Phonon dynamics in quantum spin liquid and valence bond crystal states in the barlowite family of kagome magnets

The barlowite $[{\mathrm{Cu}}_{4}{(\mathrm{OD})}_{6}\mathrm{FBr}]$ family of materials is characterized by antiferromagnetic spin-1/2 kagome layers and are believed to host interesting ground states of quantum magnetism. Substituting the interlayer sites with zinc ions yields Zn-barlowite (${\mathrm{Zn}}_{x}{\mathrm{Cu}}_{4\ensuremath{-}x}{(\mathrm{OD})}_{6}\mathrm{FBr}, x\ensuremath{\approx}0.80$) which is a strong candidate to have a quantum spin liquid (QSL) state. Experimentally distinguishing between valence bond crystal (VBC) and QSL states in the absence of magnetic ordering can prove challenging as both states exhibit similar average spin-spin correlations. Using high-resolution inelastic x-ray scattering with 1.4 meV energy resolution, we probe acoustic phonons in these structurally similar materials at various temperatures. Our measurements uncover robust differences possibly driven by different spin-phonon physics in VBC and QSL states, particularly at the $M$-point Brillouin zone boundary. Over a large $T=[15,200]\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ temperature range, where neither material undergoes magnetic ordering nor a structural transition, we observe phonon softening in Zn-barlowite in contrast to a hardening of the same phonon in barlowite. These results indicate that acoustic phonons in the barlowite system can be used to study and possibly distinguish between QSL and disordered VBC states in quantum magnets.