The spin-1/2 kagome Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ${\mathrm{ZnCu}}_3{\left(\mathrm{OH}\right)}_6{\mathrm{Cl}}_2$, which unfortunately suffers from the notorious orphan spin problem caused by magnetic disorders. Here, we turn to ${\mathrm{YCu}}_3{\left(\mathrm{OH}\right)}_{6.5}{\mathrm{Br}}_{2.5}$, recently recognized as another host of a globally undistorted kagome ${\mathrm{Cu}}^{2+}$ lattice free from orphan spins, and thus a more feasible system for studying the intrinsic kagome quantum spin liquid physics. Our high-resolution low-temperature thermal conductivity measurements yield a vanishingly small residual linear term of $\kappa /T$ ($T\to 0$), and thus clearly rule out itinerant gapless fermionic excitations. An unusual scattering of phonons grows exponentially with temperature, suggesting thermally activated phonon-spin scattering and hence a gapped magnetic excitation, consistent with a ${\mathbb{Z}}_2$ quantum spin liquid ground state. Additionally, an analysis of the magnetic field impact on the thermal conductivity reveals a field closing of the spin gap, while the excitations remain localized.

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• Acoustic phonons
• Frustrated magnetism
• Quantum spin liquid
• Thermal conductivity
• Topological phases of matter
• Kagome lattice
• Strongly correlated systems
• Transport techniques