6⁢𝐻-perovskite dimer lattice with antiferromagnetic interactions: Ba3⁢Zn1−𝑥⁢Ca𝑥⁢Ru2⁢O9

Abstract

We investigate the magnetic behavior of the 6⁢𝐻-perovskite dimer lattice Ba3⁢Zn1−𝑥⁢Ca𝑥⁢Ru2⁢O9 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 calculations on selected compounds, together with neutron spectroscopy of dilute Ba3⁢Zn⁢(Ru1−𝑥⁢Sb𝑥)2⁢O9, 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.