Employing the mean-field approximation founded on the Gibbs-Bogoliubov inequality, the magnetic and critical behaviors of an Ising system with mixed spins ( \(\sigma = 1\) ; \(S = 3/2\) ) on a two-dimensional CrI \(_3-\) like structure were examined. The effects of exchange couplings ( \(J_{\sigma }\) and \(J_S\) ), crystal fields ( \(\Delta _{\sigma }\) and \(\Delta _S\) ), temperature (T), and external magnetic field (h) on the lattice’s magnetization, susceptibility, phase diagrams, and hysteresis loops were investigated. This CrI \(_3-\) like monolayer features second- and first-order phase transitions, isolated critical points, and compensation behavior. For selected system parameter values, the values \(\Delta _{\sigma } = -3.75\) and \(\Delta _S = -7.5\) correspond to the points at \(T=0\) , where a first-order phase transition occurs between two ferrimagnetic phases. Furthermore, the compensation phenomenon appears in the following ranges: \(\Delta _{\sigma } > -3.75\) , \(\Delta _S > -5.48\) , \(J_{\sigma } < 4.62\) , and \(J_S > 0.83\) . We also demonstrated the existence of multiple hysteresis loops under certain physical conditions. The results achieved in this work could contribute to the advancement of potential CrI \(_3\) -based applications, such as spintronics, sensing, magnetic information storage, and magneto-optical recording.
