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

Abstract

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.