Disorder driven spin-orbital liquid behaviour in the Ba${}_3$XSb${}_2$O${}_9$ materials

Abstract

Recent experiments on the Ba${}_3$XSb${}_2$O${}_9$ family have revealed materials that potentially realise spin- and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X${}^{2+}$-Sb${}^{5+}$ dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, $T_{\mathsf{frz}}$, at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba${}_3$CuSb${}_2$O${}_9$. At $T=T_{\mathsf{frz}}$ we find a complicated ``branching'' structure of superexchange-linked X${}^{2+}$ clusters, and show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalised orphan spins.

10 pages, 11 figures

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