There are various reasons for which high temperature superconductivity in the cuprates is a hard problem but it is now clear that one of these reasons is that, in some instances, the superconducting state impedes ordering of the spin or charge degrees of freedom. Because of this competition effect, ordered phases may thus remain hidden, which hampers full understanding of the cuprate electronic properties. Nevertheless, tremendous progress has been accomplished in the last two decades as experiments using magnetic fields to quench superconductivity have revealed the fate of spin and/or charge orders that compete with superconductivity.

Such phase competition is illustrated by our recent study of spin-glass freezing in La2−xSrxCuO4, combining nuclear magnetic resonance (NMR) and sound velocity measurements (1). We found that, once competing effects from superconductivity are removed by high magnetic fields, the spin-glass phase of La2−xSrxCuO4 survives up to much higher doping than hitherto believed, actually up to a doping level consistent with p*, the boundary of the pseudogap phase at T=0. Said differently, the antiferromagnetic-glass phase extends from the doped Mott insulator at p = 0.02 all the way up to p* ≈ 0.19, which thus marks a quantum phase transition in the non-superconducting ground state.

In this talk, I will present NMR results in La2−xSrxCuO4 (1), together with more recent results in Eu-doped La2−xSrxCuO4 (2), and I will discuss possible implications of the results in the context of ongoing debates regarding the nature of the pseudogap phase and of its critical end point.

(1) M. Frachet, I. Vinograd et al., Hidden magnetism at the pseudogap critical point of a cuprate superconductor. Nat. Phys. 16, 1064 (2020)

(2) A. Missiaen et al., unpublished.