Correlated impurities and intrinsic spin-liquid physics in the kagome material herbertsmithite

Abstract

Low energy inelastic neutron scattering on single crystals of the kagome spin-liquid compound ${\mathrm{ZnCu}}_{3}{(\mathrm{OD})}_{6}{\mathrm{Cl}}_{2}$ (herbertsmithite) reveals antiferromagnetic correlations between impurity spins for energy transfers $\ensuremath{\hbar}\ensuremath{\omega}<0.8\phantom{\rule{0.28em}{0ex}}\mathrm{meV} (\ensuremath{\sim}J/20)$. The momentum dependence differs significantly from higher energy scattering which arises from the intrinsic kagome spins. The low energy fluctuations are characterized by diffuse scattering near wave vectors (100) and $\left(00\frac{3}{2}\right)$, which is consistent with antiferromagnetic correlations between pairs of nearest-neighbor Cu impurities on adjacent triangular (Zn) interlayers. The corresponding impurity lattice resembles a simple cubic lattice in the dilute limit below the percolation threshold. Such an impurity model can describe prior neutron, NMR, and specific heat data. The low energy neutron data are consistent with the presence of a small spin gap $(\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}0.7\phantom{\rule{0.28em}{0ex}}\mathrm{meV})$ in the kagome layers, similar to that recently observed by NMR. The ability to distinguish the scattering due to Cu impurities from that of the planar kagome Cu spins provides an important avenue for probing intrinsic spin-liquid physics.