The excellent magnetic entropy change ($\mathrm{\Delta }{S}_T$) in the temperature range of 20 $\sim$ 77 K due to the first-order phase transition makes ${\mathrm{Pr}}_2\mathrm{In}$ an intriguing candidate for magnetocaloric hydrogen liquefaction. As an equally important magnetocaloric parameter, the adiabatic temperature change ($\mathrm{\Delta }{T}_{ad}$) of ${\mathrm{Pr}}_2\mathrm{In}$ associated with the first-order phase transition has not yet been reported. In this work, the $\mathrm{\Delta }{T}_{ad}$ of ${\mathrm{Pr}}_2\mathrm{In}$ is obtained from heat capacity measurements: 2 K in fields of 2 T and 4.3 K in fields of 5 T. While demonstrating a $\mathrm{\Delta }{T}_{ad}$ that is not as impressive as its remarkable $\mathrm{\Delta }{S}_T, {\mathrm{Pr}}_2\mathrm{In}$ exhibits a low Debye temperature ($T_D$) of around 110 K. Based on these two observations, an approach that combines the mean-field and Debye models is developed to study the correlation between $\mathrm{\Delta }{T}_{ad}$, one of the most important magnetocaloric parameters, and $T_D$, one important property of a material. The role of $T_D$ in achieving large $\mathrm{\Delta }{T}_{ad}$ is revealed: materials with higher $T_D$ tend to exhibit larger $\mathrm{\Delta }{T}_{ad}$, particularly in the cryogenic temperature range. This discovery explains the absence of an outstanding $\mathrm{\Delta }{T}_{ad}$ in ${\mathrm{Pr}}_2\mathrm{In}$ and can serve as a tool for designing or searching for materials with both a large $\mathrm{\Delta }{S}_T$ and a $\mathrm{\Delta }{T}_{ad}$.

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• Liquified hydrogen
• Magnetic phase transitions
• Magnetism
• Magnetocaloric effect
• Magnetic refrigeration
• Solid-state refrigeration
• Magnetization measurements