Theories of the origin of superconductivity in cuprates depend on an understanding of their normal state, which exhibits various competing orders. Transport and thermodynamic measurements on La_2 − xSr_xCuO₄ show signatures of a quantum critical point and the associated fluctuations, including a peak in the electronic specific heat versus doping, near the doping p* where the pseudogap collapses. The fundamental nature of these quantum fluctuations is unclear. Here we use inelastic neutron scattering to show that, close to the superconducting critical temperature and near p*, there are very-low-energy collective spin excitations with characteristic energies of ~5 meV. Cooling and applying a magnetic field creates a mixed state with a stronger magnetic response below 10 meV. We conclude that the low-energy spin fluctuations are due to the collapse of the pseudogap combined with an underlying tendency to magnetic order. We show that the large specific heat near p* can be understood in terms of collective spin fluctuations. The spin fluctuations we measure exist across the superconducting phase diagram and may be related to the strange metal behaviour observed in overdoped cuprates.

铜酸盐中超导性起源的理论取决于对其正常状态的理解，该状态表现出各种竞争秩序。La _{2 −  x} Sr _x CuO ₄的传输和热力学测量显示了量子临界点和相关波动的特征，包括电子比热与掺杂的峰值，靠近掺杂p *，其中赝能隙坍塌。这些量子涨落的基本性质尚不清楚。这里我们使用非弹性中子散射来表明，接近超导临界温度和p附近*，有非常低能量的集体自旋激发，其特征能量为 ~5 meV。冷却和施加磁场会产生混合态，在 10 meV 以下具有更强的磁响应。我们得出结论，低能自旋涨落是由于赝能隙的坍塌以及潜在的磁有序趋势。我们表明p*附近的大比热可以根据集体自旋波动来理解。我们测量的自旋波动存在于超导相图中，可能与在过量掺杂的铜酸盐中观察到的奇怪金属行为有关。