标题： 具有反铁磁相互作用的6H-钙钛矿二聚体晶格：Ba$_3$ARu$_2$O$_9$ 显示英文标题

标题： The 6H-Perovskite Dimer Lattice with Antiferromagnetic Interactions: Ba$_3$ARu$_2$O$_9$

摘要： 我们研究了六方钙钛矿二聚体晶格 Ba$_3$Zn$_{1-x}$Ca$_x$Ru$_2$O$_9$的磁行为，使用了分析理论、密度泛函理论、非弹性中子散射以及历史磁化和中子散射数据的建模。 基于经典 Luttinger-Tisza 分析构建的二聚体平均场理论生成了一个相图，揭示了随着二聚体间耦合的增加，从非磁单态到有限磁矩基态的转变。 （广义）线性自旋波理论捕捉了多重态混合、激发能隙关闭和涨落引起的磁矩抑制。 密度泛函理论在选定化合物上的应用以及稀释的Ba$_3$Zn(Ru$_{1-x}$Sb$_x$)$_2$O$_9$的中子光谱确认了交换层次，使得在此框架内对之前发表的实验进行量化成为可能。 我们的结果确定了三种磁矩抑制机制：量子涨落、配体杂化以及非磁单态/磁多重态混合。 显示英文摘要

摘要： We investigate the magnetic behavior of the 6H-perovskite dimer lattice Ba$_3$Zn$_{1-x}$Ca$_x$Ru$_2$O$_9$ using analytical theory, density functional theory, inelastic neutron scattering, and modeling of historical magnetization and neutron-scattering data. A dimer mean-field theory built upon classical Luttinger-Tisza analysis generates a phase diagram revealing a transition from a nonmagnetic singlet to a finite-moment ground state as interdimer couplings increase. A (generalized) linear spin-wave theory captures multiplet mixing, excitation gap closing, and fluctuation-induced moment suppression. Density functional theory on select compounds and neutron spectroscopy on dilute Ba$_3$Zn(Ru$_{1-x}$Sb$_x$)$_2$O$_9$ confirm the exchange hierarchy, enabling quantification of previously published experiments within this framework. Our results identify three mechanisms for magnetic moment suppression: quantum fluctuations, ligand hybridization, and nonmagnetic-singlet/magnetic-multiplet mixing.