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There are two types of magnetocaloric effects that are the so-called direct and inverse effects originating from ferromagnetic–paramagnetic (FM–PM) and antiferromagnetic–ferromagnetic (AFM–FM) phase transitions, respectively. Here, the magnetocaloric effects of FeRh alloy, which exhibit both the direct and inverse effects, have been studied by combining first-principles calculations and Monte Carlo simulations. The magnetic exchange coupling constants in the AFM and FM phases are evaluated by first-principles calculations based on the Liechtenstein formula. The Monte Carlo calculations considering the two-phase mixtures of AFM and FM well reproduce the experimental magnetization curves at zero external magnetic field. It is also shown that the isothermal magnetic entropy changes near the AFM–FM transition temperature under magnetic fields are successfully reproduced based on the Maxwell relation. The entropy changes in a wide range of the magnetic fields near the AFM–FM and FM–PM transition temperatures are investigated and the direct and inverse magnetocaloric effects of FeRh are discussed. The giant relative cooling power of FeRh alloy is achieved due to the large saturation magnetizations and the first-order AFM–FM phase transition. [Display omitted] • Theoretical interpretation of direct and inverse magnetocaloric effect in FeRh alloys. • DFT calculations for electronic structure and magnetic coupling constants and Monte-Carlo simulation. • Comparison of isothermal magnetic entropy change of inverse magnetocaloric effect with experimental work. [ABSTRACT FROM AUTHOR]