Resonant x-ray scattering study of charge-density wave correlations in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$

We report the results of a comprehensive study of charge-density wave (CDW) correlations in untwinned ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ single crystals with $0.4\le x\le 0.99$ using Cu $L_3$ edge resonant x-ray scattering (RXS). Evidence of CDW formation is found for $0.45\le x\le 0.93$ (hole-doping levels $0.086\lesssim p\lesssim 0.163$), but not for samples with $x\le 0.44$ ($p\lesssim 0.084$) that exhibit incommensurate spin-density-wave order, and in slightly overdoped samples with $x=0.99$ ($p\sim 0.19$). This suggests the presence of two proximate zero-temperature CDW critical points at $p_{c1}\sim 0.08$ and $p_{c2}\sim 0.18$. Remarkably, $p_{c2}$ is close to the doping level that is optimal for superconductivity. The CDW reflections are observed at incommensurate in-plane wave vectors (${\delta }_a$, 0) and (0, ${\delta }_b$) with ${\delta }_a\lesssim {\delta }_b$. Both ${\delta }_a$ and ${\delta }_b$ decrease linearly with increasing doping, in agreement with recent reports on Bi-based high-$T_c$ superconductors, but in sharp contrast to the behavior of the ${\mathrm{La}}_{2-x}$(Ba,Sr)${}_x{\mathrm{CuO}}_4$ family. The CDW intensity and correlation length exhibit maxima at $p\sim 0.12$, coincident with a plateau in the superconducting transition temperature $T_c$. The onset temperature of the CDW reflections depends nonmonotonically on $p$, with a maximum of $\sim 160$ K for $p\sim 0.12$. The RXS reflections exhibit a uniaxial intensity anisotropy. Whereas in strongly underdoped samples the reflections at (${\delta }_a$, 0) are much weaker than those at (0, ${\delta }_b$), the anisotropy is minimal for $p\sim 0.12$, and reversed close to optimal doping. We further observe a depression of CDW correlations upon cooling below $T_c$, and (for samples with $p\ge 0.09$) an enhancement of the signal when an external magnetic field up to 6 T is applied in the superconducting state. For samples with $p\sim 0.08$, where prior work has revealed a field-enhancement of incommensurate magnetic order, the RXS signal is field independent. This supports a previously suggested scenario in which incommensurate charge and spin orders compete against each other, in addition to individually competing against superconductivity [Blanco-Canosa et al., Phys. Rev. Lett. 110, 187001 (2013)]. We discuss the relationship of these results to prior observations of “stripe” order in ${\mathrm{La}}_{2-x}$(Ba,Sr)${}_x{\mathrm{CuO}}_4$, the “pseudogap” phenomenon, superconducting fluctuations, and quantum oscillations, as well as their implications for the mechanism of high-temperature superconductivity.

Figure 1

Magnetization curves of the set of samples investigated here.

Figure 2

Full width at half maximum of the ortho-II superstructure peak measured at $q=(0.5,0,l)$ with photon energy tuned to the $L_3$ absorption edge of the chain Cu atoms as a function of the oxygen content $x$ in ${\mathrm{YBCO}}_{6+x}$.

Figure 3

Raw data measured along the (0,1,0) direction for ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ samples with $x=0.45$, 0.55, 0.86, and 0.93 close to their respective $T_c$ (full symbols) and above the onset of the CDW signal (empty symbols).

Figure 4

Background-subtracted RXS intensity measured along the (0,1,0) direction for a set of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ samples with $0.44<x<0.99$. Solid lines are the results of fits to Lorentzian profiles.

Figure 5

In-plane anisotropy of the background-subtracted RXS signal in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.86}$, ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.6}$, ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.55}$, and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.51}$ (Note that in this figure the overall intensities between the samples have been rescaled for clarity). Full and empty symbols stand for data taken along the (0,1,0) and (1,0,0) directions, respectively.

Figure 6

Doping dependence of the CDW wave vector in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ compared to the wave vector characterizing charge order in the “striped” state of ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ (Ref. [6]) and ${\mathrm{La}}_{1.8-x}{\mathrm{Eu}}_{0.2}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ (Ref. [5]).

Figure 7

(a) CDW peak full width at half maximum (FWHM) as a function of doping, given in reciprocal lattice units (r.l.u.) and measured at $T=T_c$ in our ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ samples. (b) Corresponding correlation length, defined as ${\xi }_{a,b}=\frac{a,b}{\pi \times \mathrm{FWHM}}$. Dashed lines are guides to the eyes.

Figure 8

Temperature dependence of the CDW peak intensity for a set of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ samples with $0.44<x<0.86$ along the (0,1,0) direction. The plots have been shifted vertically for clarity, and the arrows correspond to the superconducting $T_c$.

Figure 9

Temperature dependence of the CDW peak FWHM for a set of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ samples with $0.44<x<0.86$ along the (0,1,0) direction. The plots have been shifted vertically for clarity, and the arrows correspond to the superconducting $T_c$.

Figure 10

Doping dependence of the onset temperature of the CDW in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$. The point at $p\sim 0.13$ has been taken from Ref. [23].

Figure 11

Comparison of the RXS data along the $k$ direction for ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$, with $x=0.45$, 0.48, and 0.55 for magnetic fields $H=0$ and 6 T at $T=4$ K. A vertical offset has been applied for clarity.

Figure 12

Magnetic field dependence of the integrated intensity of the RXS reflections (along the $k$ direction) in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.55}$, ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.48}$, and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.55}$. Dashed lines are guides to the eye.