In this work, we investigate the magnetic, magnetocaloric, and hysteresis properties of the Spin-2 Blume–Capel model with second nearest neighbor interaction, which is a good candidate for exploring the magnetic properties of the compound LaMnO3, within the mean-field approximation. The Hamiltonian considered includes exchange interactions between first and second neighbors ( \(J_1\) and \(J_2\) ), the crystal field D, and an external magnetic field h. Phase diagrams reveal the presence of a tricritical point separating first- and second-order transitions. The magnetization shows a second-order transition in the absence of the external magnetic field and a transition to a superparamagnetic phase for \(h/J_{2} \ne 0\) . The magnetic entropy \(-\Delta S_m\) increases with field strength, reaching a maximum of 0.272 for \(h/J_2 = 5\) , while the relative cooling power (RCP) increases linearly. Finally, the system exhibits complex hysteresis behavior, with one, three, or four loops depending on the physical parameters considered. These results highlight the potential of the compound \(\hbox {LaMnO}_3\) for magnetic refrigeration applications.
