Role of Debye temperature in achieving large adiabatic temperature changes at cryogenic temperatures: A case study on Pr₂In

The excellent magnetic entropy change (ΔS_T ) in the temperature range of 20 ∼ 77 K due to the first-order phase transition makes Pr₂In an intriguing candidate for magnetocaloric hydrogen liquefaction. As an equally important magnetocaloric parameter, the adiabatic temperature change (ΔT_ad) of Pr₂In associated with the first-order phase transition has not yet been reported. In this work, the ΔT_ad of Pr₂In 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 ΔT_ad that is not as impressive as its remarkable ΔS_T, Pr₂In 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 ΔT_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 ΔT_ad is revealed: materials with higher T_D tend to exhibit larger ΔT_ad , particularly in the cryogenic temperature range. This discovery explains the absence of an outstanding ΔT_ad in Pr₂In and can serve as a tool for designing or searching for materials with both a large ΔS_T and a ΔT_ad.