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

TL;DR

This paper models the complex lattice structure of Ba$_3$XSb$_2$O$_9$ materials with charged dumbbells using Monte Carlo simulations, revealing a freezing transition and mechanisms for spin-orbital liquid behavior.

Contribution

It introduces a frustrated Coulomb model for dumbbell arrangements and explains how disorder promotes spin-orbital resonant states with orphan spins.

Findings

Identification of a freezing temperature matching experimental data

Discovery of a branching structure of X$^{2+}$ clusters

Proposal of a mechanism for spin-orbital liquid behavior

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, $T_{\sf frz}$, at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba$_3$CuSb$_2$O$_9$. At $T=T_{\sf frz}$ 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.