Orbital effects and Affleck-Haldane-type spin dimerization in \nBa4Ru3O10

Abstract

${\\mathrm{Ba}}_{4}{\\mathrm{Ru}}_{3}{\\mathrm{O}}_{10}$, the quasi-one-dimensional spin-1 ($S$ = 1) compound, has rather intricate magnetic properties. The compound consists of structural Ru trimers, which together form the zig-zag chains where the Ru has two inequivalent crystallographic sites. While at high temperature both the inequivalent Ru ions stay in the $4+$ state with effective $S=$ 1 spin state, upon lowering the temperature, the magnetic moment of the central Ru atom is completely quenched accompanied by a change in the octahedral environment. This effectively gives rise to a bond-alternating chain and provides an opportunity to study the excitation of such a spin network in a real material. We have used microscopic tools such as neutron scattering and muon spin relaxation along with the density functional theory based calculations to address the spin state of the two inequivalent Ru ions in this material. From our neutron powder diffraction, on lowering of temperature, we find a large tetragonal distortion of the central ${\\mathrm{RuO}}_{6}$ octahedra of the trimer. The splitting of the ${t}_{2g}$ level of the central Ru due to this distortion is found to be significant leading to the quenching of the moment underscoring the Hund s exchange. The nonmagnetic central Ru promotes a strong antiferromagnetic superexchange between the other two Ru ions in the trimer, which gives rise to a dimeric state. The presence of spin dimers is reflected by the manifestation of a gap in the spin excitation spectra. The spin-dimer formation in ${\\mathrm{Ba}}_{4}{\\mathrm{Ru}}_{3}{\\mathrm{O}}_{10}$ is at par with the effective model proposed by Affleck and Haldane for the $S$ = 1 bond alternating chains in the light of valence bond solid formalism. Eventually, at a lower temperature, a long-range ordered antiferromagnetic state emerges from the gapped dimer state due to the significant interdimer interactions.