17-O NMR site-selective study of the quantum kagome antiferromagnet ZnCu3(OH)6Cl2 : a gapless ground state.*

Herbertsmithite ZnCu₃(OH)₆Cl₂ is known as one of the most emblematic and deeply studied quantum spin liquid representative of the Quantum Kagome Heisenberg Antiferromagnet Hamiltonian physics. On the theory side, the ground state has been heavily debated for more than 30 years with no definitive solution to-date. Yet, defects, have been ubiquitous in all experiments so far and one of the key issues is to disentangle what would be the intrinsic physics of an isolated kagome plane and that impacted by 20-30% interlayer Cu’s  replacing non-magnetic Zn²⁺. At this stage, the need of including defects - but which defects? - into models represents a difficult task but one of the most promising avenues to conclude on the ground state of the KHAF.

Here, we present site-resolved ¹⁷O NMR experiments on herbertsmithite single crystals using contrast methods analogous to MRI ones, which clearly separate slow from fast relaxing sites. The ¹⁷O nucleus being a very sensitive probe of the kagome  planes, the spectral analysis yield different signatures for these sites and unambiguously shows that interlayer defects, initially thought to behave as independent paramagnetic spins also impact the physics of the kagome planes. We attribute the fast relaxing and gapless spectral contribution representing a ~70-75% fraction to O probing the least impurity-disturbed Cu sites. This, in our opinion, strongly argues in favor of a gapless model for the KHAF. Our results will be put into perspective of other experiments especially recent Cu NQR and specific heat ones.