Detection of the Unusual Magnetic Orders in the Pseudogap Region of a High-Temperature Superconducting ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathbf{O}}_{6.6}$ Crystal by Muon-Spin Relaxation

We present muon-spin relaxation ($\mu \mathrm{SR}$) measurements on a large ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.6}$ single crystal in which two kinds of unusual magnetic order have been detected in the pseudogap region by neutron scattering. A comparison is made to measurements on smaller, higher quality ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ single crystals. One type of magnetic order is observed in all samples, but does not evolve significantly with hole doping. A second type of unusual magnetic order is observed only in the ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.6}$ single crystal. This magnetism has an ordered magnetic moment that is quantitatively consistent with the neutron experiments, but is confined to just a small volume of the sample ($\sim 3\%$). Our findings do not support theories that ascribe the pseudogap to a state characterized by loop-current order, but instead indicate that dilute impurity phases are the source of the unusual magnetic orders in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$.

Figure 1

(a) Representative $\mathrm{ZF}\mathrm{\text{−}}\mu \mathrm{SR}$ signals for the large $y=6.6$ single crystal. The solid curves are fits to Eq. (1). Also, temperature dependence of ${\nu }_1$ for the smaller YBCO single crystals with oxygen content (b) $y=6.50$, (c) $y=6.57$, (e) $y=6.80$, (f) $y=6.95$, and for (g) the small Ca-doped YBCO single crystals with $y=6.98$, and for (d) the large $y=6.6$ single crystal. The solid curves in (b)–(g) are guides to the eye. The error bars come from the fits. The hole-doping concentration $p$ for each sample is shown in the respective panel.

Figure 2

A comparison of the temperature dependence of ${\nu }_1$ for the large $y=6.6$ single crystal with the square root of the neutron scattering rate at wave vector (0.5, 0.5, 2) from Ref. 4. Both quantities are proportional to the ordered magnetic moment.

Figure 3

Time evolution of the $\mathrm{ZF}\mathrm{\text{−}}\mu \mathrm{SR}$ signal at early times for (a)–(d) the large $y=6.6$ single crystal, (e)–(g) the mosaic of $y=6.57$ single crystals, and (h) a single crystal of ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_4$. The spectra are made up of $\sim 11$ million muon-decay events, with the exception of (e) and (h), which have 3 and 5 times this number of statistics, respectively. The solid curve in each panel is a fit to Eq. (2). Note the difference in the time scale of (a) relative to (b)–(h).

Figure 4

Temperature dependence of (a) $f$ and (b) ${\nu }_2$ from fits of the $\mathrm{ZF}\mathrm{\text{−}}\mu \mathrm{SR}$ signals for the $y=6.6$ single crystal to Eq. (2). (c) A staggered arrangement of spins on the oxygen sites in the ${\mathrm{CuO}}_2$ planes that accounts for the average field of the 3% oscillatory component. The spins are rotated in the ${\mathrm{CuO}}_2$ planes $\pm 45°$ from the $a$ axis, and are directed 55° (or 235°) from the $c$ axis. Also shown are the two muon-stopping sites in YBCO with $y=6.6$.