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Monte Carlo study of the magnetic properties of the spinel ZnFe$_2$O$_4$ compound

In this work, a study of the magnetic behavior of the spinel ZnFe2O4 is presented by using the Monte Carlo simulations (MCS). The iron atoms provide the magnetism in this material. In fact, the magnetic spin of moment of the Fe3+ ions is S=5/2. In this context, we propose a Hamiltonian describing and modeling this compound. Firstly, at zero temperature we have studied the ground state phase diagrams of the system in order to find the more stable configurations. On the other hand, for a non-null temperature values, we obtained the results of the Monte Carlo simulations, namely: the magnetizations and the susceptibilities as a function of temperature. The behavior of those physical parameters shows an anti-ferromagnetic behavior with a Neel-temperature of about TN=12 K. This value is found to be in good agreement with the literature. Moreover, the effect of varying the crystal field, the exchange coupling interactions and the external magnetic field is studied and discussed on the behavior of the magnetizations. To complete this study, we presented the magnetic hysteresis loops deducing the antiferromagnetic behavior of the ZnFe2O4 compound.