Spin liquids are exotic phases of quantum matter that challenge Landau’s paradigm of symmetry-breaking phase transitions. Despite strong exchange interactions, spins do not order or freeze down to zero temperature. Although well established for one-dimensional quantum antiferromagnets, in higher dimensions where quantum fluctuations are less acute, realizing and understanding such states is a major issue, both theoretically and experimentally. In this regard, the simplest nearest-neighbour Heisenberg antiferromagnet Hamiltonian on the highly frustrated kagome lattice has proven to be a fascinating and inspiring model. The exact nature of its ground state remains elusive and the existence of a spin-gap is the first key issue to be addressed to discriminate between the various classes of proposed spin liquids. Here, through low-temperature NMR contrast experiments on high-quality single crystals, we single out the kagome susceptibility and the corresponding dynamics in the kagome archetype, the mineral herbertsmithite, ZnCu₃(OH)₆Cl₂. We firmly conclude that this material does not harbour any spin-gap, which restores a convergence with recent numerical results promoting a gapless Dirac spin liquid as the ground state of the Heisenberg kagome antiferromagnet.

自旋液体是量子物质的奇异相，挑战了朗道的对称破缺相变范式。尽管有很强的交换相互作用，但自旋不会有序或冻结到零温度。尽管一维量子反铁磁体已经很好地建立起来，但在量子涨落不那么剧烈的更高维度中，实现和理解这种状态是一个主要问题，无论是理论上还是实验上。在这方面，高度受挫的kagome晶格上最简单的最近邻海森堡反铁磁体哈密顿量已被证明是一个迷人且鼓舞人心的模型。其基态的确切性质仍然难以捉摸，自旋间隙的存在是区分各种类型的自旋液体时要解决的第一个关键问题。这里，₃ (OH) ₆ Cl ₂。我们坚定地得出结论，这种材料不存在任何自旋间隙，这恢复了与最近的数值结果的收敛性，促进了无间隙狄拉克自旋液体作为海森堡 kagome 反铁磁体的基态。