The mysterious pseudogap phase of cuprate superconductors ends at a critical hole doping level p* but the nature of the ground state below p* is still debated. Here, we show that the genuine nature of the magnetic ground state in La 2x Sr x CuO 4 is hidden by competing effects from superconductivity: applying intense magnetic fields to quench superconductivity, we uncover the presence of glassy antiferromagnetic order up to the pseudogap boundary p* ≈ 0.19, and not above. There is thus a quantum phase transition at p*, which is likely to underlie highfield observations of a fundamental change in electronic properties across p*. Furthermore, the continuous presence of quasi-static moments from the insulator up to p* suggests that the physics of the doped Mott insulator is relevant through the entire pseudogap regime and might be more fundamentally driving the transition at p* than just spin or charge ordering.

In hole-doped cuprates there is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry. In YBa 2 Cu 3 O y charge order emerges in two steps: a 2D order found at zero field and at high temperature inside the pseudogap phase, and a 3D order that is superimposed below the superconducting transition T c when superconductivity is weakened by a magnetic field. Several issues still need to be addressed such as the effect of disorder, the relationship between those charge orders and their respective impact on the Fermi surface. Here, we report high magnetic field sound velocity measurements of the 3D charge order in underdoped YBa 2 Cu 3 O y in a large doping range. We found that the 3D charge order exists over the same doping range as its 2D counterpart, indicating an intimate connection between the two distinct orders. Moreover, our data suggest that 3D charge order has only a limited impact on low-lying electronic states of YBa 2 Cu 3 O y .