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This work presents the remarkable experimental magnetocaloric properties ofthe perovskites Pr$_{0.9}$Sr$_{0.1}$Mn$_{0.9}^{3+}$Mn$_{0.1}^{4+}$O$_{3}$,including the magnetic entropy change $|\Delta S_m|$ and the Relative CoolingPower (RCP). To understand these striking properties, we elaborate in thispaper a model and use Monte Carlo (MC) simulations to study it for comparison.For the model, we take into account nearest-neighbor (NN) interactions betweenmagnetic ions Mn$^{3+}$($S=2$) and Mn$^{4+}$($S=3/2$) and the interactionsbetween these Mn ions with the magnetic Pr ions. The crystal is a body-centeredtetragonal lattice where the corner sites are occupied by Mn ions and thecenter sites by Pr and Sr ions in their respective concentrations given in thecompound formula. We use an Ising-like spin model. We show that pairwiseinteractions between ions cannot reproduce the large plateau of themagnetization experimentally observed below the phase-transition temperature.By introducing for the first time a many-spin interaction between Mn ions, weobtain an excellent agreement with experiments. Fitting the experimental Curietemperature $T_C$ with the MC transition temperature, we estimate the value ofthe effective exchange interaction in the system. From this value, we estimatevarious exchange interactions between ions: the dominant one is that betweenMn$^{3+}$ and Mn$^{4+}$ which is at the origin of the ferromagnetic orderingbelow $T_C$. We also studied the applied-field effect on the magnetization inthe region below and above $T_C$. The obtained MC results for $|\Delta S_m|$are in agreement with experiments performed for applied fields from 1 to 5Tesla. MC results of RCP are also shown and compared to experimental ones.

Magnetic properties of perovskites Pr$_{0.9}$Sr$_{0.1}$Mn$_{0.9}^{3+}$Mn$_{0.1}^{4+}$O$_{3}$: Monte Carlo simulations and experiments