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Incommensurate magnetic order and dynamics induced by spinless impurities in YBa$_2$Cu$_3$O$_{6.6}$

We report an inelastic-neutron-scattering and muon-spin-relaxation study of the effect of 2% spinless (Zn) impurities on the magnetic order and dynamics of YBa$_2$Cu$_3$O$_{6.6}$, an underdoped high-temperature superconductor that exhibits a prominent spin-pseudogap in its normal state. Zn substitution induces static magnetic order at low temperatures and triggers a large-scale spectral-weight redistribution from the magnetic resonant mode at 38 meV into uniaxial, incommensurate spin excitations with energies well below the spin-pseudogap. These observations indicate a competition between incommensurate magnetic order and superconductivity close to a quantum critical point. Comparison to prior data on La$_{2-x}$Sr$_x$CuO$_{4}$ suggests that this behavior is universal for the layered copper oxides and analogous to impurity-induced magnetic order in one-dimensional quantum magnets.