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 $\mathrm{\Delta }{T}_{ad}$.

中文翻译：

---

德拜温度在低温下实现大绝热温度变化的作用：Pr2In 的案例研究

优异的磁熵变（$\mathrm{\Delta }{S}_{\mathrm{时间}}$）在20的温度范围内$～$77 K 由于一阶相变使得${\mathrm{普罗}}_2在$磁热氢液化的一个有趣的候选者。作为一个同样重要的磁热参数，绝热温度变化（$\mathrm{\Delta }{\mathrm{时间}}_{Ad}$） 的${\mathrm{普罗}}_2在$与一级相变相关的现象尚未见报道。在这项工作中，$\mathrm{\Delta }{\mathrm{时间}}_{Ad}$的${\mathrm{普罗}}_2在$是从热容测量中获得的：2 T 场中为 2 K，5 T 场中为 4.3 K。$\mathrm{\Delta }{\mathrm{时间}}_{Ad}$这并不像其非凡的那样令人印象深刻$\mathrm{\Delta }{S}_{\mathrm{时间}}, {\mathrm{普罗}}_2在$表现出较低的德拜温度（${\mathrm{时间}}_D$）约为 110 K。基于这两个观测结果，开发了一种结合平均场和德拜模型的方法来研究之间的相关性$\mathrm{\Delta }{\mathrm{时间}}_{Ad}$，最重要的磁热参数之一，以及${\mathrm{时间}}_D$，材料的一个重要属性。的作用${\mathrm{时间}}_D$在实现大$\mathrm{\Delta }{\mathrm{时间}}_{Ad}$揭示：材料具有更高${\mathrm{时间}}_D$往往表现出较大的$\mathrm{\Delta }{\mathrm{时间}}_{Ad}$，特别是在低温范围内。这一发现解释了缺乏杰出的$\mathrm{\Delta }{\mathrm{时间}}_{Ad}$在${\mathrm{普罗}}_2在$并且可以作为设计或搜索具有大范围材料的工具$\mathrm{\Delta }{S}_{\mathrm{时间}}$和一个$\mathrm{\Delta }{\mathrm{时间}}_{Ad}$。