The phonon properties of the cage-structured compound PrRh₂Zn₂₀, whose electrical resistivity exhibits a hysteretic behavior between 140 and 470 K, have been studied by inelastic X-ray scattering (IXS) measurements and first-principles calculation. The IXS spectra for the [110] transverse and [111] longitudinal phonon modes show low-energy excitations at 6–7 meV, which are assigned to optical phonon modes. The first-principles calculation reveals that the low-lying phonon modes are ascribed to the vibration of Zn atoms at the 16c site [Zn(16c)] encapsulated in the Pr₂Zn₁₂ cage. We discuss the structural instability in PrRh₂Zn₂₀ by comparing the IXS spectra with those of RRu₂Zn₂₀ (R = La and Pr) with structural transitions and PrIr₂Zn₂₀ without the structural transition. We found that the vibration energy of Zn(16c) in PrRh₂Zn₂₀ is two times higher than 3 meV in RRu₂Zn₂₀ but close to that in PrIr₂Zn₂₀. These results imply that the phonon energy of Zn(16c) stays at 6–7 meV when the cubic symmetry of the R site is maintained in the low-temperature phase. Therefore, the driving force for the structural transition in PrRh₂Zn₂₀ is distinguished from those in RRu₂Zn₂₀ (R = La and Pr).

中文翻译：

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笼型化合物PrRh2Zn20的非弹性X射线散射研究

通过非弹性X射线散射（IXS）测量和第一性原理研究，研究了笼形结构化合物PrRh ₂ Zn ₂₀的声子性质，该化合物的电阻率在140至470 K之间表现出滞后行为。[110]横向和[111]纵向声子模式的IXS光谱显示6–7 meV的低能激发，这被分配给光学声子模式。第一性原理计算表明，低层声子模式归因于封装在Pr ₂ Zn ₁₂笼中的16 c位置[Zn（16 c）]上锌原子的振动。我们讨论PrRh ₂ Zn _20中的结构不稳定性通过比较IXS光谱与具有结构转变的R Ru ₂ Zn ₂₀（R = La和Pr）和不具有结构转变的PrIr ₂ Zn _20的光谱。我们发现PrRh ₂ Zn ₂₀中Zn（16 c）的振动能量是R Ru ₂ Zn _20中3 meV的两倍，但与PrIr ₂ Zn _20中的接近。这些结果表明，当R的立方对称性时，Zn（16 c）的声子能量保持在6–7 meV。现场保持在低温阶段。因此，PrRh ₂ Zn _20中的结构转变驱动力不同于R Ru ₂ Zn _20中的驱动力（R = La和Pr）。