Highly disordered magnetism confined to individual weakly interacting vortices is detected by muon spin rotation in two different families of high-transition-temperature superconductors, but only in samples on the low-doping side of the low-temperature normal state metal-to-insulator crossover (MIC). The results support an extended quantum phase transition (QPT) theory of competing magnetic and superconducting orders that incorporates the coupling between CuO2 planes. Contrary to what has been inferred from previous experiments, the static magnetism that coexists with superconductivity near the field-induced QPT is not ordered. Our findings unravel the mystery of the MIC and establish that the normal state of high-temperature superconductors is ubiquitously governed by a magnetic quantum critical point in the superconducting phase.
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