Herbertsmithite is one of the most extensively studied QSL candidate materials. It is a mineral with chemical composition ZnCu(OH)Cl and a rhombohedral crystal structure. Notably, the copper ions within this structure form stacked two-dimensional layers of kagome lattices. Additionally, superexchange over the oxygen bonds creates a strong antiferromagnetic interaction between the  copper spins within a single layer, whereas coupling between layers is negligible.  Therefore, it is a good realization of the antiferromagnetic spin-1/2 Heisenberg model on the kagome lattice, which is a prototypical theoretical example of a quantum spin liquid.
Synthetic, polycrystalline herbertsmithite powder was first reported in 2005, and initial magnetic susceptibility studies showed no signs of magnetic order down to 2K.  In a subsequent study, the absence of magnetic order was verified down to 50 mK, inelastic neutron scattering measurements revealed a broad spectrum of low energy spin excitations, and low-temperature specific heat measurements had power law scaling. This gave compelling evidence for a spin liquid state with gapless  spinon excitations.  A broad array of additional experiments, including O NMR, and neutron spectroscopy of the dynamic magnetic structure factor,  reinforced the identification of herbertsmithite as a gapless spin liquid material, although the exact characterization remained unclear as of 2010.
Large (millimeter size) single crystals of herbertsmithite were grown and characterized in 2011.  These enabled more precise measurements of possible spin liquid properties. In particular, momentum-resolved inelastic neutron scattering experiments showed a broad continuum of excitations. This was interpreted as evidence for gapless, fractionalized spinons.  Follow-up experiments (using O NMR and high-resolution, low-energy neutron scattering) refined this picture and determined there was actually a small spinon excitation gap of 0.07–0.09 meV.
Some measurements were suggestive of quantum critical behavior. Magnetic response of this material displays scaling relation in both the bulk ac susceptibility and the low energy dynamic susceptibility, with the low temperature heat capacity strongly depending on magnetic field. This scaling is seen in certain quantum antiferromagnets, heavy-fermion metals, and two-dimensional He as a signature of proximity to a quantum critical point.
In 2020, monodisperse single-crystal nanoparticles of herbertsmithite (~10 nm) were synthesized at room temperature, using gas-diffusion electrocrystallization, showing that their spin liquid nature persists at such small dimensions.
It may realize a U(1)-Dirac spin liquid.