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

TL;DR

This study uses nuclear quadrupole resonance to reveal that in kagome antiferromagnets Zn-barlowite and herbertsmithite, spin singlets with inhomogeneous gaps emerge gradually, with about 60% of spins forming singlets at low temperatures.

Contribution

It provides experimental evidence of inhomogeneous spin singlet formation in kagome antiferromagnets, highlighting the role of disorder in their quantum ground states.

Findings

Spin singlets emerge gradually with spatially varying gaps.

Approximately 60% of spins form singlets at low temperatures.

Disorder influences the inhomogeneous gapped behavior.

Abstract

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 singlets. But the existence of various competing states makes a convincing theoretical prediction of the QSL ground state difficult, calling for experimental clues from model materials. The kagome lattice materials Zn-barlowite ZnCu$_{3}$(OD)$_{6}$FBr and herbertsmithite ZnCu$_{3}$(OD)$_{6}$Cl$_2$ do not exhibit long range order, and they are considered the best realizations of the kagome Heisenberg antiferromagnet known to date. Here we use $^{63}$Cu nuclear quadrupole resonance combined with the inverse Laplace transform (ILT) to probe locally the inhomogeneity of delicate quantum ground states affected by disorder. 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 approximately 60\% of the total spins. Theoretical models need to incorporate the role of disorder to account for the observed inhomogeneously gapped behaviour.