monte Carlo simulations (MCS) and DFT method in order to deduce the critical magnetic behavior of the rare earth-based alloy GdN. The Monte Carlo method is based on the Metropolis algorithm, while the DFT method is applied under the generalized gradient approximation. In a first step, we discuss and study the density of states, the exchange coupling interactions, the crystal field and the Curie temperature within the mean-field approximation. We started by studying the ground state phase diagrams in the different planes of the physical parameters. In fact, we present and discuss the behavior of total magnetizations and susceptibilities as a function of: the temperature, the crystal field, the exchange coupling interactions and the external magnetic field. To complete this study, the hysteresis loops are illustrated and analyzed when varying the external magnetic field for fixed specific values of the other physical parameters. The obtained values of the critical exponents of the GdN compound have been deduced and compared with those existing in the literature.