Incommensurate Magnetic Order and Dynamics Induced by Spinless Impurities in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathbf{O}}_{6.6}$

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 ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.6}$, 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 ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ suggests that this behavior is universal for the layered copper oxides and analogous to impurity-induced magnetic order in one-dimensional quantum magnets.

Figure 1

Constant-energy scans in ${\mathrm{YBCO}}_{6.6}\mathrm{\text{:}}\mathrm{Zn}$ at $T=10\mathrm{K}$. (a, b) Uncorrected scans along (a) $\mathbf{Q}=(H,0.5,1.7)$ and (b) ($H$, 1.5, 1.7). The extraneous background was determined by rotating the sample by (a) 30°, (b) 10° and repeating the scans (open symbols). (c–f) Background-corrected scans along $\mathbf{Q}=(H,1.5,1.7)$ (solid symbols) and (1.5, $K$, 1.7) (open symbols) at $E=5$, 7, 10, and 38 meV.

Figure 2

(a) Zero-field and (b) longitudinal-field $\mu \mathrm{SR}$ data for ${\mathrm{YBCO}}_{6.6}\mathrm{\text{:}}\mathrm{Zn}$ at $T=2\mathrm{K}$. Panel (a) also shows data on ${\mathrm{YBCO}}_{6.6}$ and ${\mathrm{YBCO}}_{6.45}$. The different amplitudes of the nonrelaxing signals in the ZF spectra of ${\mathrm{YBCO}}_{6.6}\mathrm{\text{:}}\mathrm{Zn}$ in panels (a) and (b) arise because these were measured in different geometries where the muon spin was rotated by $\sim 60°$ and 0°, respectively, with respect to the muon beam direction. The lines are the results of fits described in the text.

Figure 3

Temperature dependence of the spin fluctuation intensity. (a, b) Scans of the dynamical magnetic susceptibility, ${\chi }^{\prime \prime }(\mathbf{Q},E)$ (derived from the INS data by correcting for the detailed-balance factor), around $\mathbf{Q}=(0.5,0.5,1.7)$ in Zn-substituted and Zn-free ${\mathrm{YBCO}}_{6.6}$ at energies and temperatures marked in the legend. The data were background-corrected as described in Fig. 1. The lines are the results of fits described in the text. (c) Amplitude of ${\chi }^{\prime \prime }$ in ${\mathrm{YBCO}}_{6.6}\mathrm{\text{:}}\mathrm{Zn}$ at $E=5$ and 7 meV extracted from fits to constant-energy scans. (d) Amplitude of ${\chi }^{\prime \prime }$ for ${\mathrm{YBCO}}_{6.6}\mathrm{\text{:}}\mathrm{Zn}$ (${\mathrm{YBCO}}_{6.6}$) at $E=38$ (37) meV. The lines are guides to the eye.

Figure 4

Energy dependence of the peak susceptibility ${\chi }^{\prime \prime }$ at $T=2\mathrm{K}$ extracted from constant-energy scans on ${\mathrm{YBCO}}_{6.6}\mathrm{\text{:}}\mathrm{Zn}$ and ${\mathrm{YBCO}}_{6.6}$. Normal-state data on pure ${\mathrm{YBCO}}_{6.6}$ are shown for comparison. The lines are guides to the eye.