AI 中文总结
研究多铁性Ba3HoRu2O9中自旋、晶体场和晶格自由度的相互作用，结合非弹性中子散射、线性自旋波计算、晶体场分析、拉曼光谱和机器学习力场声子计算，确定不同激发贡献，建立微观框架。
AI 中文摘要
理解相关4d-4f多铁性氧化物中自旋偶极耦合和高能激发的微观起源具有挑战性，因为磁、晶体场和晶格激发在能量上经常重叠。六角形6H钙钛矿Ba3HoRu2O9由于Ru2O9分子单元和局域Ho3+磁矩的共存，为研究这种相互作用提供了理想平台。为识别不同激发的贡献，结合了非弹性中子散射（INS）、线性自旋波计算、晶体场分析、拉曼光谱和机器学习力场（MLFF）声子计算。线性自旋波理论准确再现了低于6.2 meV的色散磁激发，确定其为耦合Ru-Ho磁网络的集体自旋波激发。在更高能量下，观察到以20、39、70和90 meV为中心的宽激发，远高于磁有序温度。基于史蒂文斯形式的晶体场计算将最强的Ho3+跃迁置于实验观察到的能量窗口内，而拉曼光谱和MLFF声子计算识别出具有可比能量的光学声子。这些互补结果表明，39 meV附近的宽INS特征与Ho3+晶体场激发、晶格振动和先前报道的Ru2O9分子磁激发的重叠贡献一致。这些发现为理解这种多铁性4d-4f化合物中自旋、晶体场和晶格自由度之间的相互作用建立了微观框架。
英文摘要
Understanding the microscopic origin of spin-dipole coupling and high-energy excitations in correlated 4d-4f multiferroic oxides is challenging because magnetic, crystal-field, and lattice excitations frequently overlap in energy. The hexagonal 6H perovskite Ba3HoRu2O9 provides an ideal platform to investigate this interplay owing to the coexistence of Ru2O9 molecular units and localized Ho3+ moments. To identify the contributions from these different excitations, we combine inelastic neutron scattering (INS) with linear spin-wave calculations, crystal-field analysis, Raman spectroscopy, and machine-learned force field (MLFF) phonon calculations. A dispersive magnetic excitation below 6.2 meV is accurately reproduced by linear spin-wave theory, establishing its origin as a collective spin-wave excitation of the coupled Ru-Ho magnetic network. At higher energies, broad excitations centered near 20, 39, 70, and 90 meV is observed that are present far above magnetic ordering temperature. Crystal-field calculations based on the Stevens formalism place the strongest Ho3+ transitions within the experimentally observed energy window, while Raman spectroscopy and MLFF phonon calculations identify optical phonons with comparable energies. Together, these complementary results show that the broad INS feature near 39 meV is consistent with overlapping contributions from Ho3+ crystal-field excitations, lattice vibrations, and previously reported Ru2O9 molecular magnetic excitations. These findings establish a microscopic framework for understanding the interplay between spin, crystal-field, and lattice degrees of freedom in this multiferroic 4d-4f compound.
