Emergence of spin singlets with inhomogeneous gaps in the kagome lattice Heisenberg antiferromagnets Zn-barlowite and herbertsmithite

The kagome Heisenberg antiferromagnet formed by frustrated spins arranged in a lattice of corner-sharing triangles is a prime candidate for hosting a quantum spin liquid (QSL) ground state consisting of entangled spin singlets1. However, the existence of various competing states makes a convincing theoretical prediction of the QSL ground state difficult2, calling for experimental clues from model materials. The kagome lattice materials Zn-barlowite (ZnCu3(OD)6FBr)3–5 and herbertsmithite (ZnCu3(OD)6Cl2)6–10 do not exhibit long-range order and are considered the best realizations of the kagome Heisenberg antiferromagnet known so far. Here we use 63Cu nuclear quadrupole resonance combined with the inverse Laplace transform11–13 to locally probe the inhomogeneity of delicate quantum ground states affected by disorder14–17. We present direct evidence for the gradual emergence of spin singlets with spatially varying excitation gaps, but even at temperatures far below the super-exchange energy scale their fraction is limited to ~60% of the total spins. Theoretical models18,19 need to incorporate the role of disorder to account for the observed inhomogeneously gapped behaviour.