The role of Debye temperature in achieving large adiabatic temperature changes at cryogenic temperatures: a case study on Pr_2In

The excellent magnetic entropy change (Δ S_T) in the temperature range of 20 ∼ 77 K due to the first-order phase transition makes Pr_2In an intriguing candidate for magnetocaloric hydrogen liquefaction. As an equally important magnetocaloric parameter, the adiabatic temperature change (Δ T_ad) of Pr_2In associated with the first-order phase transition has not yet been reported. In this work, the Δ T_ad of Pr_2In 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 Δ T_ad that is not as impressive as its remarkable Δ S_T, Pr_2In exhibits an unusual 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 Δ T_ad and T_D. The role of T_D in achieving large Δ T_ad is revealed: materials with higher T_D tend to exhibit larger Δ T_ad, particularly in the cryogenic temperature range. This discovery explains the absence of an outstanding Δ T_ad in Pr_2In and can serve as a tool for designing or searching materials with both a large Δ S_T and a Δ T_ad.